Abstract:
A self-transforming structure is formed from a flexible, fibrous composite having a weave pattern of fibers woven at intersecting angles, the weave pattern having a boundary and one or more axes for the fibers, and an added material coupled to the flexible, fibrous composite to form a structure, wherein the flexible, fibrous composite and the added material have different expansion or contraction rates in response to an external stimulus to cause the structure to self-transform, and wherein the added material has a grain pattern oriented relative the weave pattern of the flexible, fibrous composite. Applications of the self-transforming structures include aviation, automotive, apparel/footwear, furniture, and building materials. One particular example is for providing adaptive control of fluid flow, such as in a jet engine air inlet.

Description:
RELATED APPLICATION(S) 
       [0001]    This application claims the benefit of U.S. Provisional Application No. 62/061,197, filed on Oct. 8, 2014. The entire teachings of the above application are incorporated herein by reference. 
     
    
     BACKGROUND OF THE INVENTION 
       [0002]    Additive manufacturing, sometimes referred to as “3D printing,” permits the precise application of materials onto substrates. Recent advances in 3D printing have enabled the fabrication of printed objects encoded with predicted shape change. These objects can transform over time from a first, printed shape to a second, predetermined shape. 
       SUMMARY OF THE INVENTION 
       [0003]    Described herein is a self-transforming structure. The self-transforming structure includes a flexible, fibrous composite having a boundary and fibers along one or more axes that form a weave pattern, and an added material having a grain pattern. The added material can be coupled to the flexible, fibrous composite to form a structure. The flexible, fibrous composite and the added material have different expansion or contraction rates in response to an external stimulus to cause the structure to self-transform. The grain pattern of the added material can be oriented relative the weave pattern of the flexible, fibrous composite to cause a predictable self-transformation of the structure responsive to the external stimulus. The flexible, fibrous composite can be carbon fiber, glass fiber, basalt fiber, liquid crystal polymers, and hybrids thereof. 
         [0004]    The weave pattern of the flexible, fibrous composite can be biaxial. The grain pattern of the added material can be orthogonal, oriented at a 45° angle, or oriented at any other angle to an axis of a fiber of the flexible, fibrous composite. The grain pattern of the added material can be 45° to an axis of a fiber of the flexible, fibrous composite. The grain of the added material can be oriented at a 45° angle to a boundary of the flexible, fibrous composite. The grain of the added material can be orthogonal to a boundary of the flexible, fibrous composite. The length of the boundary of the added material can be shorter than the length of the boundary of the flexible, fibrous composite. The length of the boundary of the added material can be the same as the length of the boundary of the flexible, fibrous composite. The fibers of the flexible, fibrous added material can be oriented at 45° angles relative to the boundary of the flexible, fibrous composite. The fibers of the flexible, fibrous added material can be orthogonal to the boundary of the flexible, fibrous composite. The flexible, fibrous composite can be square, rectangular, round, or an arbitrary shape. The flexible, fibrous composite can be rectangular. 
         [0005]    In one embodiment having a biaxial, flexible fibrous composite, a) the grain of the added material can be orthogonal to an axis of a fiber of the flexible, fibrous composite; b) the grain of the added material can be oriented at 45° relative to the boundary of the flexible, fibrous composite; c) the length of the boundary of the added material can be shorter than the length of the boundary of the flexible, fibrous composite; and d) the fibers of the flexible, fibrous composite can be oriented at 45° relative to the boundary of the flexible, fibrous composite. 
         [0006]    In another embodiment having a biaxial, flexible fibrous composite, a) the grain of the added material can be orthogonal to an axis of a fiber of the flexible, fibrous composite; b) the grain of the added material can be oriented at 45° relative to the boundary of the flexible, fibrous composite; c) the length of the boundary of the added material can be the same as the length of the boundary of the flexible, fibrous composite; and d) the fibers of the flexible, fibrous composite are oriented at 45° relative to the boundary of the flexible, fibrous composite. 
