Patent Publication Number: US-11375770-B2

Title: Sole structure for an article of footwear with side wall notch and nonlinear bending stiffness

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application is a continuation of U.S. Nonprovisional application Ser. No. 15/423,882 filed Feb. 3, 2017, which claims the benefit of priority to U.S. Provisional Application No. 62/293,085 filed Feb. 9, 2016, and both of which are hereby incorporated by reference in their entirety. 
    
    
     TECHNICAL FIELD 
     The present teachings generally include a sole structure for an article of footwear. 
     BACKGROUND 
     Footwear typically includes a sole structure configured to be located under a wearer&#39;s foot to space the foot away from the ground. Sole assemblies in athletic footwear are configured to provide desired cushioning, motion control, and resiliency. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic perspective illustration of a first embodiment of a sole structure for an article of footwear. 
         FIG. 2  is a schematic illustration in medial side view of the sole structure of  FIG. 1  with an upper and showing a foot in phantom. 
         FIG. 3  is a schematic illustration in plan view of the sole structure of  FIG. 1 . 
         FIG. 4  is a schematic illustration in bottom view of the sole structure of  FIG. 1   
         FIG. 5  is a schematic illustration in medial side view of the sole structure of  FIG. 1 , flexed in a first portion of a range of flexion. 
         FIG. 6  is a schematic illustration in medial side view of the sole structure of  FIG. 5  flexed at a first predetermined flex angle. 
         FIG. 7  is a plot of torque versus flex angle for the sole structure of  FIGS. 1-6 . 
         FIG. 8  is a schematic perspective illustration of a second embodiment of a sole structure for an article of footwear in accordance with an alternative aspect of the present teachings. 
         FIG. 9  is a schematic illustration in medial side view of the sole structure of  FIG. 8  with an upper and showing a foot in phantom. 
         FIG. 10  is a schematic illustration in plan view of the sole structure of  FIG. 8 . 
         FIG. 11  is a schematic illustration in bottom view of the sole structure of  FIG. 9 . 
         FIG. 12  is a schematic illustration in medial side view of the sole structure of  FIG. 8 , flexed in a first portion of a range of flexion. 
         FIG. 13  is a schematic illustration in medial side view of the sole structure of  FIG. 8  flexed at a first predetermined flex angle. 
     
    
    
     DESCRIPTION 
     A sole structure for an article of footwear comprises a sole plate that includes a forefoot portion with a foot-facing surface. The sole plate may be a unisole plate, an inner board plate, an outsole plate, a midsole plate, or any combination of an inner board plate, an outsole plate, and a midsole plate. 
     The sole plate has at least one side wall extending upward from the foot-facing surface. The at least one side wall has a notch in an upper periphery of the side wall in the forefoot portion. The notch is configured to be open when the forefoot portion of the sole plate is dorsiflexed in a first portion of a flexion range and closed when the forefoot portion of the sole plate is dorsiflexed in a second portion of the flexion range greater than the first portion. The notch has a forward face and a rearward face that are non-parallel and spaced apart from one another when the sole plate is in an unflexed, relaxed state, and that are parallel and in contact with one another when the sole plate is dorsiflexed in the longitudinal direction in the second portion of the flexion range. 
     In an embodiment, the first portion of the flexion range includes flex angles of the sole plate less than a first predetermined flex angle, and the second portion of the sole plate includes flex angles of the sole plate greater than or equal to the first predetermined flex angle. The closing of the notch increases resistance to flexion of the sole plate, and the sole plate provides a change in bending stiffness, with a greater bending stiffness in the second portion of the flexion range than in the first portion of the flexion range. 
     In an embodiment, the at least one side wall may be at a medial side of the sole plate and the notch may be the only notch in the forefoot portion of the at least one side wall. Alternatively, the at least one side wall may be at the lateral side of the sole plate, and the notch may be the only notch in the forefoot portion of the at least one side wall. Still further, both the medial side wall and the lateral side wall may have one or more notches in the forefoot portion. 
     In an embodiment, the forward face of the notch inclines in a forward direction, and the rearward face of the notch inclines a rearward direction when the sole plate is in the unflexed, relaxed state. 
     In an embodiment, the notch may have a rounded base connecting a forward face and a rearward face of the notch. The notch is open at the rounded base both when the forward face and the rearward face are spaced apart from one another (i.e., when the notch is open), and when the forward face and the rearward face are in contact with one another (i.e., when the notch is closed). Stated differently, the notch has a rounded base disposed between the forward face and the rearward face, and the notch is open at the rounded base in both the first portion of the flexion range and the second portion of the flexion range 
     A height of a forefoot portion of the at least one side wall may be greatest at the first notch. The forefoot portion of the upper periphery of the at least one side wall may have a first peak at the forward face, and a second peak at the rearward face. The at least one side wall may taper in height from the first peak in a forward direction, and taper in height from the second peak in a rearward direction. 
     In an embodiment, a forward flange extends along the forward face, and a rearward flange extends along the rearward face. The forward flange and the rearward flange are thicker than a portion of the at least one side wall adjacent the forward flange and the rearward flange. 
