Patent Description:
The human foot is a complex and remarkable piece of machinery, capable of withstanding and dissipating many impact forces. The natural padding of fat at the heel and forefoot, as well as the flexibility of the arch, help to cushion the foot. Although the human foot possesses natural cushioning and rebounding characteristics, the foot alone is incapable of effectively overcoming many of the forces encountered during everyday activity. Unless an individual is wearing shoes that provide proper cushioning and support, the soreness and fatigue associated with every day activity is more acute, and its onset may be accelerated. This discomfort for the wearer may diminish the incentive for further activity. Equally important, inadequately cushioned footwear can lead to injuries such as blisters; muscle, tendon, and ligament damage; and bone stress fractures. Improper footwear can also lead to other ailments, including back pain. <CIT> relates to a sole comprising a lattice structure, the lattice structure comprising a plurality of cell elements. <CIT> relates to a midsole for an article of footwear including a three-dimensional mesh including interconnected unit cells. <CIT> relates to a sole or midsole for footwear. <CIT> relates to a shoe insole for a shoe product. <CIT> relates to a sole for an article of footwear comprising a three-dimensional mesh.

Individuals are often concerned with the amount of cushioning an article of footwear provides. This is true for articles of footwear worn for non-performance activities, such as a leisurely stroll, and for performance activities, such as running, because throughout the course of an average day, the feet and legs of an individual are subjected to substantial impact forces. When an article of footwear contacts a surface, considerable forces may act on the article of footwear and, correspondingly, the wearer's foot. The sole of an article of footwear functions, in part, to provide cushioning to the wearer's foot and to protect it from these forces.

Proper footwear should be durable, comfortable, and provide other beneficial characteristics for an individual. Therefore, a continuing need exists for innovations in footwear.

The invention relates to a sole for an article of footwear as specified in appended independent claim <NUM>. Additional embodiments of the invention are disclosed in the dependent claims.

The present invention(s) will now be described in detail with reference to embodiments thereof as illustrated in the accompanying drawings. References to "one embodiment", "an embodiment", "an exemplary embodiment", etc., indicate that the embodiment described may include a particular feature, structure, or characteristic, but every embodiment may not necessarily include the particular feature, structure, or characteristic.

An article of footwear has many purposes. Among other things, an article of footwear can cushion a wearer's foot, support a wearer's foot, protect a wearer's foot (e.g., from injury), and optimize the performance of a wearer's foot. Each of these purposes, alone or in combination, provides for a comfortable article of footwear suitable for use in a variety of scenarios (e.g., exercise and every day activities). The features of an article of footwear (e.g., shape, components, and materials used to make footwear) can be altered to produce desired characteristics, for example, cushioning, support, stability, ride, and propulsion characteristics.

Stability provided by an article of footwear can protect a wearer's foot from injury, such as spraining his or her ankle. Propulsion provided by an article of footwear can optimize the performance of a wearer' s foot by, for example, maximizing the energy transfer from the individual's foot to the surface his or her foot is in contact with (e.g., the ground) via the article of footwear. Maximizing the energy transfer between the individual's foot and a surface (i.e., reducing energy lost via and/or absorbed by an article of footwear) can help an athlete, for example, accelerate faster, maintain a higher maximum speed, change directions faster, and jump higher. Cushioning and ride characteristics provided by an article of footwear can provide comfort for an individual during an athletic or everyday activity.

Three-dimensional meshes described herein can leverage characteristics of unit cells that make up the three-dimensional meshes to create mechanically anisotropic properties. These mechanically anisotropic properties can be designed to provide desired mechanical characteristics for a three-dimensional mesh defining all or a portion of a sole. One such property that can be designed to achieve specific mechanical characteristics is "lattice shear modulus. " In some embodiments, all or a portion of a three-dimensional mesh can be designed to include anisotropic lattice shear moduli that impart desired mechanical characteristics to the three-dimensional mesh. In some embodiments, a plurality of regions of a three-dimensional mesh can be designed to include anisotropic lattice shear moduli that impart desired mechanical characteristics to the different regions of the three-dimensional mesh. Desired mechanical characteristics for a three-dimensional mesh may in turn create desired footwear sole characteristics, for example, cushioning, propulsion, stability, ride, and/or weight characteristics.

The mechanically anisotropic properties of three-dimensional meshes as described herein can be designed to create forward propulsion when a sole including the three-dimensional mesh contacts the ground. Thus, the three-dimensional mesh includes a lattice shear modulus measured in a forward direction that is less than a lattice shear modulus measured in a rearward direction. By designing a three-dimensional mesh in this fashion, the three-dimensional mesh can convert vertical loading energy into forward displacement, which propels a wearer's foot forward when a sole including the three-dimensional mesh contacts the ground during use. In other words, by designing a three-dimensional mesh in this fashion, the three-dimensional mesh can be predisposed to deform forwards when a sole including the three-dimensional mesh contacts the ground during use.

A three-dimensional mesh predisposed to deform in a particular direction (for example, in a forward direction) can offer multiple advantages for a wearer. For example, forward motion created by the three-dimensional mesh can yield improved efficiency while running. In other words, a three-dimensional mesh predisposed to deform forward can reduce the energy a wearer is required expend to continue his or her forward motion. As another example, a three-dimensional mesh predisposed to deform laterally (for example medially) can improve efficiency when a wearer changes direction by providing additional support under typical lateral loading conditions associated with, for example a lateral or medial cut during running.

Three-dimensional meshes described herein include unit cells composed of different types of sub-cells, which can also be referred to as "partial unit cells. " As described herein, unit cells can be constructed by assembling sub-cells in certain arrangements to create anisotropic lattice shear moduli. In particular embodiments, unit cells can be constructed by assembling sub-cells in certain arrangements to create anisotropic lattice shear moduli that create forward propulsion when a sole including the three-dimensional mesh contacts the ground.

As used herein, the term "three-dimensional mesh" means a three-dimensional structure comprising interconnected structural members defining a plurality of unit cells. The structural members, and thus the unit cells, are connected at nodes. The unit cells are arranged in a lattice configuration. Thus, the interconnected structural members are struts that are connected at nodes and that define unit cells arranged in a lattice configuration. Exemplary lattice configurations include, but are not limited to modified basic cubic lattices, modified body-centered cubic lattices, and modified face-centered cubic lattices. Modified lattices based on these lattice configurations can be created by combining sub-cells of these lattice configurations as described herein. Exemplary modified lattice configurations are shown in <FIG>.

As used herein, the term "lattice shear modulus" means the shear modulus (slope of the shear stress versus shear strain curve in the elastic region) for a three-dimensional mesh, or a portion thereof. A "lattice shear modulus" as described herein is measured using the following solid model simulation. A <NUM> x <NUM> x <NUM> unit cell puck composed of unit cells for the three-dimensional mesh is modeled using FEA (finite element analysis) modeling software. Suitable FEA modeling software includes Abaqus FEA modeling software. The <NUM> x <NUM> x <NUM> unit cell puck includes two layers of seven longitudinal rows of seven unit cells arranged adjacent to each other in the transverse direction as described herein. The unit cell puck is modeled as being sandwiched between and in contact with a top plate and a bottom plate. The following parameters were input into the FEA modeling software for the simulation: (<NUM>) material characteristics of the modeled struts for the unit cell puck (including density and tensile properties), (<NUM>) the loading conditions, and (<NUM>) the contact mechanics between the unit cell puck and the two plates (including the frictional properties).

Lattice shear moduli of the <NUM> x <NUM> x <NUM> unit cell puck in different directions is determined by a shear simulation with <NUM>-degree load in the direction in which the lattice shear modulus is being evaluated. To determine the lattice shear modulus in a forward longitudinal direction, a <NUM>-degree load in the forward longitudinal direction is modeled. To determine the lattice shear modulus in a rearward longitudinal direction, a <NUM>-degree load in the rearward longitudinal direction is modeled. To determine the lattice shear modulus in a medial transverse direction, a <NUM>-degree load in the medial transverse direction is modeled. To determine the lattice shear modulus in a lateral transverse direction, a <NUM>-degree load in the lateral transverse direction is modeled.

The modeled stress-strain behavior of the <NUM> × <NUM> × <NUM> unit cell puck is plotted and the lattice shear modulus in the different directions is calculated by measuring the slope of the stress-strain curve in the elastic deformation region in the plot. <FIG> show stress-strain plots for exemplary modeled <NUM> × <NUM> × <NUM> unit cell pucks.