         [0007]    In another embodiment having a biaxial, flexible fibrous composite, a) the grain of the added material can be orthogonal relative to an axis of a fiber of the flexible, fibrous composite; b) the grain of the added material can be orthogonal relative to the boundary of the flexible, fibrous composite; c) the length of the boundary of the added material can be shorter than the length of the boundary of the flexible, fibrous composite; and d) the fibers of the flexible, fibrous composite are orthogonal relative to the boundary of the flexible, fibrous composite. 
         [0008]    In another embodiment having a biaxial, flexible fibrous composite, a) the grain of the added material can be oriented at a 45° angle relative to an axis of a fiber of the flexible, fibrous composite; b) the grain of the added material can be orthogonal relative to the boundary of the flexible, fibrous composite; c) the length of the boundary of the added material can be the same length as the boundary of the flexible, fibrous composite; and d) the fibers of the flexible, fibrous composite are oriented at a 45° angle relative to the boundary of the flexible, fibrous composite. In some instances, parallel grains of the added material can be on opposite sides of the flexible, fibrous composite. 
         [0009]    In another embodiment having a biaxial, flexible fibrous composite, a) the grain of the added material can be orthogonal to an axis of a fiber of the flexible, fibrous composite; b) the grain of the added material can be oriented at 45° relative to the boundary of the flexible, fibrous composite; c) the length of the boundary of the added material can be the same as the length of the boundary of the flexible, fibrous composite; and d) the fibers of the flexible, fibrous composite are oriented at 45° relative to the boundary of the flexible, fibrous composite. Additionally, the added material can provide equal forces in two directions, thereby providing bi-stability. 
         [0010]    The weave pattern of the flexible, fibrous composite can be triaxial. The grain of the added material can be orthogonal to an axis of a fiber of the flexible, fibrous composite. The grain of the added material can be oriented at an angle of 0°, 60°, or 120° relative to the boundary of the flexible, fibrous composite. The length of the boundary of the added material can be the same length as the boundary of the flexible, fibrous composite. The fibers of the flexible, fibrous composite are oriented at 60° and 120° angles relative to the boundary of the flexible, fibrous composite. 
         [0011]    In one embodiment having a triaxial, flexible fibrous composite, a) the grain of the added material can be orthogonal to an axis of a fiber of the flexible, fibrous composite; b) the grain of the added material can be oriented at a 0° angle relative to the boundary of the flexible, fibrous composite; c) the length of the boundary of the added material can be the same length as the boundary of the flexible, fibrous composite; and d) the fibers of the flexible, fibrous composite are oriented at 60° and 120° angles relative to the boundary of the flexible, fibrous composite. 
         [0012]    In one embodiment having a triaxial, flexible fibrous composite, a) the grain of the added material can be orthogonal to an axis of a fiber of the flexible, fibrous composite; b) the grain of the added material can be oriented at a 60° angle relative to the boundary of the flexible, fibrous composite; c) the length of the boundary of the added material can be the same length as the boundary of the flexible, fibrous composite; and d) the fibers of the flexible, fibrous composite are oriented at 60° and 120° angles relative to the boundary of the flexible, fibrous composite. 
         [0013]    In one embodiment having a triaxial, flexible fibrous composite, a) the grain of the added material can be orthogonal to an axis of a fiber of the flexible, fibrous composite; b) the grain of the added material can be oriented at a 120° angle relative to the boundary of the flexible, fibrous composite; c) the length of the boundary of the added material can be the same length as the boundary of the flexible, fibrous composite; and d) the fibers of the flexible, fibrous composite are oriented at 60° and 120° angles relative to the boundary of the flexible, fibrous composite. 
         [0014]    The weave pattern of the flexible, fibrous composite can be uniaxial. The grain of the added material can be orthogonal to an axis of a fiber of the flexible, fibrous composite. The grain of the added material can be oriented at an angle of 0°, orthogonal, or 45° relative to the boundary of the flexible, fibrous composite. The length of the boundary of the added material can be the same length as the boundary of the flexible, fibrous composite. The fibers of the flexible, fibrous composite can be orthogonal relative to the boundary of the flexible, fibrous composite. 