     Optionally, a ground-facing surface of the sole plate opposite from the foot-facing surface may include a flex groove that extends generally transversely in the ground-facing surface toward the notch. 
     Still further, the sole plate may have at least one rib at a surface of the at least one side wall. The at least one rib may extend generally downward from the upper periphery of the at least one side wall and may be adjacent to the notch. 
     In an embodiment, a sole structure for an article of footwear comprises a sole plate that includes a forefoot portion with a foot-facing surface. The sole plate has at least one side wall extending upward from the foot-facing surface. The at least one side wall has a first notch in an upper periphery of the at least one side wall in the forefoot portion of the sole plate. The first notch includes a rounded base and extends from the upper periphery to the rounded base. The first notch is configured to be open between the upper periphery and the rounded base when the forefoot portion of the sole plate is dorsiflexed in a first portion of a flexion range and closed between the upper periphery and the rounded base when the forefoot portion of the sole plate is dorsiflexed in a second portion of the flexion range greater than the first portion. The first notch is open at the rounded base in both the first portion of the flexion range and the second portion of the flexion range. 
     In an embodiment, the at least one side wall includes a medial side wall at a medial side of the sole plate and a lateral side wall at a lateral side of the sole plate. The first notch is in the medial side wall. The lateral side wall has at least one notch in an upper periphery of the lateral side wall in the forefoot portion of the sole plate. 
     In an embodiment, the medial side wall has a second notch in the upper periphery of the medial side wall in the forefoot portion of the sole plate anterior to the first notch. The lateral side wall has two notches in the upper periphery of the lateral side wall in the forefoot portion of the sole plate. 
     In an embodiment, a ground-facing surface of the sole plate has a flex groove extending generally transversely in the ground-facing surface toward the first notch. 
     In an embodiment, a height of a forefoot portion of the at least one side wall is greatest at the notch. 
     The above features and advantages and other features and advantages of the present teachings are readily apparent from the following detailed description of the modes for carrying out the present teachings when taken in connection with the accompanying drawings. 
     Referring to the drawings, wherein like reference numbers refer to like components throughout the views,  FIG. 1  shows a sole structure  10  for an article of footwear  11  shown in  FIG. 2 . The sole structure  10  has a resistance to flexion that increases with increasing dorsiflexion of the forefoot portion  14  of the sole structure  10  (i.e., flexing of the forefoot portion  14  in the longitudinal direction as discussed herein). As further explained herein, due to a notch  28  provided in side wall  26 , the sole structure  10  (and more specifically the sole plate  12  described herein), provides an increase in bending stiffness when flexed in a longitudinal direction at one or more predetermined flex angles. More particularly, the sole structure  10  has a bending stiffness that is a piecewise function with a change at a first predetermined flex angle. The bending stiffness is tuned by the selection of various structural parameters discussed herein that determine the first predetermined flex angle. As used herein, “bending stiffness” and “bend stiffness” may be used interchangeably. 
     Referring to  FIGS. 1 and 2 , the sole structure  10  includes a sole plate  12 , and may include one or more additional plates, layers, or components, as discussed herein. The article of footwear  11  includes an upper  13  (shown in  FIG. 2 ). The sole plate  12  is configured to be operatively connected to the upper  13  as discussed herein. The upper  13  may incorporate a plurality of material elements (e.g., textiles, foam, leather, and synthetic leather) that are stitched or adhesively bonded together to form an interior void  15  for securely and comfortably receiving a foot  52  as shown. The material elements may be selected and located with respect to upper  13  in order to selectively impart properties of durability, air-permeability, wear-resistance, flexibility, and comfort, for example. An ankle opening  17  provides access to the interior void  15 . In addition, upper  13  may include a lace or other tightening mechanism that is utilized to modify the dimensions of the interior void  15 , thereby securing the foot  52  within the interior void  15  and facilitating entry and removal of the foot  52  from the interior void  15 . For example, a lace may extend through apertures in upper  13 , and a tongue portion of upper  13  may extend between the interior void  15  and the lace. The upper  13  may exhibit the general configuration discussed above or a different configuration. Accordingly, the structure of the upper  13  may vary significantly within the scope of the present teachings. 
     Sole structure  10  is secured to the upper  13  and has a configuration that extends between the upper  13  and the ground G. In addition to attenuating ground reaction forces (i.e., providing cushioning for the foot), the sole structure  10  may provide traction, impart stability, and limit various foot motions. 
     In the embodiment shown, the sole plate  12  is a full-length, unitary sole plate  12  that has a forefoot portion  14 , a midfoot portion  16 , and a heel portion  18  which may also be referred to respectively as a forefoot region  14 , a midfoot region  16 , and a heel region  18 . The sole plate  12  provides a foot-receiving surface  20  (also referred to as a foot-facing surface) that extends over the forefoot portion  14 , the midfoot portion  16 , and the heel portion  18 . In other embodiments, the sole plate  12  may be a partial length plate member. For example, in some cases, the sole plate  12  may include only a forefoot portion that may be operatively connected to other components of the article of footwear that comprise a midfoot portion and a heel portion. 