In some cases, uniaxial compression loading can be modeled using the FEA modeling software to determine a "lattice compressive modulus" for a three-dimensional mesh, or a portion thereof. To determine the lattice compressive modulus for a three-dimensional mesh, the same model <NUM> × <NUM> × <NUM> unit cell puck is compressed at up to <NUM>% strain. For this model, the tow plates are free to move in the longitudinal and transverse directions, and therefore the unit cell pucks are free to deform in the longitudinal and transverse directions. The modeled stress-strain behavior of the <NUM> × <NUM> × <NUM> unit cell puck is plotted and the lattice compressive modulus is calculated by measuring the slope of the stress-strain curve in the elastic deformation region in the plot. Further, this uniaxial compression loading can be used to determine a lattice displacement in the forward direction for a three-dimensional mesh, or a portion thereof. The lattice displacement in the forward direction is the amount the <NUM> × <NUM> × <NUM> puck deforms forward under the uniaxial compression loading, measured in millimeters. <FIG> shows a graph <NUM> that plots the lattice compressive modulus ("Comp. Stiffness") versus the lattice displacement in the forward direction for various exemplary <NUM> × <NUM> × <NUM> unit cell pucks.

As used herein, "anisotropic" means dependent on direction. "Isotropic" generally means independent of direction. A material or component with a particular property that is isotropic at a particular point would have that same property regardless of measurement direction. For example, if Young's modulus is isotropic at a point, the value of the Young's modulus is the same regardless of the stretching direction used to measure Young's modulus.

An isotropic material or component has <NUM> independent elastic constants, often expressed as the Young's modulus and Poison's ratio of the material (although other ways to express may be used), which do not depend on position in such a material or component. A fully anisotropic material or component has <NUM> independent elastic constants. An orthotropic material or component has <NUM> independent elastic constants.

Orthotropic materials or components are a sub-set of anisotropic materials or components. By definition, an orthotropic material or component has at least two orthogonal planes of symmetry where material properties are independent of direction within each plane. An orthotropic material or component has nine independent variables (i.e. elastic constants) in its stiffness matrix. An anisotropic material or component can have up <NUM> elastic constants to define its stiffness matrix, if the material or component completely lacks planes of symmetry.

The mechanically anisotropic characteristic(s) of midsoles disclosed herein may offer a multitude of different options for customizing (tailoring) a midsole to an individual's, or group of individuals' needs. For example, lattice shear moduli may vary between different zones or portions on a midsole to provide desired characteristics (e.g., cushioning, support, stability, ride, and/or propulsion characteristics) for an individual, or group of individuals.

Midsoles including a three-dimensional mesh as discussed herein can be manufactured using one or more additive manufacturing methods. Additive manufacturing methods can allow for fabrication of three-dimensional objects without the need for a mold. By reducing or eliminating the need for molds, additive manufacturing methods can reduce costs for a manufacturer, and in turn a consumer, of a product (e.g., a shoe). Integral manufacturing of a midsole using additive manufacturing can make the assembly of separate elements of the midsole unnecessary. Similarly, an additively manufactured midsole can be fabricated from single material, which may facilitate easy recycling of the midsole.

Further, since molds may not be required, additive manufacturing methods facilitate customization of products. Additive manufacturing methods can be leveraged to provide customized and affordable footwear for individuals. Exemplary additive manufacturing techniques include for example, selective laser sintering, selective laser melting, selective heat sintering, stereo lithography, fused deposition modeling, or <NUM>-D printing in general. Various additive manufacturing techniques related to articles of footwear are described for example in <CIT>, <CIT>, <CIT>, <CIT>, <CIT>, <CIT>, <CIT>, <CIT>, <CIT>, <CIT>, <CIT>, <CIT>, and <CIT>. In some embodiments, the additive manufacturing process can include a continuous liquid interface production process. For example, the additive manufacturing process can include a continuous liquid interface production process as described in <CIT>.

In some embodiments, <NUM>-D printing a three-dimensional mesh can include <NUM>-D printing the mesh in an intermediate green state, shaping the mesh in the green state, and curing the green mesh in its final shape.

Techniques for producing an intermediate object from resins by additive manufacturing are known. Suitable techniques include bottom-up and top-down additive manufacturing, generally known as stereolithography. Such methods are known and described in, for example, <CIT>, <CIT> and <CIT>, <CIT>, <CIT>, <CIT>, <CIT>, and <CIT>.

In some embodiments, the additive manufacturing step is carried out by one of the family of methods sometimes referred to as continuous liquid interface production (CLIP). CLIP is known and described in, for example, <CIT>; <CIT>; <CIT>; and others; in<NPL>); and in<NPL>). Other examples of methods and apparatus for carrying out particular embodiments of CLIP include, but are not limited to: <CIT>); <CIT>); <CIT>); Lin et al. , US Patent.

Application Pub. No. <CIT>); <CIT>). <CIT>); <CIT>); <CIT>)<CIT> (see also <CIT> and <CIT>); and <CIT> (see also <CIT>).

While stereolithography techniques such as CLIP can be preferred, it will be appreciated that other additive manufacturing techniques, such as jet printing (see, e.g., <CIT>and <CIT>) can also be used.

In some embodiments, a three-dimensional mesh can have anisotropic lattice shear moduli in forward and rearward directions as described herein. In some embodiments, one or more regions of a three-dimensional mesh can have anisotropic lattice shear moduli in forward and rearward directions as described herein. According to the invention, the lattice shear modulus in the forward direction is less than the lattice shear modulus in the rearward direction.

By tailoring the lattice shear modulus in the forward direction to be greater than or less than the lattice shear modulus in the rearward direction, a sole can be designed to have desired characteristics when acted on by vertical forces, forward forces, and rearward forces during use. For example, a lattice shear modulus in the rearward direction can be designed to be relatively stiff to provide propulsion while an athlete is accelerating in a forward direction (which applies a significant rearward force on a sole). A relatively stiff lattice shear modulus, and therefore a relatively flexible lattice shear modulus in the forward direction, can also provide forward propulsion by transforming vertical forces applied to the sole into forward displacement while an athlete is accelerating forward, thereby facilitating the forward acceleration. As another example, a lattice shear modulus in the forward direction can be designed to be relatively flexible to provide cushion during a heel strike or while an athlete is deaccelerating (both of which can apply a significant forward force on a sole).

<FIG> and <FIG> show an article of footwear <NUM> according to some embodiments. Article of footwear <NUM> can include an upper <NUM> coupled to a midsole <NUM>. Article of footwear <NUM> includes a forefoot end <NUM>, a heel end <NUM>, a medial side <NUM>, and a lateral side <NUM> opposite medial side <NUM>. Also, as shown for example in <FIG>, article of footwear <NUM> includes a forefoot portion <NUM>, a midfoot portion <NUM>, and a heel portion <NUM>. Portions <NUM>, <NUM>, and <NUM> are not intended to demarcate precise areas of article of footwear <NUM>. Rather, portions <NUM>, <NUM>, and <NUM> are intended to represent general areas of article of footwear <NUM> that provide a frame of reference. Although portions <NUM>, <NUM>, and <NUM> apply generally to article of footwear <NUM>, references to portions <NUM>, <NUM>, and <NUM> also may apply specifically to upper <NUM> or midsole <NUM>, or individual components of upper <NUM> or midsole <NUM>.

In some embodiments, article of footwear <NUM> can include an outsole <NUM> coupled to midsole <NUM>. Together, midsole <NUM> and outsole <NUM> can define a sole <NUM> of article of footwear <NUM>. In some embodiments, outsole <NUM> can be directly manufactured (e.g., <NUM>-D printed) on the bottom side of midsole <NUM>. In some embodiments, outsole <NUM> and midsole <NUM> can be manufactured in one manufacturing process (e.g., one <NUM>-D printing process) and no bonding, e.g. via adhesives, may be necessary. In some embodiments, outsole <NUM> can include a plurality of protrusions <NUM> to provide traction for article of footwear <NUM>. Protrusions <NUM> can be referred to as tread.

As shown for example in <FIG>, midsole <NUM> can include a three-dimensional mesh <NUM> composed of a plurality of interconnected unit cells <NUM>. Midsole <NUM> can be any of the midsoles described herein, for example, midsole <NUM>, midsole <NUM>, and midsole <NUM>. Also, midsole <NUM> can include any of the three-dimensional meshes discussed herein.

Upper <NUM> and sole <NUM> can be configured for a specific type of footwear, including, but not limited to, a running shoe, a hiking shoe, a water shoe, a training shoe, a fitness shoe, a dancing shoe, a biking shoe, a tennis shoe, a cleat (e.g., a baseball cleat, a soccer cleat, or a football cleat), a basketball shoe, a boot, a walking shoe, a casual shoe, or a dress shoe. Moreover, sole <NUM> can be sized and shaped to provide a desired combination of cushioning, stability, propulsion, and ride characteristics to article of footwear <NUM>. The term "ride" may be used herein in describing a sense of smoothness or flow occurring during a gait cycle including heel strike, midfoot stance, toe off, and the transitions between these stages. In some embodiments, sole <NUM> can provide particular ride features including, but not limited to, appropriate control of pronation and supination, support of natural movement, support of unconstrained or less constrained movement, appropriate management of rates of change and transition, and combinations thereof.