         [0015]    In one embodiment having a uniaxial, flexible fibrous composite, a) the grain of the added material can be orthogonal to an axis of a fiber of the flexible, fibrous composite; b) the grain of the added material can be oriented at a 0° angle relative to the boundary of the flexible, fibrous composite; c) the length of the boundary of the added material can be the same length as the boundary of the flexible, fibrous composite; and d) the fibers of the flexible, fibrous composite can be orthogonal to the boundary of the flexible, fibrous composite. 
         [0016]    In one embodiment having a uniaxial, flexible fibrous composite, a) the grain of the added material can be orthogonal to an axis of a fiber of the flexible, fibrous composite; b) the grain of the added material can be orthogonal to the boundary of the flexible, fibrous composite; c) the length of the boundary of the added material can be the same length as the boundary of the flexible, fibrous composite; and d) the fibers of the flexible, fibrous composite can be orthogonal to the boundary of the flexible, fibrous composite. 
         [0017]    In one embodiment having a uniaxial, flexible fibrous composite, a) the grain of the added material can be orthogonal to an axis of a fiber of the flexible, fibrous composite; b) the grain of the added material can be oriented at a 45° angle relative to the boundary of the flexible, fibrous composite; c) the length of the boundary of the added material can be the same length as the boundary of the flexible, fibrous composite; and d) the fibers of the flexible, fibrous composite can be orthogonal to the boundary of the flexible, fibrous composite. 
         [0018]    The external stimulus can be exposure to a temperature change. In some instances, exposure to a temperature change can be caused by a laser, infrared light, or electrical resistive heating. The external stimulus can be exposure to water or removal of exposure to water. 
         [0019]    Described herein is a method of making a self-transforming structure. The method can include coupling an added material to a flexible, fibrous composite to form a structure. The flexible, fibrous composite can have a boundary and fibers along axes that form a weave pattern. The flexible, fibrous composite and the added material can have different expansion or contraction rates in response to an external stimulus to cause the structure to self-transform. The added material can have a grain pattern oriented relative the weave pattern of the flexible, fibrous composite. Coupling the added material to the flexible, fibrous composite can include printing the added material onto the flexible, fibrous composite by additive manufacturing. Coupling the added material to the flexible, fibrous composite can include laminating the added material onto the flexible, fibrous composite. 
         [0020]    The methods and resulting products described herein provide numerous advantages compared to prior 3D printed structures. Flexible, fibrous composite composites have an ordered structure that provides strength and elasticity, which provide benefits in self-transforming structures. The self-transforming structure can be packaged in a flat configuration, and later transformed into a three-dimensional structure at a later time or at a different location. 
         [0021]    The self-transforming structures described herein have applications in numerous industries, including aviation, automotive, apparel/footwear, furniture, and building materials. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0022]    The foregoing will be apparent from the following more particular description of example embodiments of the invention, as illustrated in the accompanying drawings in which like reference characters refer to the same parts throughout the different views. The drawings are not necessarily to scale, emphasis instead being placed upon illustrating embodiments of the present invention. 
           [0023]      FIG. 1  is an illustration of an embodiment showing self-transformation angles. The angle of self-transformation (a) varies depending on the width (b) of the added material. 
           [0024]      FIGS. 2A-G  are illustrations of transformations on a biaxial fibrous composite:  2 A) Fold;  2 B) Curve;  2 C) Twist;  2 D) Spiral;  2 E) Wave;  2 F) Bi-stable transformation; G) Fold. 
           [0025]      FIGS. 3A-C  are illustrations of transformation on a triaxial fibrous composite:  3 A) Curve;  3 B) Curve;  3 C) Curve. 