     The heel portion  18  generally includes the region of the sole plate  12  corresponding with the rear portion of a human foot, including the calcaneus bone, when the human foot is supported on the sole structure  10  and is a size corresponding with the sole structure  10 . The forefoot portion  14  generally includes the region of the sole plate  12  corresponding with the toes and the joints connecting the metatarsal bones with the phalange bones of the human foot (interchangeably referred to herein as the “metatarsal-phalangeal joints” or “MPJ” joints). The midfoot portion  16  generally includes the region of the sole plate  12  corresponding with an arch area of the human foot, including the navicular joint. Portions  14 ,  16 ,  18  are not intended to demarcate precise areas of the sole structure  10 . Rather, portions  14 ,  16 ,  18  are intended to represent general areas relative to one another, to aid in the following discussion. As shown, the sole plate  12  extends from a lateral side  22  to a medial side  24 . As used herein, a lateral side of a component for an article of footwear, including the lateral side  22  of the sole plate  12 , is a side that corresponds with an outside area of the human foot  52  (i.e., the side closer to the fifth toe of the wearer). The fifth toe is commonly referred to as the little toe. A medial side of a component for an article of footwear, including the medial side  24  of the sole plate  12 , is the side that corresponds with an inside area of the human foot  52  (i.e., the side closer to the hallux of the foot of the wearer). The hallux is commonly referred to as the big toe. Both the lateral side  22  and the medial side  24  extend from a foremost extent  25  to a rearmost extent  29  of a periphery of the sole plate  12 . In the embodiment shown, the medial side  24  is established by side wall  26 , which varies in height. The lateral side  22  is established by side wall  48 , which tapers to minimal or no height in the forefoot portion  14  generally under the MPJ joints of the foot  52 . These descriptions of the relative positions of a heel portion, a midfoot portion, a forefoot portion, a medial side, and a lateral side may also be used to describe portions of the article of footwear  11 , including the sole structure, and individual components thereof. 
     The sole plate  12  is referred to as a plate, but is not necessarily flat and need not be a single component but instead can be multiple interconnected components. For example, both an upward-facing portion of the foot-facing surface  20  and the opposite ground-facing surface  21  may be pre-formed with some amount of curvature and variations in thickness when molded or otherwise formed in order to provide a shaped footbed and/or increased thickness for reinforcement in desired areas. For example, the sole plate  12  could have a curved or contoured geometry that may be similar to the lower contours of the foot  52 . In the example shown, the sole plate  12  includes the side walls as a contoured periphery that slope upward toward any overlaying layers, such as a midsole component or the upper  13 . The side walls  26 ,  48  extend upward around a periphery of a generally upward-facing bottom portion  23  of the foot-facing surface  20 . The side walls  26 ,  48  may be a single, unitary component with the bottom portion  23 , or these may each be separate components operatively connected to one another such as with adhesive or by thermal bonding. 
     The sole plate  12  may be entirely of a single, uniform material, or may have different portions comprising different materials. For example, a first material of the forefoot portion  14  can be selected to achieve, in conjunction with the parameters of the side walls  26 ,  48 , the desired bending stiffness in the forefoot portion  14 , while a second material of the midfoot portion  16  and the heel portion  18  can be a different material that has little effect on the bending stiffness of the forefoot portion  14  at the notch  28 . By way of non-limiting example, the second portion can be over-molded on or co-injection molded with the first portion. Example materials for the sole plate  12  include durable, wear resistant materials such as but not limited to nylon, thermoplastic polyurethane, or carbon fiber. 
     The term “longitudinal,” as used herein, refers to a direction extending along a length of the sole structure  10 , e.g., extending from the forefoot portion  14  to the heel portion  18  of the sole structure  10 . The term “forward” is used to refer to the general direction from the heel portion  18  toward the forefoot portion  14 , and the term “rearward” is used to refer to the opposite direction, i.e., the direction from the forefoot portion  14  toward the heel portion  18 . The term “anterior” is used to refer to a front or forward component or portion of a component. The term “posterior” is used to refer to a rear or rearward component or portion of a component. 
     As shown in  FIGS. 2 and 5 , a foot  52  can be supported by the foot-facing surface  20 , with the foot  52  above the foot-facing surface  20 . The foot-facing surface  20  may be referred to as a foot-receiving surface or an upper surface or upward-facing surface of the sole plate  12 . The foot-facing surface  20  supports the foot  52  but need not be in contact with the foot  52 . For example, an insole, midsole, strobel, or other layers or components may be positioned between the foot  52  and the foot-facing surface  20 . 
     In the embodiment shown, the sole plate  12  may be an inner board plate, also referred to as an inner board, an insole board, or a lasting board. In other embodiments, the sole plate  12  may be an outsole. Still further, the sole plate  12  could be a midsole plate or a unisole plate, or may be any combination of an inner board plate, a midsole plate, or an outsole. 