Sole <NUM> and portions thereof (e.g., midsole <NUM> and outsole <NUM>) can comprise material(s) for providing desired cushioning, ride, propulsion, support, and stability. Suitable materials for sole <NUM> (e.g., midsole <NUM> and/or outsole <NUM>) include, but are not limited to, a foam, a rubber, ethyl vinyl acetate (EVA), thermoplastic polyurethane (TPU), expanded thermoplastic polyurethane (eTPU), polyether block amide (PEBA), expanded polyether block amide (ePEBA), thermoplastic rubber (TPR), and a thermoplastic polyurethane (PU). In some embodiments, the foam can comprise, for example, an EVA based foam or a PU based foam and the foam may be an open-cell foam or a closed-cell foam. In some embodiments, midsole <NUM> and/or outsole <NUM> can comprise elastomers, thermoplastic elastomers (TPE), foam-like plastics, gel-like plastics, and combinations thereof. In some embodiments, midsole <NUM> and/or outsole <NUM> can comprise polyolefins, for example polyethylene (PE), polystyrene (PS) and/or polypropylene (PP). In some embodiments, sole <NUM> can include a shank or torsion bar. In such embodiments, the shank or torsion bar may be made of a Nylon polymer.

Sole <NUM> and portions thereof (e.g., midsole <NUM> and outsole <NUM>) can be formed using an additive manufacturing process, including, but not limited to, selective laser sintering, selective laser melting, selective heat sintering, stereo lithography, fused deposition modeling etc., or <NUM>-D printing in general. In some embodiments, midsole <NUM> and/or outsole <NUM> can be formed using an additive manufacturing process including a continuous liquid interface production process. For example, midsole <NUM> and/or outsole <NUM> can be formed using a continuous liquid interface production process as described in <CIT>, issued on September <NUM>, <NUM>. In some embodiments, midsole <NUM> and outsole <NUM> can be formed as a single piece via an additive manufacturing process. In such embodiments, midsole <NUM> and outsole <NUM> can be a single integrally formed piece.

In some embodiments, outsole <NUM> can be formed by injection molding, blow molding, compression molding, rotational molding, or dipping. In such embodiments, midsole <NUM> and outsole <NUM> can be discrete components that are formed separately and attached. In some embodiments, midsole <NUM> can be attached to outsole <NUM> via, for example, but not limited to, adhesive bonding, stitching, welding, or a combination thereof. In some embodiments, midsole <NUM> can be attached to outsole <NUM> via an adhesive disposed between midsole <NUM> and outsole <NUM>. Similarly, midsole <NUM> can be attached to upper <NUM> via, for example, but not limited to, adhesive bonding, stitching, welding, or a combination thereof.

<FIG> shows a midsole <NUM> according to some embodiments. Midsole <NUM> includes a forefoot end <NUM>, a heel end <NUM>, a medial side <NUM>, a lateral side <NUM>, a top side <NUM>, and a bottom side <NUM>. A longitudinal direction <NUM> of midsole <NUM> extends between forefoot end <NUM> and heel end <NUM>. Longitudinal direction <NUM> includes a forward longitudinal direction ("forward direction") extending from heel end <NUM> to forefoot end <NUM> and a rearward longitudinal direction ("rearward direction") extending from forefoot end <NUM> to heel end <NUM>. A transverse direction <NUM> of midsole <NUM> extends between medial side <NUM> and lateral side <NUM> of midsole <NUM>. Transverse direction <NUM> includes a medial transverse direction ("medial direction") extending from lateral side <NUM> to medial side <NUM> and a lateral transverse direction ("lateral direction") extending from medial side <NUM> to lateral side <NUM>. A vertical direction <NUM> of midsole <NUM> extends between top side <NUM> and bottom side <NUM> of midsole <NUM>. Vertical direction <NUM> includes an upward vertical direction ("upward direction") extending from bottom side <NUM> to top side <NUM> and a downward vertical direction ("downward direction") extending from top side <NUM> to bottom side <NUM>. Top side <NUM> can be considered an "upper-facing side" and bottom side <NUM> can be considered a "ground-facing side.

Midsole <NUM> can be defined, in whole or in part, by a three-dimensional mesh <NUM>. For example, in some embodiments, three-dimensional mesh <NUM> can define one or more of a forefoot portion <NUM> of midsole <NUM>, a midfoot portion <NUM> of midsole <NUM>, and/or a heel portion <NUM> of midsole. In some embodiments, three-dimensional mesh <NUM> can define all or a portion of forefoot portion <NUM> of midsole <NUM>. In some embodiments, three-dimensional mesh <NUM> can define all or a portion of midfoot portion <NUM> of midsole <NUM>. In some embodiments, three-dimensional mesh <NUM> can define all or a portion of heel portion <NUM> of midsole <NUM>.

Similar to midsole <NUM>, three-dimensional mesh <NUM> can be described as having a forefoot end <NUM>, a heel end <NUM>, a medial side <NUM>, a lateral side <NUM>, a top side <NUM>, and a bottom side <NUM>. Unless specified otherwise, a forefoot end <NUM>, heel end <NUM>, medial side <NUM>, lateral side <NUM>, top side <NUM>, and bottom side <NUM> for a three-dimensional mesh <NUM> does not necessarily correspond to a forefoot end <NUM>, heel end <NUM>, medial side <NUM>, lateral side <NUM>, top side <NUM>, or bottom side <NUM> of midsole <NUM>. A forefoot end <NUM> of three-dimensional mesh <NUM> refers to a foremost end of three-dimensional mesh <NUM> and a heel end <NUM> of three-dimensional mesh <NUM> refers to a rearmost end of three-dimensional mesh <NUM>. A medial side <NUM> of three-dimensional mesh <NUM> refers to a medial-most side of three-dimensional mesh <NUM> and a lateral side <NUM> of three-dimensional mesh <NUM> refers to a lateral-most side of three-dimensional mesh <NUM>. A top side <NUM> of three-dimensional mesh <NUM> refers to a topmost side of three-dimensional mesh <NUM> and a bottom side <NUM> of three-dimensional mesh <NUM> refers to a bottommost side of three-dimensional mesh <NUM>.

In some embodiments, midsole <NUM> can include a rim <NUM> disposed around all or a portion of the perimeter of top side <NUM> of midsole <NUM>. In some embodiments, rim <NUM> can be disposed around all or a portion of the perimeter of medial and lateral sides <NUM>/<NUM> of midsole <NUM>. In embodiments including rim <NUM>, rim <NUM> can provide stability for the perimeter of midsole <NUM> and/or can facilitate attachment of midsole <NUM> to an upper (e.g., upper <NUM>). In some embodiments, an outsole <NUM> can be coupled to bottom side <NUM> of midsole <NUM>.

Three-dimensional mesh <NUM> includes a plurality of interconnected unit cells <NUM>. The interconnected unit cells <NUM> include a plurality of struts <NUM> defining a three-dimensional shape of a respective unit cell <NUM>. A plurality of struts <NUM> of three-dimensional mesh <NUM> are connected at nodes <NUM>. The number of struts <NUM> that are connected at a node <NUM> is the "valence number" of the node <NUM>. For example, if four struts <NUM> are connected at a node <NUM>, that node <NUM> has a valence of four. In some embodiments, nodes <NUM> can have a valence number in the range of two to twelve. For example, a node <NUM> can have a valence number of two, three, four, five, six, seven, eight, nine, ten, eleven, or twelve, or within a range having any two of these values as endpoints.

Interconnected unit cells <NUM> can be organized in a lattice framework that defines a volume of three-dimensional mesh <NUM>. A lattice framework is composed of a plurality of lattice cells in which unit cells <NUM> are populated and arranged. A lattice framework is an invisible framework used to arrange unit cells <NUM>, or partial unit cells (i.e., sub-cells), and construct a three-dimensional mesh <NUM> as described herein. In some embodiments, the lattice framework can be an unwarped lattice framework, for example a purely cubic lattice framework. In some embodiments, the lattice framework can be a warped lattice framework, for example a warped cubic lattice framework. A warped lattice framework can include warped lattice cells and unwarped lattice cells. Other exemplary lattice frameworks include, but are not limited to, a tetrahedron lattice framework, a warped tetrahedron lattice framework, a dodecahedron lattice framework, or a warped dodecahedron lattice framework.

A lattice framework can be generated using a computer modeling program such, as but not limited to, Grasshopper 3D and/or Rhinoceros 3D CAD software. <FIG> and <FIG> show an exemplary warped cubic lattice framework <NUM> including a plurality of lattice cells <NUM>, including both unwrapped lattice cells <NUM> and warped lattice cells <NUM>. In some embodiments, a lattice framework can be created and/or populated in the same or a similar manner as described in <CIT>.

Three-dimensional mesh <NUM> can include one or more mechanically anisotropic regions. A three-dimensional mesh <NUM> with one or more mechanically anisotropic regions can define all or a portion of a forefoot portion <NUM> of midsole <NUM>, a midfoot portion <NUM> of midsole <NUM>, and/or a heel portion <NUM> of midsole. In some embodiments, a mechanically anisotropic region can define all or a portion of forefoot portion <NUM> of midsole <NUM>. In some embodiments, a mechanically anisotropic region can define all or a portion of midfoot portion <NUM> of midsole <NUM>. In some embodiments, a mechanically anisotropic region can define all or a portion of heel portion <NUM> of midsole <NUM>. In some embodiments, three-dimensional mesh <NUM> can include at least two mechanically anisotropic regions.