           [0026]      FIGS. 4A-C  are illustrations of transformations on a uniaxial fibrous composite:  4 A) Curve;  4 B) Curve;  4 C) Bi-stable transformation. 
           [0027]      FIG. 5  is an annotated photograph of an experimental setup for making a self-transforming structure. 
           [0028]      FIGS. 6A-C  are photographs of observed transformation for one inch, two inch, and three inch nylon strips laminated onto a four inch-by-four inch flexible carbon fiber sample at 280° F. for 300 seconds. 
           [0029]      FIGS. 7A-C  are photographs of observed transformation for one inch, two inch, and three inch nylon strips laminated onto a four inch-by-four inch flexible carbon fiber sample at 400° F. for 300 seconds. 
           [0030]      FIGS. 8A and 8B  are illustrations showing nylon coupled to a carbon fiber.  FIG. 8A  shows nylon adjacent to carbon fiber prior to lamination.  FIG. 8B  shows nylon coupled to carbon fiber after lamination and the shape transformation that has occurred. 
           [0031]      FIG. 9  is an annotated photograph of an experimental setup for observing temperature-dependent self-transformation. 
           [0032]      FIGS. 10A-I  are a series of photographs showing the transformation over time (mm:ss). A) Time=0:00, Temperature=83° F.; B) Time=1:00, Temperature=119° F.; C) Time=2:00, Temperature=150° F.; D) Time=3:00, Temperature=187° F.; E) Time=4:00, Temperature=221° F.; F) Time=5:00, Temperature=240° F.; G) Time=7:00, Temperature=246° F.; H) Time=10:12, Temperature=261° F.; I) Time=10:32, Temperature=273° F. 
           [0033]      FIG. 11  is a graph showing the change in the angle of self-transformation as temperature increases. 
           [0034]      FIG. 12A  is a series of time-lapsed photographs showing a twisting transformation.  FIG. 12B  shows superimposed photos of a time-lapsed twisting transformation. 
           [0035]      FIG. 13A  is a series of time-lapsed photographs showing a folding transformation.  FIG. 13B  shows superimposed photos of a time-lapsed folding transformation. 
           [0036]      FIG. 14  is a time-lapse photograph showing the self-transformation of programmable carbon fiber within a jet engine air inlet. The dynamic carbon fiber regulates the amount of airflow for active engine cooling. 
           [0037]      FIG. 15  is an example of a triaxial weave with 22 mm wide strips of fiber woven in 0 degree, +60 degree and −60 degree orientation. The laminated sheet on top of the weave can be placed in-line with the fiber orientation at 0°, 120°, or 60° to achieve a 1-curve, 2-curve, or 3-curve type behavior, respectively. 
           [0038]      FIG. 16  is an example of a uniaxial weave orientation. The print pattern on top of the weave can be placed in-line with the fiber orientation or at 90° to achieve a 1-fold or 2-fold type behavior, respectively. 
           [0039]      FIGS. 17A and 17B  are photographs of self-transforming structures made using a triaxial flexible, fibrous composite. The grain direction of the added material is indicated with arrows and is patterned as illustrated in  FIG. 3A . 
           [0040]      FIGS. 18A-D  are photographs of self-transforming structures made using a biaxial flexible, fibrous composite. A) Curve; B) Fold; C) Wave; D) Spiral. 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0041]    A description of example embodiments of the invention follows. 
         [0042]    Self-transforming structures according to example embodiments can be made according to the processes described herein. In general, a flexible, fibrous composite provides a substrate for an added material. Together, the flexible, fibrous composite and the added material form a combined structure. The flexible, fibrous composite and the added material typically have different expansion or contraction rates in response to an external stimulus, which causes the combined structure to self-transform upon exposure to the external stimulus. 
         [0043]    As used herein, the term “weave pattern” refers to an ordered arrangement of fibers, which can be intersecting or non-intersecting. Examples of intersecting weave patterns include biaxial and triaxial weave patterns. An example of a nonintersecting weave pattern is a uniaxial weave pattern. 
         [0044]    As used herein, a “flexible, fibrous composite” is a composite that provides sufficient ability to bend without delaminating or detaching from the added material coupled to it. Thus, when the self-transforming structure is exposed to an external stimulus, thereby causing the flexible, fibrous composite and the added material to have different expansion or contraction rates, the added material remains laminated or coupled to the flexible, fibrous composite, thereby causing a transformation in shape. Methods of making a flexible, fibrous composite are described in U.S. Patent Publication No. 2015/0174885. 