     The sole plate  12  has at least one notch  28  that affects the bending stiffness of the sole structure  10 . Stated differently, the side wall  26  of the sole plate  12  defines a first notch  28 . The notch  28  extends downward from an upper periphery  27  of the side wall  26  toward the foot-facing surface  20 . The notch  28  is configured to be open when the forefoot portion  14  of the sole plate  12  and the sole structure  10  is dorsiflexed in a first portion of a flexion range (i.e., at flex angles less than a first predetermined flex angle A 1  (indicated in  FIG. 6 )), and closed when the forefoot portion  14  is dorsiflexed in a second portion of the flexion range greater than the first portion (i.e., at flex angles such as flex angle A that are greater than or equal to the first predetermined flex angle A 1 ). The first predetermined flex angle A 1  is defined as the angle formed at the intersection between a first axis LM 1  and a second axis LM 2  where the first axis generally extends along a longitudinal midline LM at a ground-facing surface  21  of sole plate  12  (best shown in  FIG. 4 ) anterior to the side wall notch  28 , and the second axis LM 2  generally extends along the longitudinal midline LM at the ground-facing surface  21  of the sole plate  12  posterior to the side wall notch  28 . The sole plate  12  is configured so that the intersection of the first and second axes LM 1  and LM 2  will typically be approximately centered both longitudinally and transversely below the side wall notch  28  discussed herein, and below the metatarsal-phalangeal joints of the foot  52  supported on the foot-facing surface  20 . 
     By way of non-limiting example, the first predetermined flex angle A 1  may be from about 30 degrees to about 65 degrees. In one exemplary embodiment, the first predetermined flex angle A 1  is found in the range of between about 30 degrees and about 60 degrees, with a typical value of about 55 degrees. In another exemplary embodiment, the first predetermined flex angle A 1  is found in the range of between about 15 degrees and about 30 degrees, with a typical value of about 25 degrees. In another example, the first predetermined flex angle A 1  is found in the range of between about 20 degrees and about 40 degrees, with a typical value of about 30 degrees. Generally, the specific flex angle or range of angles at which a change in the rate of increase in bending stiffness occurs is dependent upon the specific activity for which the article of footwear is designed. 
     As an ordinarily skilled artisan will recognize in view of the present disclosure, a sole plate  12  will bend in dorsiflexion in response to forces applied by corresponding bending of a user&#39;s foot at the MPJ during physical activity. Throughout the first portion of the flexion range FR 1 , the bending stiffness (defined as the change in moment as a function of the change in angle) will remain approximately the same as bending progresses through increasing angles of flexion. Because bending within the first portion of the flexion range FR 1  is primarily governed by inherent material properties of the materials of the plate, a graph of torque on the plate versus angle of flexion (the slope of which is the bending stiffness) in the first portion of the flexion range FR 1  will typically demonstrate a smoothly but relatively gradually inclining curve (referred to herein as a “linear” region with constant bending stiffness). At the boundary between the first and second portions of the range of flexion, however, the closure of the notch  28  engages additional material and mechanical properties that exert a notable increase in resistance to further dorsiflexion. Therefore, a corresponding graph of torque versus angle of deflection (the slope of which is the bending stiffness) that also includes the second portion of the flexion range FR 2  would show—beginning at an angle of flexion approximately corresponding to angle A 1 —a departure from the gradually and smoothly inclining curve characteristic of the first portion of the flexion range FR 1 . This departure is referred to herein as a “nonlinear” increase in bend stiffness, and would manifest as either or both of a stepwise increase in bending stiffness and/or a change in the rate of increase in the bending stiffness. The change in rate can be either abrupt, or it can manifest over a short range of increase in the bend angle of the sole plate  12 . In either case, a mathematical function describing a bending stiffness in the second portion of the flexion range FR 2  will differ from a mathematical function describing bending stiffness in the first portion of the flexion range.  FIG. 7  is an example plot depicting an expected increase in resistance to flexion at increasing flex angles, as exhibited by the increasing magnitude of torque required at the heel portion  18  for dorsiflexion of the forefoot portion  14 . The bending stiffness in the first range of flexion FR 1  may be constant (thus the plot would have a linear slope) or substantially linear or may increase gradually (which would show a change in slope in FR 1 ). The bending stiffness in the second range of flexion FR 2  may be linear or nonlinear, but will depart from the bending stiffness of the first range of flexion FR 1  at the first predetermined flex angle A 1 , either markedly or gradually (such as over a range of several degrees) at the first predetermined flex angle A 1  due to the closing of the notch  28 . 
     As will be understood by those skilled in the art, during bending of the sole plate  12  as the foot  52  is dorsiflexed, there is a layer in the sole plate  12  referred to as a neutral plane (although not necessarily planar) or neutral axis above which the sole plate  12  is in compression, and below which the sole plate  12  is in tension. The closing of the side wall notch  28  places additional compressive forces on the sole plate  12  above the neutral plane, and additional tensile forces below the neutral plane, nearer the ground-facing surface  21 , as indicated by tensile forces TF 2  in  FIG. 6 . In addition to the mechanical (e.g., tensile, compression, etc.) properties of the sole plate  12 , structural factors that likewise affect changes in bending stiffness during dorsiflexion include but are not limited to the thicknesses, the longitudinal lengths, and the medial-lateral widths of different portions of the sole plate  12 . 