A mechanically anisotropic region of three-dimensional mesh <NUM> can have a first lattice shear modulus measured in a first direction and a second lattice shear modulus different from the first lattice shear modulus and measured in a second direction opposite to the first direction. In some embodiments, a mechanically anisotropic region of three-dimensional mesh <NUM> can have a third lattice shear modulus measured in a third direction and a fourth lattice shear modulus different from the third lattice shear modulus and measured in a fourth direction opposite to the third direction.

As used herein, unless specified otherwise, references to "first," "second," "third," "fourth," etc. are not intended to denote order, or that an earlier-numbered feature is required for a later-numbered feature. Also, unless specified otherwise, the use of "first," "second," "third," "fourth," etc. does not necessarily mean that the "first," "second," "third," "fourth," etc. features have different properties or values.

In some embodiments, a plurality of interconnected unit cells <NUM> defining three-dimensional mesh <NUM>, or an anisotropic region thereof, can each include a soft sub-cell and a stiff sub-cell. In some embodiments, each of the plurality of interconnected unit cells <NUM> can each include a plurality of soft sub-cells and a plurality of stiff sub-cells. In some embodiments, each of the plurality of interconnected unit cells <NUM> can each include a plurality of the same soft sub-cells and a plurality of the same stiff sub-cells. <FIG> illustrate exemplary soft-sub cells <NUM> and stiff sub-cells <NUM> according to some embodiments.

In some embodiments, every interconnected unit cell <NUM> defining three-dimensional mesh <NUM>, or an anisotropic region thereof, can include a soft sub-cell and a stiff sub-cell. In some embodiments, every interconnected unit cell <NUM> defining three-dimensional mesh <NUM>, or an anisotropic region thereof, can include a plurality of soft sub-cells and a plurality of stiff sub-cells. In some embodiments, every interconnected unit cell <NUM> located in portions of three-dimensional mesh <NUM>, or an anisotropic region thereof, having a thickness measured in vertical direction <NUM> at least a large as the thickness of a unit cell <NUM> can include a soft sub-cell and a stiff sub-cell. In some embodiments, every interconnected unit cell <NUM> located in portions of three-dimensional mesh <NUM>, or an anisotropic region thereof, having a thickness measured in vertical direction <NUM> at least a large as the thickness of a unit cell <NUM> can include a plurality of soft sub-cells and a plurality of stiff sub-cells.

In some embodiments, a plurality of interconnected unit cells <NUM> defining three-dimensional mesh <NUM>, or an anisotropic region thereof, can include eight sub-cells. In some embodiments, the eight sub-cells can include a plurality of soft sub-cells and a plurality of stiff sub-cells. In some embodiments, the eight sub-cells can include four soft sub-cells and four stiff sub-cells. In some embodiments, the eight sub-cells can include four of the same soft sub-cells and four of the same stiff sub-cells.

Soft sub-cells are composed of a plurality of struts <NUM> and one or more nodes <NUM> that define a portion of unit cell <NUM>. In other words, soft sub-cells are partial unit cells defining a portion of unit cell <NUM>. As used herein, a "soft sub-cell" is a sub-cell for a lattice structure having: (i) a modeled compressive modulus that is less than a modeled compressive modulus of a lattice structure for a "stiff sub-cell" defining a portion of the same unit cell <NUM>, (ii) a modeled shear modulus that is less than a modeled shear modulus of a lattice structure for a "stiff sub-cell" defining a portion of the same unit cell <NUM>, or (iii) both.

Stiff sub-cells are composed of a plurality of struts <NUM> and one or more nodes <NUM> that define a portion of unit cell <NUM>. In other words, stiff sub-cells are partial unit cells defining a portion of unit cell <NUM>. As used herein, a "stiff sub-cell" is a sub-cell for a lattice structure having (i) a modeled compressive modulus that is greater than a modeled compressive modulus of a lattice structure for a "soft sub-cell" defining a portion of the same unit cell <NUM>, (ii) a modeled shear modulus that is greater than a modeled shear modulus of a lattice structure for a "soft sub-cell" defining a portion of the same unit cell <NUM>, or (iii) both.

A soft sub-cell for a unit cell <NUM> can be a sub-cell for a first lattice structure and a stiff sub-cell for the unit cells <NUM> can be a sub-cell for a second lattice structure different from the first lattice structure. In some embodiments, the first lattice structure can be an isotropic lattice structure. In some embodiments, the second lattice structure can be an isotropic lattice structure. In some embodiments, the first lattice structure and the second lattice structure can be isotropic lattice structures. <FIG> show exemplary isotropic lattice structures for soft-sub cells according to some embodiments. <FIG> show exemplary isotropic lattice structures for stiff-sub cells according to some embodiments.

In some embodiments, the first lattice structure for soft sub-cells can have a first modeled compressive modulus and the second lattice structure for stiff sub-cells can have a second modeled compressive modulus <NUM>% or more greater than the first modeled compressive modulus. In some embodiments, the first lattice structure for soft sub-cells can have a first modeled compressive modulus and the second lattice structure for stiff sub-cells can have a second modeled compressive modulus greater than the first modeled compressive modulus by <NUM>% to <NUM>%, including subranges. For example, the second lattice structure can have a second modeled compressive modulus that is <NUM>% to <NUM>% greater than the first modeled compressive modulus, <NUM>% to <NUM>% greater than the first modeled compressive modulus, <NUM>% to <NUM>% greater than the first modeled compressive modulus, <NUM>% to <NUM>% greater than the first modeled compressive modulus, <NUM>% to <NUM>% greater than the first modeled compressive modulus, or <NUM>% to <NUM>% greater than the first modeled compressive modulus, or within a range having any two of these values as endpoints.

In some embodiments, the first lattice structure for soft sub-cells can have a first modeled shear modulus and the second lattice structure for stiff sub-cells can have a second modeled shear modulus <NUM>% or more greater than the first modeled shear modulus. In some embodiments, the first lattice structure for soft sub-cells can have a first modeled shear modulus and the second lattice structure for stiff sub-cells can have a second modeled shear modulus greater than the first modeled shear modulus by <NUM>% to <NUM>%, including subranges. For example, the second lattice structure can have a second modeled shear modulus that is <NUM>% to <NUM>% greater than the first modeled shear modulus, <NUM>% to <NUM>% greater than the first modeled shear modulus, <NUM>% to <NUM>% greater than the first modeled shear modulus, <NUM>% to <NUM>% greater than the first modeled shear modulus, <NUM>% to <NUM>% greater than the first modeled shear modulus, or <NUM>% to <NUM>% greater than the first modeled shear modulus, or within a range having any two of these values as endpoints.

As used herein, a "modeled compressive modulus" and a "modeled shear modulus" for a lattice structure are determined using the following model. A beam model simulation of a unit cell puck is modeled using FEA modeling software. Suitable FEA modeling software includes Abaqus FEA modeling software. For model efficiency purposes, a unit cell puck as small as a <NUM> × <NUM> × <NUM> unit cell puck can be used. A <NUM> × <NUM> × <NUM> unit cell puck includes one layer of <NUM> longitudinal rows of <NUM> unit cells arranged and adjacent to each other in the transverse direction as described herein. Other unit cell puck sizes can be used as long as the same size is used when comparing a modeled compressive modulus or a modeled shear modulus for two or more lattice structures. The unit cell puck is modeled as being sandwiched between and in contact with a top plate and a bottom plate. The following parameters were input into the FEA modeling software for the simulation: (<NUM>) material characteristics of the modeled struts for the unit cell puck (including density and elastic material properties), (<NUM>) the loading conditions, and (<NUM>) the contact mechanics between the unit cell puck and the two plates (including the frictional properties).

To determine a "modeled compressive modulus," a uniaxial compression load is applied by compressing the puck up to <NUM>% strain using the top plate and capturing the resulting stress-strain curve. The modeled compressive modulus is calculated by measuring the slope of the stress-strain curve in the elastic deformation region.

To determine a "modeled shear modulus" the top plate is compressed with a <NUM>-degree angle from the horizontal plane and the resulting stress-strain curve is captured. The modeled shear modulus is calculated by measuring the slope of the stress-strain curve in the elastic deformation region.

By arranging soft sub-cells and stiff-sub cells at different locations in unit cells <NUM>, the mechanical properties of the unit cell <NUM>, and therefore three-dimensional mesh <NUM>, can be controlled. As discussed above, unit cells <NUM> for a three-dimensional mesh <NUM> can be populated and arranged in lattice cells for a lattice framework defining the volume of a three-dimensional mesh <NUM>. The location of soft sub-cells and stiff sub-cells in unit cells <NUM> can be defined by the location of the soft sub-cells and the stiff sub-cells in a lattice cell <NUM> in which a unit cell <NUM> is populated. <FIG> show a lattice cell <NUM> according to some embodiments. <FIG> show a unit cell <NUM> composed of soft sub-cells <NUM> and stiff sub-cells <NUM> located in lattice cell <NUM> according to some embodiments.