         [0045]    Typically, a flexible, fibrous composite has at least one boundary, and often times more than one boundary. For example, a circular flexible, fibrous composite, as well as flexible fibrous composites having complex curved shapes, have a single boundary. A triangular flexible, fibrous composite has three boundaries. While many of the embodiments described herein are square or rectangular, the principles described are equally applicable to flexible, fibrous composites having other geometric shapes, as well as to flexible, fibrous composites having complex shapes. In these instances, descriptions of orientations relative to a boundary refer to the orientation at any position along a boundary. 
       Biaxial Weave Patterns and Oriented, Added Material 
       [0046]    Typically, the flexible, fibrous composite is formed of woven fibers. A variety of weave patterns are known in the art. The weave patterns described herein are generally referred to as uniaxial, biaxial, and triaxial. The added material is typically applied to the flexible, fibrous composite so that grains of the added material are patterned relative to the weave pattern. 
         [0047]      FIG. 1  is an illustration of one embodiment of a self-transforming structure  100 . The flexible, fibrous composite  110  forms a substrate for grains  130  of the added material. The flexible fibrous composite is formed of intersecting fibers  115   a  and  115   b . In this particular embodiment, the fibers intersect at 90° angles, though other angles of intersection are possible. In the particular example, the grains  130  of the added material are substantially parallel with the fibers  115   a  of the flexible, fibrous composite  110 . In this embodiment, parallel grains of the added material are aligned with and at least partially overlay fibers  115   a  of the flexible, fibrous composite. 
         [0048]    Unique orientations of the grain of the added material relative to the axis of the flexible, fibrous substrate can yield different transformations upon exposure to an external stimulus. Conceptually, four features define the relationship between a biaxial flexible, fibrous composite and the added material. First is the relationship of the grain pattern of the added material to an axis of a fiber of the flexible, fibrous composite. The grain pattern of the added material can be orthogonal to an axis of a fiber of the flexible fibrous composite, or it can be patterned at an angle, such as a 45° angle, relative to an axis of the flexible fibrous composite. Second is the orientation of the grain of the added material relative to a boundary of the flexible, fibrous composite. The grain of the added material can be orthogonal at a boundary, or it can be patterned at an angle, such as a 45° angle, relative to a boundary of the flexible, fibrous composite. Third is the length of a boundary of the added material in relation to the length of a boundary of the flexible, fibrous composite. The length of a boundary of the added material can be the same length as the length of a boundary of the flexible, fibrous composite. Alternatively, the length of a boundary of the added material can be shorter than a boundary of the flexible, fibrous composite. Fourth is the orientation of the fibers of the flexible, fibrous composite relative to a boundary of the flexible, fibrous composite. The fibers of the flexible, fibrous composite can be orthogonal to a boundary of the flexible, fibrous composite. Alternatively, the fibers of the flexible, fibrous composite can be angled, such as at a 45° angle, relative to a boundary of the flexible, fibrous composite. As another optional fifth condition, the added material can be printed on opposing sides of the flexible, fibrous composite, one particular example of which is illustrated in  FIG. 2E . 
         [0049]      FIGS. 2A-F  show six different types of transformations that can be created. In general,  FIGS. 2A-F  show the relative orientation of a biaxial flexible, fibrous composite and the added material that is coupled to it. The relationship between the four features described in the preceding paragraph and the embodiments of  FIGS. 2A-F  are summarized in Table 1. The notation underneath the images in the figures indicates the orientation of the fibers of the flexible fibrous composite (left) and the grains of the added material (middle) in degrees (e.g., in  FIG. 2A , the orientation of the fibers is at a 45 degree angle relative to the horizon, and the orientation of the grains is also at a 45 degree angle relative to the horizon). 
         [0000]    
       