     When the flex angle of the sole plate  12  reaches the predetermined flex angle A 1 , the faces  30 ,  32  of the side wall  26  at the notch  28  contact one another and the side wall notch  28  closes. Throughout any further dorsiflexion, neither of the faces  30 ,  32  is able to move further toward the other. Therefore, as the sole plate  12  bends further, compressive forces CF 1  due to the bending of the sole plate  12  are applied across the closed notch  28 , as shown in  FIG. 6 . Bending stiffness of the forefoot portion  14  in the first portion of the flexion range FR 1  is influenced mainly by the portion of the sole plate  12  below the open notch  28  (i.e., the bottom portion  23 ), while bending stiffness of the forefoot portion  14  in the second portion of the flexion range FR 2  is influenced by the full height of the side wall  26  at the closed notch  28 . As further discussed herein and as shown in  FIG. 6 , the notch  28  closes when a forward face  30  of the side wall  26  at the notch  28  (referred to as a forward face of the notch  28 ) is in contact with a rearward face  32  of the side wall  26  at the notch  28  (referred to as a rearward face of the of the notch  28 ). The side wall  26  is configured so that the notch  28  is positioned directly laterally outward of a wearer&#39;s metatarsal-phalangeal joints (i.e., of the foot  52 ) based on population averages for the particular size of footwear. 
     In the embodiment shown in  FIG. 1 , the notch  28  is in the side wall  26  at the medial side  24  of the sole structure  10  and is the only notch in the forefoot portion  14  of the side wall  26 . The side wall  48  on the lateral side  22  generally decreases in height from the rearmost extent  29  of the heel portion  18  and from the foremost extent  25  of the forefoot portion  14  to a minimal height or no height generally transverse from the notch  28  and underlying the MPJ joints. By configuring the lateral side wall  48  to have a minimal height or no height transverse from the notch  28 , the side wall  48  does not interfere with or affect the bending in the forefoot portion  14  due to flexing of the MPJ joints. In other embodiments, the lateral side wall  48  could have a greater height and have one or more notches in the forefoot portion  14 , and/or the medial side wall  26  could have more than one notch. 
     The notch  28  has a rounded base  34  that connects the forward face  30  and the rearward face  32 , referred to as a rounded base  34  of the notch  28 . The rounded base  34  is configured to remain open both when the sole structure  10  and sole plate  12  are in a relaxed, unflexed state, as shown in  FIG. 2  (i.e., when the notch  28  is open), and even when the notch  28  is closed (i.e., when the forward face  30  is in contact with the rearward face  32  due to the sole structure  10  (including the sole plate  12 ) being flexed at a flex angle greater than or equal to the first predetermined flex angle A 1 ). There is still an opening in the side wall  26  at the rounded base  34  even when the forward face  30  is in contact with the rearward face  32 , as shown in  FIG. 6 . As shown in  FIG. 2 , a distance D 1  across the notch  28  between a lowest extremity  30 A of the forward face  30  and a lowest extremity  32 A of the rearward face  32  when the sole plate  12  is in the unflexed, relaxed state is less than a distance D 2  across the notch  28  at the rounded base  34  below the lowest extremity  30 A of the forward face  30  and the lowest extremity  32 A of the rearward face  32 . As used herein, the “lowest extremity” of the forward face  30 A is the end of the face  30  closest to the rounded base  34  of the notch  28  as opposed to the end of the forward face  30  at the first peak P 1 . Similarly, the “lowest extremity” of the rearward face  32  is the end of the face  32  closest to the rounded base  34  of the notch  28  as opposed to the end of the rearward face  32  at the second peak P 2 . This configuration of the notch  28  with the rounded base  34  helps to minimize stress concentrations. In other words, bending of the sole plate  12  occurs along an expanse of the sole plate  12  below the notch  28  to the lowest height of the lateral side wall  48 , spread along the rounded base  34 , rather than at a more discreet hinge point. As shown in  FIG. 3 , a groove  35  extends from the rounded base  34  in the foot-facing surface  20  generally transversely from the first notch  28 . As used herein, a feature extends generally transversely when it extends lengthwise at least partially transversely. The groove  35  is a slight recess in the foot-facing surface  20  and extends toward the longitudinal midline LM. The groove  35  promotes flexing of the side wall  26  at the bottom of the rounded base  34 , further promoting alignment of the flanges  40 ,  42  and decreasing stress concentrations below the rounded base  34 . 