In some embodiments, the location of soft sub-cells and stiff sub-cells in a lattice cell <NUM> can be defined by the location of one or more soft sub-cells and one or more stiff sub-cells in two or more of the following quadrants of lattice cell <NUM>: (i) an upper-forward quadrant <NUM>, (ii) an upper-rearward quadrant <NUM>, (iii) a lower-forward quadrant <NUM>, and (iv) a lower-rearward quadrant <NUM>. Upper-forward quadrant <NUM> and upper-rearward quadrant <NUM> are the two upper-most quadrants of lattice cell <NUM> in upward vertical direction <NUM>. Upper-forward quadrant <NUM> and upper-rearward quadrant <NUM> are located above lower-forward quadrant <NUM> and lower-rearward quadrant <NUM>, respectively. Upper-forward quadrant <NUM> and lower-forward quadrant <NUM> are the two forward-most quadrants of lattice cell <NUM> in forward longitudinal direction <NUM>. Upper-forward quadrant <NUM> and lower-forward quadrant <NUM> are located forward of upper-rearward quadrant <NUM> and lower-rearward quadrant <NUM>, respectively. A unit cell <NUM> populated in a lattice cell <NUM> can also be described as having an upper-forward quadrant <NUM>, an upper-rearward quadrant <NUM>, a lower-forward quadrant <NUM>, and a lower-rearward quadrant <NUM>.

In some embodiments, unit cells <NUM> of three-dimensional mesh <NUM> can include one or more soft sub-cells located in upper-forward quadrant <NUM>. In some embodiments, unit cells <NUM> of three-dimensional mesh <NUM> can include two soft sub-cells located in upper-forward quadrant <NUM>.

In some embodiments, unit cells <NUM> of three-dimensional mesh <NUM> can include one or more stiff sub-cells located in upper-forward quadrant <NUM>. In some embodiments, unit cells <NUM> of three-dimensional mesh <NUM> can include two stiff sub-cells located in upper-forward quadrant <NUM>.

In some embodiments, unit cells <NUM> of three-dimensional mesh <NUM> can include one or more soft sub-cells located in upper-rearward quadrant <NUM>. In some embodiments, unit cells <NUM> of three-dimensional mesh <NUM> can include two soft sub-cells located in upper-rearward quadrant <NUM>.

In some embodiments, unit cells <NUM> of three-dimensional mesh <NUM> can include one or more stiff sub-cells located in upper-rearward quadrant <NUM>. In some embodiments, unit cells <NUM> of three-dimensional mesh <NUM> can include two stiff sub-cells located in upper-rearward quadrant <NUM>.

In some embodiments, unit cells <NUM> of three-dimensional mesh <NUM> can include one or more soft sub-cells located in lower-forward quadrant <NUM>. In some embodiments, unit cells <NUM> of three-dimensional mesh <NUM> can include two soft sub-cells located in lower-forward quadrant <NUM>.

In some embodiments, unit cells <NUM> of three-dimensional mesh <NUM> can include one or more stiff sub-cells located in lower-forward quadrant <NUM>. In some embodiments, unit cells <NUM> of three-dimensional mesh <NUM> can include two stiff sub-cells located in lower-forward quadrant <NUM>.

In some embodiments, unit cells <NUM> of three-dimensional mesh <NUM> can include one or more soft sub-cells located in lower-rearward quadrant <NUM>. In some embodiments, unit cells <NUM> of three-dimensional mesh <NUM> can include two soft sub-cells located in lower-rearward quadrant <NUM>.

In some embodiments, unit cells <NUM> of three-dimensional mesh <NUM> can include one or more stiff sub-cells located in lower-rearward quadrant <NUM>. In some embodiments, unit cells <NUM> of three-dimensional mesh <NUM> can include two stiff sub-cells located in lower-rearward quadrant <NUM>.

In some embodiments, unit cells <NUM> of three-dimensional mesh <NUM> can include the following sub-cells: (i) at least one soft sub-cell located in the upper-forward quadrant <NUM>, (ii) at least one stiff sub-cell located in the upper-rearward quadrant <NUM>, (iii) at least one stiff sub-cell located in the lower-forward quadrant <NUM>, and (iv) at least one soft sub-cell located in the lower-rearward quadrant <NUM>. In such embodiments, this arrangement of soft and stiff sub-cells can result in a three-dimensional mesh <NUM> capable of converting vertical loading energy into forward displacement, which can propel a wearer's foot forward when a sole including the three-dimensional mesh <NUM> contacts the ground during use. In other words, this arrangement of soft and stiff sub-cells can result in a three-dimensional mesh <NUM> predisposed to deform forwards (i.e., in forward longitudinal direction <NUM>) when a sole including the three-dimensional mesh <NUM> contacts the ground.

The opposite result can be achieved by rotating the orientation of the unit cells <NUM> by <NUM>°. In such embodiments, unit cells <NUM> of three-dimensional mesh <NUM> can include the following sub-cells: (i) at least one stiff sub-cell located in the upper-forward quadrant <NUM>, (ii) at least one soft sub-cell located in the upper-rearward quadrant <NUM>, (iii) at least one soft sub-cell located in the lower-forward quadrant <NUM>, and (iv) at least one stiff sub-cell located in the lower-rearward quadrant <NUM>. In such embodiments, this arrangement of soft and stiff sub-cells can result in a three-dimensional mesh <NUM> that is predisposed to deform rearwards (i.e., in rearward longitudinal direction <NUM>) when a sole including the three-dimensional mesh <NUM> contacts the ground.

<FIG> show a lattice cell <NUM> populated with soft sub-cells <NUM> and stiff sub-cells <NUM> for a unit cell <NUM> according to some embodiments. The unit cell <NUM> shown includes: (i) two soft sub-cells <NUM> located side-by-side in the upper-forward quadrant <NUM>, (ii) two stiff sub-cells <NUM> located side-by-side in the upper-rearward quadrant <NUM>, (iii) two stiff sub-cells <NUM> located in the lower-forward quadrant <NUM>, and (iv) two soft sub-cells <NUM> located in the lower-rearward quadrant <NUM>. This arrangement of soft and stiff sub-cells can result in a three-dimensional mesh <NUM> that is predisposed to deform forwards (i.e., in forward longitudinal direction <NUM>) when a sole including the three-dimensional mesh <NUM> contacts the ground.

In some embodiments, the location of soft sub-cells and stiff sub-cells in a lattice cell <NUM> can be defined by the location of a soft sub-cell or a stiff sub-cell in two or more of the following eight zones of lattice cell <NUM>: (i) an upper-forward-medial zone <NUM>, (ii) an upper-forward-lateral zone <NUM>, (iii) an upper-rearward-medial zone <NUM>, (iv) an upper-rearward-lateral zone <NUM>, (v) a lower-forward-medial zone <NUM>, (vi) a lower-forward-lateral zone <NUM>, (vii) a lower-rearward-medial zone <NUM>, and (viii) a lower-rearward-lateral zone <NUM>. Upper-forward-medial zone <NUM> and upper-forward-lateral zone <NUM> are located in upper-forward quadrant <NUM> of lattice cell <NUM>, with zone <NUM> located medially to zone <NUM> in transverse direction <NUM>. Upper-rearward-medial zone <NUM> and upper-rearward-lateral zone <NUM> are located in upper-rearward quadrant <NUM> of lattice cell <NUM>, with zone <NUM> located medially to zone <NUM> in transverse direction <NUM>. Lower-forward-medial zone <NUM> and lower-forward-lateral zone <NUM> are located in lower-forward quadrant <NUM> of lattice cell <NUM>, with zone <NUM> located medially to zone <NUM> in transverse direction <NUM>. Lower-rearward-medial zone <NUM> and lower-rearward-lateral zone <NUM> are located in lower-rearward quadrant of lattice cell <NUM>, with zone <NUM> located medially to zone <NUM> in transverse direction <NUM>.

A sub-cell located in upper-forward-medial zone <NUM> can be referred to as an upper-forward-medial sub-cell. In some embodiments, an upper-forward-medial sub-cell can be a soft sub-cell. In some embodiments, an upper-forward-medial sub-cell can be a stiff sub-cell.

A sub-cell located in upper-forward-lateral zone <NUM> can be referred to as an upper-forward-lateral sub-cell. In some embodiments, an upper-forward-lateral sub-cell can be a soft sub-cell. In some embodiments, an upper-forward-lateral sub-cell can be a stiff sub-cell.

A sub-cell located in upper-rearward-medial zone <NUM> can be referred to as an upper-rearward-medial sub-cell. In some embodiments, an upper-rearward-medial sub-cell can be a soft sub-cell. In some embodiments, an upper-rearward-medial sub-cell can be a stiff sub-cell.

A sub-cell located in upper-rearward-lateral zone <NUM> can be referred to as an upper-rearward-lateral sub-cell. In some embodiments, an upper-rearward-lateral sub-cell can be a soft sub-cell. In some embodiments, an upper-rearward-lateral sub-cell can be a stiff sub-cell.