     As the foot  52  flexes by lifting the heel portion  18  away from the ground G while maintaining contact with the ground G at a forward portion of the article of footwear  11  corresponding with a forward portion of the forefoot portion  14 , it places torque on the sole structure  10  and causes the sole plate  12  to flex at the forefoot portion  14 . With the notch  28  open, and with no compressive forces therefore applied across the open notch  28 , the bending stiffness of the sole structure  10  during the first range of flexion FR 1  will be at least partially correlated with the height of the side wall below the notch  28 , which is the thickness of the bottom portion  23  of the sole plate  12 . The bending stiffness of the sole structure  10  during the second range of flexion FR 2  will be at least partially correlated with the height of the side wall at the closed notch  28 ). The closed notch  28  provides increased bending stiffness. 
     In order to ensure that the forward face  30  and the rearward face  32  contact one another during dorsiflexion of the forefoot portion  14 , and to minimize the possibility that relative lateral movement of the forward face  30  and rearward face  32  causes the faces  30 ,  32  to bypass one another partially or completely during dorsiflexion, the faces  30 ,  32  are provided with flanges. More specifically, the sole plate  12  has a forward flange  40  along the forward face  30  and a rearward flange  42  along the rearward face  32 . As best illustrated in  FIGS. 3 and 4 , the flanges  40 ,  42  are thicker than the portion of the side wall  26  adjacent the flanges  40 ,  42 . The flanges  40 ,  42  are shown with a thickness T 1  that is greater than a thickness T 2  of the adjacent portion of the side wall  26 . 
     In addition to the thicker flanges  40 ,  42 , the inner surface  44  of the side wall  26 , indicated in  FIG. 1 , is operatively connected to an outer surface  46  of the upper  13 , such as with adhesive or thermal bonding. The upper  13  is configured to be generally flexible in the vicinity of the notch  28  such that the upper  13  does not interfere with the movement of the faces  30 ,  32  into contact with one another. 
     At least one rib  50  may extend along an outer or inner surface of the side wall  26  generally downward from the upper periphery  27  toward the foot-facing surface  20  and adjacent the notch  28 . As used herein, a feature extends generally downward when it extends at least partially downward. As shown in  FIG. 4 , the ribs  50  also extend partly along the ground-facing surface  21 . In the embodiments shown, there are multiple ribs  50  on the outer surface of the side wall  26  and positioned both anterior to and posterior of the first notch  28  in the forefoot portion  14 . In other embodiments, there may be only one rib  50  either anterior to or posterior of the notch in the forefoot portion  14 . The ribs  50  brace the side wall  26  to prevent inward or outward bowing under the compressive forces CF 1  across the closed notch  28 . This helps to maintain alignment of the forward flange  40  and the rearward flange  42  with one another during dorsiflexion. 
     With reference to  FIGS. 1 and 2 , the forward face  30  of the first notch  28  inclines in a forward direction, the rearward face  32  of the first notch  28  inclines a rearward direction. The forward face  30  and the rearward face  32  are non-parallel and spaced apart from one another when the sole structure  10  including the sole plate  12  is in an unflexed, relaxed state, as shown in  FIG. 2 . The forward face  30  and the rearward face  32  are parallel and in contact with one another when the sole structure  10  including the sole plate  12  is flexed in the longitudinal direction to at least the first predetermined flex angle A 1 , i.e., in the second portion of the flexion range FR 2 , as illustrated in  FIG. 6 . 
     By configuring the sole plate  12  so that the forward and rearward faces  30 ,  32  and the accompanying flanges  40 ,  42  are nonparallel in the open position, surface area contact of the flanges  40 ,  42  is maximized when the notch  28  is closed. In such an embodiment, the entire planar surface area of the flanges  40 ,  42  can simultaneously come into contact when the notch  28  closes. In contrast, if the faces  30 ,  32  and flanges  40 ,  42  were parallel when the notch  28  was open, then the flanges  40 ,  42  would be non-parallel at least when the notch  28  initially closes, potentially resulting in a reduced contact area of the flanges  40 ,  42  and/or stress concentrations. 
     The relative inclinations of the forward face  30  and the rearward face  32  can be selected to provide a desired numerical value of the first predetermined flex angle, A 1 . Optionally, the notch  28  can be configured so that forward face  30  inclines forward more than rearward face  32  inclines rearward when the notch  28  is open and the sole plate  12  is in an unflexed position. The unflexed position is the position of the sole plate  12  when the heel portion  18  is not lifted and traction elements  69  at both the forefoot portion  14  and the heel portion  18  are in contact with the ground G. In  FIG. 2 , the sole structure  10  is shown in an unflexed position at a flex angle of 0 degrees. 
     The relative inclinations of the faces  30 ,  32  affects the angle at which the notch  28  closes (i.e., the numerical value of the first predetermined flex angle A 1 ). A greater inclination of the forward face  30  in the forward direction and/or the rearward face  32  in the rearward direction ensures that the notch  28  closes at a greater first predetermined flex angle A 1  than otherwise. 