A sub-cell located in lower-forward-medial zone <NUM> can be referred to as a lower-forward-medial sub-cell. In some embodiments, a lower-forward-medial sub-cell can be a soft sub-cell. In some embodiments, a lower-forward-medial sub-cell can be a stiff sub-cell.

A sub-cell located in lower-forward-lateral zone <NUM> can be referred to as a lower-forward-lateral sub-cell. In some embodiments, a lower-forward-lateral sub-cell can be a soft sub-cell. In some embodiments, a lower-forward-lateral sub-cell can be a stiff sub-cell.

A sub-cell located in lower-rearward-medial zone <NUM> can be referred to as a lower-rearward-medial sub-cell. In some embodiments, a lower-rearward-medial sub-cell can be a soft sub-cell. In some embodiments, a lower-rearward-medial sub-cell can be a stiff sub-cell.

A sub-cell located in lower-rearward-lateral zone <NUM> can be referred to as a lower-rearward-lateral sub-cell. In some embodiments, a lower-rearward lateral sub-cell can be a soft sub-cell. In some embodiments, a lower-rearward lateral sub-cell can be a stiff sub-cell.

<FIG> show lattice cell <NUM> populated with four soft sub-cells <NUM> and four stiff sub-cells <NUM> for a unit cell <NUM> according to some embodiments. The unit cell <NUM> shown includes: (i) an upper-forward-medial soft sub-cell <NUM> located in upper-forward-medial zone <NUM>, (ii) an upper-forward-lateral soft sub-cell <NUM> located in upper-forward-lateral zone <NUM>, (iii) an upper-rearward-medial stiff sub-cell <NUM> located in upper-rearward-medial zone <NUM>, (iv) an upper-rearward-lateral stiff sub-cell <NUM> located in upper-rearward-lateral zone <NUM>, (v) a lower-forward-medial stiff sub-cell <NUM> located in lower-forward-medial zone <NUM>, (vi) a lower-forward-lateral stiff sub-cell <NUM> located in lower-forward-lateral zone <NUM>, (vii) a lower-rearward-medial soft sub-cell <NUM> located in lower-rearward-medial zone <NUM>, and (viii) a lower-rearward-lateral soft-sub cell <NUM> located in lower-rearward-lateral zone <NUM>.

Sub-cells populated in lattice cell <NUM> can include struts <NUM> connected at a plurality of edge nodes <NUM> located at edges of lattice cell <NUM>. In some embodiments, sub-cells populated lattice cell <NUM> can include struts <NUM> connected at a plurality of face nodes <NUM> located on faces of lattice cell <NUM>. For structural integrity of mesh <NUM>, it is preferred to populate lattice cells <NUM> with soft and stiff sub-cells that share the same edge nodes <NUM>, and in embodiments including face nodes <NUM>, that share the same face nodes <NUM>. If soft and stiff sub-cells that do not share the same edge nodes <NUM> and/or face nodes <NUM> are populated into lattice cell <NUM>, it can result in a unit cell with one or more struts <NUM> not connected to another strut <NUM> within mesh <NUM>.

By arranging soft and stiff sub-cells in any of the various combinations discussed above, mechanical properties of three-dimensional mesh <NUM>, or an anisotropic region thereof, can be manipulated and leveraged to create desired performance characteristics for three-dimensional mesh <NUM>. Exemplary mechanical properties that be manipulated and leveraged include, but are not limited to, lattice shear moduli in different directions and lattice compressive modulus. The position of soft and stiff sub-cells in the different zones and quadrants of lattice cell <NUM> can influence the mechanical properties of unit cells <NUM>, and therefore three-dimensional mesh <NUM>, in different directions. In some embodiments, soft and stiff sub-cells can be positioned to create unit cells <NUM> that result in a three-dimensional mesh <NUM> with different lattice shear moduli in forward and rearward directions. In some embodiments, soft and stiff sub-cells can be positioned to create unit cells <NUM> that result in a three-dimensional mesh <NUM> with different lattice shear moduli in a medial and lateral directions.

<FIG> and <FIG> illustrate a midsole <NUM> with a three-dimensional mesh <NUM> having a mechanically anisotropic region <NUM> according to some embodiments. Midsole <NUM> includes a forefoot end <NUM>, a heel end <NUM>, a medial side <NUM>, and a lateral side <NUM>. Mechanically anisotropic region <NUM> of midsole <NUM> includes a plurality of unit cells <NUM> composed of soft sub-cells <NUM> and stiff sub-cells <NUM> arranged in lattice cells <NUM> as shown in <FIG>. Anisotropic region <NUM> extends from forefoot portion <NUM> of midsole <NUM>, through midfoot portion <NUM> of midsole <NUM>, and to heel portion <NUM> of midsole <NUM>. Anisotropic region <NUM> of three-dimensional mesh <NUM> includes the anisotropic lattice structure <NUM> shown in <FIG>. Mechanically anisotropic region <NUM> can be predisposed to deform forward under a vertical load as described herein.

According to the invention, three-dimensional mesh <NUM>, or an anisotropic region thereof (for example, anisotropic region <NUM>), includes a lattice shear modulus measured in a forward direction (i.e., forward longitudinal direction <NUM>) and a lattice shear modulus measured in a rearward direction (i.e., rearward longitudinal direction <NUM>) greater than the lattice shear modulus measured in the forward direction. Thus, the lattice shear modulus measured in the rearward direction is greater than the lattice shear modulus measured in the forward direction by <NUM>% or more. In some embodiments, the lattice shear modulus measured in the rearward direction can be greater than the lattice shear modulus measured in the forward direction by <NUM>% to <NUM>%, including subranges. For example, the lattice shear modulus measured in the rearward direction can be greater than the lattice shear modulus measured in the forward direction by <NUM>% to <NUM>%, <NUM>% to <NUM>%, <NUM>% to <NUM>%, or <NUM>% to <NUM>%, or within a range having any two of these values as endpoints.

Thus, three-dimensional mesh <NUM>, or an anisotropic region thereof, has a ratio of the lattice shear modulus measured in the rearward direction to the lattice shear modulus in the forward direction that is at least <NUM>. For example, in some embodiments, three-dimensional mesh <NUM>, or an anisotropic region thereof, can have a ratio of the lattice shear modulus measured in the rearward direction to the lattice shear modulus in the forward direction ranging from <NUM> to <NUM>, <NUM> to <NUM>, or <NUM> to <NUM>.

A three-dimensional mesh, or an anisotropic region thereof, with a lattice shear modulus measured in the rearward direction that is greater than the lattice shear modulus measured in the forward direction by <NUM>% or more can be predisposed to sufficiently deform forwards (i.e., in forward longitudinal direction <NUM>) when a sole including the three-dimensional mesh contacts the ground. Similarly, a three-dimensional mesh, or anisotropic region thereof, having a ratio of the lattice shear modulus measured in the rearward direction to the lattice shear modulus in the forward direction that is more than <NUM> can be predisposed to sufficiently deform forwards (i.e., in forward longitudinal direction <NUM>) when a sole including the three-dimensional mesh contacts the ground.

In some embodiments, a three-dimensional mesh, or an anisotropic region thereof, can have a third lattice shear modulus measured in a transverse direction orthogonal to the forward direction (i.e., lateral or medial transverse direction <NUM>) that is greater than the lattice shear modulus measured in the forward direction and less than the lattice shear modulus measured in the rearward direction. In other words, in such embodiments, the lattice shear modulus measured in the forward direction can be less than the lattice shear modulus measured in the transverse direction and the lattice shear modulus measured in the rearward direction can be greater than the lattice shear modulus measured in the transverse direction. In some embodiments, the value of the transverse lattice shear modulus can be between the value of the forward lattice shear modulus and the value of the rearward lattice shear modulus, and closer to the value of the stiffer rearward lattice shear modulus. This relationship between the values can help provide stability for a three-dimensional mesh, or an anisotropic region thereof.

The graphs shown in <FIG> illustrate how arranging soft and stiff sub-cells in lattice cells as discussed herein can create anisotropic lattice shear moduli that predispose a three-dimension mesh to deform forward. The graph <NUM> of <FIG> shows the lattice shear moduli modeling results for the lattice structure <NUM> shown in <FIG> shows a first side view (Si) and a second side view (S2) of lattice structure <NUM>. The graph <NUM> of <FIG> shows the lattice shear moduli modeling results for the lattice structure <NUM> shown in <FIG> shows a first side view (Si) and a second side view (S2) of lattice structure <NUM>. The graph <NUM> of <FIG> shows the lattice shear moduli modeling results for the lattice structure <NUM> shown in <FIG> shows a first side view (S1) and a second side view (S2) of lattice structure <NUM>. The mechanical characteristics of the struts, the loading characteristics, and the contact mechanics for each model used to generate the results shown in <FIG> were the same.