     The height of the side wall  26  at the notch  28  also enhances the function of the notch  28  to increase the bending stiffness in a nonlinear manner. The height of the forefoot portion  14  of the side wall  26  forward of the notch  28  is less than the height H 1  at the notch  28 , i.e., at a first peak P 1  formed by the meeting of the forward face  30  and the upper periphery  27 . The height of the forefoot portion  14  of the side wall  26  rearward of the notch  28  is less than the height H 2  at the notch  28 , (i.e., at a second peak P 2  formed by the meeting of the rearward face  32  with the upper periphery  27 . The heights H 1 , H 2  are measured from the bottom of the notch  28  at the base  34  to the respective peaks P 1 , P 2 . In the embodiment shown, the heights H 1  and H 2  are equal. The side wall  26  tapers in height from the first peak P 1  in a forward direction (i.e., generally toward the foremost extent  25 ), and tapers in height from the second peak P 2  in a rearward direction (i.e., generally toward the rearmost extent  29 ). The greater height at the notch  28  enables the forward face  30  and the rearward face  32  to have a greater length, spreading the compressive forces CF 1  across the greater length of the faces  30 ,  32  and associated greater area of the flanges  40 ,  42 . 
     As best shown in  FIG. 4 , the ground-facing surface  21  of the sole plate  12  includes a flex groove  60  that extends generally transversely in the ground-facing surface  21  toward the first notch  28 . In the embodiment shown, the flex groove  60  extends from the lateral side  22  across the longitudinal midline LM and ends just before the rounded base  34 . A centerline  62  of the flex groove  60  is parallel with a center axis  64  of the notch  28  (i.e., a center axis of the rounded base  34 ). The flex groove  60  is a recess in the ground-facing surface  21 . The flex groove  60  and the notch  28  both increase flexibility and decrease bending stiffness of the forefoot portion  14  during dorsiflexion at flex angles less than the first predetermined flex angle A 1  (i.e., when the notch  28  is open) relative to a sole plate without the groove  60  and without the notch  28  in the side wall  26 . 
     Traction elements  69  are shown in phantom in  FIG. 2 . The traction elements  69  may be integrally formed as part of the sole plate  12  (e.g., if the sole plate is an outsole or a unisole plate), may be attached to the sole plate  12 , or may be formed with or attached to another plate underlying the sole plate  12 , such as if the sole plate  12  is an inner board plate and the sole structure  10  includes an underlying outsole. For example, the traction elements  69  may be integrally formed cleats. In other embodiments, the traction elements may be, for example, removable spikes. The traction elements  69  protrude below the ground-facing surface  21  of the sole plate  12 . Direct ground reaction forces on the sole plate  12  that could affect opening and closing of notch  28  are thus minimized. In other embodiments, however, the sole structure  10  may have no traction elements  69 , the ground-facing surface  21  may be the ground-contact surface, or other plates or components may underlie the sole plate  12 . 
       FIGS. 8-13  show an alternative embodiment of a sole structure  110 . The sole structure  110  is alike in many aspects to the sole structure  10  of  FIG. 1 , and like reference numbers are used to denote like features. The sole structure  110  has a sole plate  112  that may be an inner board plate, an outsole plate, a midsole plate, combinations thereof, or a unisole plate. The sole plate  112  has two notches  128  in a medial side wall  126 , and two notches  128  in a lateral side wall  148 . In other words, the medial side wall  126  has a first notch (the more rearward notch  128 ) and a second notch (the more forward notch  128 ) spaced apart from the first notch  128 , and the lateral side wall  148  has two notches  128  spaced apart from one another. The notches  128  are in the forefoot portion  14  of the sole plate  112 . The side wall  126  forms a tab  133  between the spaced notches  128 , and the side wall  148  also forms a tab  133  between the spaced notches  128 . The tab  133  and notches  128  are positioned to be directly laterally outward of a wearer&#39;s metatarsal-phalangeal joints based on population averages for the particular size of footwear. 
     Each notch  128  extends downward toward the foot-facing surface  120  from an upper periphery  127  of the side walls  126 ,  148 . The notches  128  are configured to be open when the forefoot portion  14  of the sole plate  112  is dorsiflexed in the first portion of a flexion range FR 1  and closed when the forefoot portion  14  of the sole plate  112  is dorsiflexed in a second portion of the flexion range FR 2  greater than the first portion FR 1 . The first portion of the flexion range FR 1 , the second portion of the flexion range FR 2 , and the predetermined flex angle A 1  may be the same as those illustrated in the plot of  FIG. 7 , or may have different numerical values. For example, the predetermined flex angle is the sum of the angles formed between the forward face  130  and the rearward face  132  of the notches  128  in the medial side wall  126 , which are configured to be identical to one another and to the angles between the identical forward faces  130  and rearward faces  132  of the notches  128  in the lateral side wall  148 . If the first predetermined flex angle A 1  of the sole plate  12  has the same numerical value as that of the sole plate  112 , then the angle formed between the faces  30 ,  32  of the sole plate  12  would be equal to the sum of the angles between the faces  130 ,  132  on the medial side wall  126  of the sole plate  112 . If the sole plate  112  is configured so that the sum of the angles of the notches  128  on the medial side wall  126  (i.e., between the forward face  130  and the rearward face  132  of each notch  128  on the medial side wall  126 ) is not the same as the sum of the angles of the notches on the lateral side wall  148  (i.e., between the forward face  130  and the rearward face  132  of each notch  128  on the lateral side wall  148 ), then whichever sum is lower determines the first predetermined flex angle, as those notches would close first. 