Lattice structure <NUM> is composed of soft sub-cells from isotropic lattice structure <NUM> shown in <FIG> and stiff sub-cells from isotropic lattice structure <NUM> shown in <FIG>. The soft sub-cells and the stiff sub-cells for lattice structure <NUM> are arranged in lattice cells as shown in <FIG>. Lattice structure <NUM> is composed of soft sub-cells from isotropic lattice structure <NUM> shown in <FIG> and stiff sub-cells from isotropic lattice structure <NUM> shown in <FIG>. The soft sub-cells and the stiff sub-cells for lattice structure <NUM> are arranged in lattice cells as shown in <FIG>. Lattice structure <NUM> is composed of soft sub-cells from isotropic lattice structure <NUM> shown in <FIG> and stiff sub-cells from isotropic lattice structure <NUM> shown in <FIG>. The soft sub-cells and the stiff sub-cells for lattice structure <NUM> are arranged in lattice cells as shown in <FIG>.

The lattice shear moduli for each of lattice structures <NUM>, <NUM>, and <NUM> are summarized below in Table <NUM>. In graphs <NUM> - <NUM>, curve "<NUM>" is the force-displacement curve (stress-stain curve) of the lattice structure when loaded in the forward longitudinal direction, curve "<NUM>" is the force-displacement curve of the lattice structure when loaded in the rearward longitudinal direction, and curve "<NUM>" is the force-displacement curve of the lattice structure when loaded in the transverse direction. In Table <NUM>, "delta shear modulus" is the percent difference between the forward shear modulus and the rearward shear modulus, and "shear modulus ratio" is equal to the rearward shear modulus divided by the forward shear modulus. The lattice shear moduli are reported in Netwons per millimeter (N/mm).

Lattice structure <NUM> has a delta shear modulus value of <NUM>%, meaning that the lattice shear modulus measured in the rearward direction is greater than the lattice shear modulus measured in the forward direction by <NUM>%. The ratio of the lattice shear modulus measured in the rearward direction to the lattice shear modulus in the forward direction for lattice structure <NUM> is <NUM>. Like lattice structure <NUM>, lattice structure <NUM> has a delta shear modulus value of greater than <NUM>%. Lattice structure <NUM> has a delta shear modulus value of <NUM>%, meaning that the lattice shear modulus measured in the rearward direction is greater than the lattice shear modulus measured in the forward direction by <NUM>%. The ratio of the lattice shear modulus measured in the rearward direction to the lattice shear modulus in the forward direction for lattice structure <NUM> is <NUM>. Three-dimensional meshes composed of unit cells <NUM> arranged in the anisotropic lattice structures <NUM> and <NUM> should be capable of sufficiently deforming forward under a vertical load and converting vertical loading energy into forward displacement to help propel a wearer's foot forward when a sole including the three-dimensional mesh contacts the ground.

In contrast to lattice structures <NUM> and <NUM>, lattice structure <NUM> has a relatively small delta shear modulus. Lattice structure <NUM> has a delta shear modulus value of <NUM>%, meaning that the lattice shear modulus measured in the rearward direction is greater than the lattice shear modulus measured in the forward direction by <NUM>%. The ratio of the lattice shear modulus measured in the rearward direction to the lattice shear modulus in the forward direction for lattice structure <NUM> is <NUM>. Three-dimensional meshes composed of unit cells <NUM> arranged in the anisotropic lattice structure <NUM> may not be capable of converting enough vertical loading energy into forward displacement to meaningfully help propel a wearer's foot forward when a sole including the three-dimensional mesh contacts the ground.

The results summarized in Table <NUM> show that certain combinations of soft and stiff sub-cells can provide desired forward motion characteristics for a sole. However, not all combinations of soft and stiff sub-cell will necessarily provide desired characteristics.

In some embodiments, a three-dimensional mesh, or a mechanically anisotropic region thereof, can have a lattice compressive modulus of <NUM> N/mm or more. In some embodiments, a three-dimensional mesh, or a mechanically anisotropic region thereof, can have a lattice compressive modulus ranging from <NUM> N/mm to <NUM> N/mm. A lattice compressive modulus of <NUM> N/mm or more can provide a desired amount of cushioning for a wearer's foot when the three-dimensional mesh is incorporated into a sole for an article of footwear.

In some embodiments, a three-dimensional mesh, or a mechanically anisotropic region thereof, can have a lattice displacement in the forward direction of <NUM> or more. In some embodiments, a three-dimensional mesh, or a mechanically anisotropic region thereof, can have a lattice displacement in the forward direction of <NUM> to <NUM>. A lattice displacement in the forward direction of <NUM> or more can provide a suitable amount of forward displacement to meaningfully help propel a wearer's foot forward when a sole including the three-dimensional mesh contacts the ground.

Graph <NUM> in <FIG> is a plot of the lattice compressive modulus ("Comp. Stiffness") versus the lattice displacement in the forward direction for various lattice structures according to some embodiments. In graph <NUM>, lattice structure <NUM> is labeled as "Multi <NUM>", lattice structure <NUM> is labeled as "Multi <NUM>" and lattice structure <NUM> is labeled as "Multi <NUM>.

A three-dimensional mesh <NUM> as described herein can be made using a three-dimensional (<NUM>-D) printing process. In such embodiments, <NUM>-D printing three-dimensional mesh <NUM> for a sole includes printing a plurality of interconnected unit cells <NUM>, with each interconnected unit cell <NUM> including a plurality of struts <NUM> defining a three-dimensional shape and a plurality of nodes <NUM> at which one or more struts <NUM> are connected. In some embodiments, the <NUM>-D printing process can include printing a set of interconnected unit cells <NUM> that define one or more mechanically anisotropic regions for the three-dimensional mesh <NUM>. The mechanically anisotropic region(s) for the three-dimensional mesh <NUM> can include unit cells <NUM> and anisotropic lattice shear moduli as discussed herein.

In some embodiments, the arrangement of soft sub-cells and stiff sub-cells as described herein can be leveraged to create a three-dimensional mesh <NUM> with a perimeter structure having a unique pattern. In some embodiments, a three-dimensional mesh <NUM> can have a perimeter sidewall defining a perimeter structure defined by soft sub-cells and stiff sub-cells arranged as described herein. The perimeter sidewall of a three-dimensional mesh <NUM> is defined by the forefoot end, heel end, medial side, and lateral side of the three-dimensional mesh <NUM>. The perimeter structure of the perimeter sidewall can be the perimeter structure in side view from medial transverse direction <NUM> or lateral transverse direction <NUM> of a three-dimensional mesh <NUM>.

In some embodiments, a three-dimensional mesh as described herein can have a perimeter sidewall defining a perimeter structure including the structure shown in FIG. In some embodiments, a three-dimensional mesh as described herein can have a perimeter sidewall defining a perimeter structure including the structure shown in <FIG>. In some embodiments, a three-dimensional mesh as described herein can have a perimeter sidewall defining a perimeter structure including the structure shown in <FIG>. In some embodiments, a three-dimensional mesh as described herein can have a perimeter sidewall defining a perimeter structure including the structure shown in <FIG>. In some embodiments, a three-dimensional mesh as described herein can have a perimeter sidewall defining a perimeter structure including the structure shown in <FIG>. In some embodiments, a three-dimensional mesh as described herein can have a perimeter sidewall defining a perimeter structure including the structure shown in <FIG>. In some embodiments, a three-dimensional mesh as described herein can have a perimeter sidewall defining a perimeter structure including the structure shown in <FIG>. In some embodiments, a three-dimensional mesh as described herein can have a perimeter sidewall defining a perimeter structure including the structure shown in <FIG>. In some embodiments, a three-dimensional mesh as described herein can have a perimeter sidewall defining a perimeter structure including the structure shown in <FIG>. In some embodiments, a three-dimensional mesh as described herein can have a perimeter sidewall defining a perimeter structure including the structure shown in <FIG>.

In some embodiments, a three-dimensional mesh as described herein can have a perimeter sidewall defining a perimeter structure having a plurality of eight-sided regions defined by eight struts <NUM> and arranged in a pattern at the perimeter sidewall. The plurality of eight-sided regions defined by eight struts <NUM> can have substantially the same size. In some embodiments, the plurality of eight-sided regions defined by eight struts <NUM> can be arranged directly adjacent to each other at the perimeter sidewall. Directly adjacent eight-sided regions share one or more struts defining their eight-sided shapes. In some embodiments, the plurality of eight-sided regions defined by eight struts <NUM> can each have a bowtie perimeter shape.

<FIG> and <FIG> show a midsole <NUM> having a perimeter sidewall <NUM> with a perimeter structure <NUM> according to some embodiments. Perimeter structure <NUM> includes a plurality of eight-sided regions <NUM> arranged directly adjacent to each other and having substantially the same size. Directly adjacent eight-sided regions <NUM> share one or more border struts <NUM>. The plurality of eight-sided regions <NUM> can be defined by eight border struts <NUM> connected at eight nodes <NUM>. As shown in <FIG> and <FIG>, these eight-sided regions <NUM> can have a bowtie perimeter shape (see dotted lines in <FIG>).

In some embodiments, the plurality of eight-sided regions <NUM> can include a first eight-sided region <NUM> having four openings <NUM> defined by four interior struts <NUM> connected at an interior node <NUM> and a second eight-sided region <NUM> having a single opening <NUM> defined by eight border struts <NUM>. In some embodiments, the plurality of eight-sided regions <NUM> can include a plurality of first eight-sided regions <NUM> having four openings <NUM> defined by four interior struts <NUM> connected at an interior node <NUM> and a plurality of second eight-sided regions <NUM> having a single opening <NUM> defined by eight border struts <NUM>. An interior node <NUM> is a node located within an eight-sided region <NUM>. Similarly, an interior strut <NUM> is a strut that extends into an eight-sided region <NUM>. Border struts <NUM> for an eight-sided region <NUM> define the perimeter shape of the region <NUM>.

In some embodiments, the plurality of first eight-sided regions <NUM> can be arranged in a first row <NUM> extending in longitudinal direction <NUM> between forefoot end <NUM> of midsole <NUM> and heel end <NUM> of midsole <NUM>. In some embodiments, the plurality of second eight-sided regions <NUM> can be arranged in a second row <NUM> extending in longitudinal direction <NUM> between forefoot end <NUM> of midsole <NUM> and heel end <NUM> of midsole <NUM>. In some embodiments, first row <NUM> can be located above second row <NUM> in vertical direction <NUM>. In some embodiments, first row <NUM> can be located below second row <NUM> in vertical direction <NUM>. In some embodiments, as shown in <FIG> and <FIG>, perimeter structure <NUM> can include the structure shown in <FIG>.

In some embodiments, all or a portion of a three-dimensional mesh as described herein can be coated with a color coating. In some embodiments, the color coating can be an internal color coating configured to accentuate all or a portion of a perimeter structure of a three-dimensional mesh. In some embodiments, the color coating can be coated directly on surfaces of struts and nodes for unit cells defining a three-dimensional mesh. In some embodiments, the color coating can be a powder coating. In some embodiments, color coating can be a paint coating.

<FIG> and <FIG> show a color-coated midsole <NUM> according to some embodiments. Midsole <NUM> includes a three-dimensional mesh <NUM> having a forefoot end <NUM>, a heel end <NUM>, a medial side <NUM>, and a lateral side <NUM>. Three-dimensional mesh <NUM> includes a plurality of interconnected unit cells <NUM> with a plurality of struts <NUM> connected at nodes <NUM> defining a three-dimensional shape of the unit cells <NUM>. A plurality of interconnected unit cells <NUM> define at least a portion of a perimeter sidewall <NUM> of three-dimensional mesh <NUM>. In some embodiments, unit cells <NUM> defining a perimeter of forefoot end <NUM>, heel end <NUM>, medial side <NUM>, and lateral side <NUM> define a perimeter sidewall <NUM> of three-dimensional mesh <NUM>.

Three-dimensional mesh <NUM> includes a color coating <NUM> coated on a portion of three-dimensional mesh <NUM>. Color coating <NUM> is not coated on at least a portion of perimeter sidewall <NUM> of three-dimensional mesh <NUM>. In some embodiments, color coating <NUM> is not coated on any portion of perimeter sidewall <NUM> of three-dimensional mesh <NUM>. By not coating color coating <NUM> on at least a portion of perimeter sidewall <NUM>, the perimeter structure of perimeter sidewall <NUM> can be accentuated by the color contrast between the perimeter sidewall <NUM> and interior portions of three-dimensional mesh <NUM> coated with color coating <NUM>. In some embodiments, the perimeter structure of perimeter sidewall <NUM> can include one or more of the structures shown in <FIG>.

In some embodiments, one or more perimeter columns of unit cells <NUM> defining perimeter sidewall <NUM> of three-dimensional mesh <NUM> may not be coated with color coating <NUM> to accentuate the perimeter structure of perimeter sidewall <NUM>. <FIG> is a schematic of a transverse stack <NUM> of the unit cells <NUM>. Transverse stack <NUM> can extend from medial side <NUM> to lateral side <NUM> of three-dimensional mesh <NUM>. The transverse stack <NUM> includes an exterior column <NUM> of unit cells <NUM> defining at least a portion of perimeter sidewall <NUM> of three-dimensional mesh <NUM> and one or more interior columns <NUM> of unit cells <NUM> disposed interior of exterior column <NUM>. In some embodiments, color coating <NUM> can be coated on at least a portion of one or more interior columns <NUM> of unit cells <NUM> and is not coated on the exterior column <NUM> of unit cells <NUM>.

In some embodiments, the plurality of interconnected unit cells <NUM> defining three-dimensional mesh <NUM> can have a first color and the color coating <NUM> has a second color different from the first color. The colors of color coating <NUM> and three-dimensional mesh <NUM> can be characterized by a three-coordinate color space, for example the CIELab space. In this system, each color is characterized by the lightness value (L*), a chroma value (a*), and a hue value (b*). Through use of a spectrophotometer, these three values can be measured and differences in color can be characterized. CIELab colors can be measured using ISO/CIE <NUM>-<NUM>:<NUM> ("Colorimetry - Part <NUM>: CIE <NUM>*a*b Colour Space"). A first color described as being different from a second color has one or more of a lightness value, a chroma value, or a hue value that is at least <NUM>% higher or at least <NUM>% lower than the lightness value, chroma value, and hue value the second color. In some embodiments, the first color can have a lightness value of at least <NUM>% higher or at least <NUM>% lower than the lightness value of the second color. In some embodiments, the first color can have a chroma value of at least <NUM>% higher or at least <NUM>% lower than the chroma value of the second color. In some embodiments, the first color can have a hue value of at least about <NUM>% higher or at least about <NUM>% lower than the hue value of the second color.

In some embodiments, the first color can be selected from the group of: red, crimson, maroon, magenta, pink, orange, yellow, gold, chartreuse, green, blue, navy, aqua, teal, cerulean, indigo, violet, purple, brown, black, grey, white, beige, silver, or taupe. In some embodiments, the second color can be selected from the group of: red, crimson, maroon, magenta, pink, orange, yellow, gold, chartreuse, green, blue, navy, aqua, teal, cerulean, indigo, violet, purple, brown, black, grey, white, beige, silver, or taupe.

In some embodiments, color coating <NUM> does not fill spaces <NUM> between a plurality of struts <NUM> defining unit cells <NUM> of three-dimensional mesh <NUM>. In some embodiments, color coating <NUM> does not extend between individual struts <NUM> not connected to each other at a node <NUM>. In such embodiments, color coating <NUM> can provide desired aesthetic benefits without masking the three-dimensional shape of unit cells <NUM> defining three-dimensional mesh <NUM>.

Where a range of numerical values comprising upper and lower values is recited herein, unless otherwise stated in specific circumstances, the range is intended to include the endpoints thereof, and all integers and fractions within the range. It is not intended that the disclosure or claims be limited to the specific values recited when defining a range. Further, when an amount, concentration, or other value or parameter is given as a range, one or more ranges, or as list of upper values and lower values, this is to be understood as specifically disclosing all ranges formed from any pair of any upper range limit or value and any lower range limit or value, regardless of whether such pairs are separately disclosed. Finally, when the term "about" is used in describing a value or an end-point of a range, the disclosure should be understood to include the specific value or end-point referred to. Whether or not a numerical value or end-point of a range recites "about," the numerical value or end-point of a range is intended to include two embodiments: one modified by "about," and one not modified by "about.

As used herein, the term "about" refers to a value that is within ± <NUM>% of the value stated. For example, about <NUM>% can include any percentage between <NUM>% and <NUM>%.

Claim 1:
A sole (<NUM>, <NUM>, <NUM>, <NUM>) for an article of footwear (<NUM>), the sole (<NUM>) comprising:
a three-dimensional mesh (<NUM>, <NUM>) comprising:
a plurality of interconnected unit cells (<NUM>, <NUM>), each interconnected unit cell (<NUM>) comprising a plurality of struts (<NUM>) defining a three-dimensional shape and a plurality of nodes (<NUM>) at which one or more struts (<NUM>) are connected, wherein each unit cell (<NUM>) comprises a soft sub-cell (<NUM>) and a stiff sub-cell (<NUM>),
wherein the soft sub-cell (<NUM>) comprises a sub-cell for a first lattice structure (<NUM>, <NUM>, <NUM>) and wherein the stiff sub-cell (<NUM>) comprises a sub-cell for a second lattice (<NUM>, <NUM>, <NUM>) structure different from the first lattice structure, wherein the first lattice structure (<NUM>, <NUM>, <NUM>) comprises a first modeled compressive modulus and the second lattice structure (<NUM>, <NUM>, <NUM>) comprises a second modeled compressive modulus <NUM>% or more greater than the first modeled compressive modulus,
wherein the three-dimensional mesh (<NUM>) comprises: a lattice shear modulus measured in a forward direction, and
a lattice shear modulus measured in a rearward direction greater than the lattice shear modulus measured in the forward direction,
wherein the lattice shear modulus measured in a rearward direction is greater than the lattice shear modulus measured in the forward direction by <NUM>% or more.