     With reference to  FIG. 9 , the forward faces  130  incline in a forward direction, and at least a portion of the rearward faces  132  incline a rearward direction. The forward face  130  and the rearward face  132  of each notch  128  are non-parallel and spaced apart from one another when the sole structure  110  is in an unflexed, relaxed state, as shown in  FIG. 9 . The forward face  130  and the rearward face  132  of each notch  128  are parallel and in contact with one another when the sole structure  110  is dorsiflexed (i.e., flexed in the longitudinal direction) to at least the first predetermined flex angle A 1 , as illustrated in  FIG. 13 . A rounded base  134  connects the forward face  130  and the rearward face  132  at each notch  128 . The rounded base  134  is configured to remain open both when the notches  128  are open ( FIG. 9 ), and when the notches  128  close during dorsiflexion of the forefoot portion  14  as described herein (i.e., when the forward face  130  and the rearward face  132  contact each other, as shown in  FIG. 13 ). 
       FIG. 11  shows that the ground-facing surface  121  opposite to the foot-facing surface  120  does not include the flex groove  60  of  FIG. 4 . Alternatively, one or more flex grooves similar to flex groove  60  could be included on the ground-facing surface  121 . 
     Similar to the sole plate  12 , flanges  140 , 142  extend along the respective forward and rearward faces  130 ,  132  and are thicker than the adjacent side wall  126  or  148 , respectively. The flanges  140 ,  142  are shown in  FIG. 10  with a thickness T 1  that is greater than a thickness T 2  of the adjacent portion of the side wall  126 . On both the side wall  126  and the side wall  148 , the thickness of the upper periphery  127  along the tab  133  is also the same as the thickness T 2 , as best shown in  FIG. 8 . 
     The height of the side wall  126  and  148  at the tab  133 , at the forward face  130  of the forward notch  128 , and at the rearward face  132  of the rearward notch  128  on both side walls  126 ,  148  also promotes the function of the notches  128 . The height of the forefoot portion  14  of the side wall  126  forward of the forward notch  128  is less than the height H 1  at the notch  128 , which is at a first peak P 1  formed by the meeting of the forward face  130  with the upper periphery  127 . The height of the forefoot portion  14  of the side wall  126  rearward of the notch  128  is less than the height H 2  at the notch  128 , which is at a second peak P 2  formed by the meeting of the rearward face  132  with the upper periphery  127 . The heights H 1 , H 2  are measured from the bottom of the notch  128  at the base  134  to the respective peaks P 1 , P 2 . In the embodiment shown, the heights H 1  and H 2  are equal, and the tab  133  has the same height H 1 . The side wall  126  tapers in height from the first peak P 1  in a forward direction, and tapers in height from the second peak P 2  in a rearward direction. In the embodiment shown, the side wall  148  is configured with the same heights and peaks as side wall  126 . Alternatively, the heights and peaks of the side wall  148  could be different than those of the side wall  126 . 
     “A,” “an,” “the,” “at least one,” and “one or more” are used interchangeably to indicate that at least one of the items is present. A plurality of such items may be present unless the context clearly indicates otherwise. All numerical values of parameters (e.g., of quantities or conditions) in this specification, unless otherwise indicated expressly or clearly in view of the context, including the appended claims, are to be understood as being modified in all instances by the term “about” whether or not “about” actually appears before the numerical value. “About” indicates that the stated numerical value allows some slight imprecision (with some approach to exactness in the value; approximately or reasonably close to the value; nearly). If the imprecision provided by “about” is not otherwise understood in the art with this ordinary meaning, then “about” as used herein indicates at least variations that may arise from ordinary methods of measuring and using such parameters. In addition, a disclosure of a range is to be understood as specifically disclosing all values and further divided ranges within the range. All references referred to are incorporated herein in their entirety. 
     The terms “comprising,” “including,” and “having” are inclusive and therefore specify the presence of stated features, steps, operations, elements, or components, but do not preclude the presence or addition of one or more other features, steps, operations, elements, or components. Orders of steps, processes, and operations may be altered when possible, and additional or alternative steps may be employed. As used in this specification, the term “or” includes any one and all combinations of the associated listed items. The term “any of” is understood to include any possible combination of referenced items, including “any one of” the referenced items. The term “any of” is understood to include any possible combination of referenced claims of the appended claims, including “any one of” the referenced claims. 
     Those having ordinary skill in the art will recognize that terms such as “above,” “below,” “upward,” “downward,” “top,” “bottom,” etc., are used descriptively relative to the figures, and do not represent limitations on the scope of the invention, as defined by the claims. 
     While several modes for carrying out the many aspects of the present teachings have been described in detail, those familiar with the art to which these teachings relate will recognize various alternative aspects for practicing the present teachings that are within the scope of the appended claims. It is intended that all matter contained in the above description or shown in the accompanying drawings shall be interpreted as illustrative only and not as limiting.