         
               
             
               
               
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 Features of biaxial flexible, fibrous composite and added material illustrated in FIGS. 2A-F. 
               
             
          
           
               
                   
                   
                   
                 3. Length of a 
                   
               
               
                   
                 1. Relationship of 
                 2. Orientation of 
                 boundary of the 
                 4. Orientation of 
               
               
                   
                 the grain pattern 
                 the grain of the 
                 added material 
                 the fibers of the 
               
               
                   
                 of added material 
                 added material 
                 in relation to 
                 flexible, fibrous 
               
               
                   
                 to an axis of a 
                 relative to a 
                 the length of a 
                 composite relative 
               
               
                   
                 fiber of the 
                 boundary of the 
                 boundary of the 
                 to a boundary of the 
               
               
                 FIG. and 
                 flexible, fibrous 
                 flexible, fibrous 
                 flexible, fibrous 
                 flexible, fibrous 
               
               
                 Transformation 
                 composite 
                 composite 
                 composite 
                 composite 
               
               
                   
               
               
                 2A: Fold 
                 Orthogonal 
                 45° to one another 
                 Shorter 
                 45° to one another 
               
               
                 2B: Curve 
                 Orthogonal 
                 45° to one another 
                 Same length 
                 45° to one another 
               
               
                 2C: Twist 
                 Orthogonal 
                 Orthogonal 
                 Shorter 
                 Orthogonal 
               
               
                 2D: Spiral 
                 45° to one another 
                 Orthogonal 
                 Same length 
                 45° to one another 
               
               
                 2E: Wave 
                 Orthogonal 
                 45° to one another 
                 Shorter 
                 45° to one another 
               
               
                 2F: Bi-stable 
                 Orthogonal 
                 45° to one another 
                 Same length 
                 45° to one another 
               
               
                 2G: Fold 
                 Orthogonal 
                 45° to two 
                 Shorter 
                 45° to one another 
               
               
                   
                   
                 boundaries 
               
               
                   
               
             
          
         
       
     
         [0050]      FIG. 2A  shows a fold transformation. Parallel grains  130  of the added material are orthogonal to an axis of a fiber  115   a  of the flexible, fibrous composite, and coaxial with an axis of the other fiber  115   b . The grain  130  of the added material is oriented at a 45° angle relative to its own boundary  135  and relative to the boundary  120  of the flexible, fibrous composite. The length of a boundary  135  of the added material  130  is shorter than the length of a boundary  120  of the flexible, fibrous composite. The fibers  115   a  and  115   b  of the flexible, fibrous composite are oriented at a 45° angle relative to its own boundary  120 . In this particular example, the flexible, fibrous composite  110  is square; however, it need not be square in order to achieve a folding transformation. 
         [0051]      FIG. 2B  shows a curve transformation. Parallel grains  130  of the added material are orthogonal to an axis of a fiber  115   a  of the flexible, fibrous composite, and coaxial with an axis of the other fiber  115   b . The grain  130  of the added material is oriented at a 45° angle relative to its own boundary  135  and relative to the boundary  120  of the flexible, fibrous composite. The length of a boundary  135  of the added material  130  is the same, or substantially the same, as the length of a boundary  120  of the flexible, fibrous composite. The fibers  115   a  and  115   b  of the flexible, fibrous composite are oriented at a 45° angle relative to its own boundary  120 . In this particular example, the flexible, fibrous composite  110  is square; however, it need not be square in order to achieve a folding transformation. Unlike the fold shown in  FIG. 2A , a curve can occur when the added material covers all, or substantially all, of a surface of the flexible, fibrous composite. 
         [0052]      FIG. 2C  shows a twist transformation. Parallel grains  130  of the added material are orthogonal to an axis of a fiber  115   a  of the flexible, fibrous composite, and coaxial with an axis of the other fiber  115   b . The grain  130  of the added material is oriented orthogonally relative to its own boundary  135  and relative to the boundary  120  of the flexible, fibrous composite. The length of a boundary  135  of the added material  130  is shorter than the length of a boundary  120  of the flexible, fibrous composite. The fibers  115   a  and  115   b  of the flexible, fibrous composite are oriented orthogonally relative to its own boundary  120 . The flexible, fibrous composite  110  is square; however, it need not be square in order to achieve a twist transformation. 
         [0053]      FIG. 2D  shows a spiral transformation. Parallel grains  130  of the added material are oriented at 45° angles relative to both axes of fiber  115   a  and  115   b  of the flexible, fibrous composite. The grain  130  of the added material is oriented orthogonally relative to its own boundary  135  and relative to the boundary  120  of the flexible, fibrous composite. The length of a boundary  135  of the added material  130  is the same as, or substantially similar to, the length of a boundary  120  of the flexible, fibrous composite. The fibers  115   a  and  115   b  of the flexible, fibrous composite are oriented at 45° angles relative to its own boundary  120 . Unlike the twist shown in  FIG. 2C , a spiral can occur when the added material covers all, or substantially all, of a surface of the flexible, fibrous composite. 
         [0054]      FIG. 2E  shows a wave transformation. Parallel grains  130  of the added material are orthogonal to an axis of a fiber  115   a  of the flexible, fibrous composite, and coaxial with an axis of the other fiber  115   b . The grain  130  of the added material is oriented at a 45° angle relative to its own boundary  135  and relative to the boundary  120  of the flexible, fibrous composite. The length of a boundary  135  of the added material  130  is shorter than the length of a boundary  120  of the flexible, fibrous composite. The fibers  115   a  and  115   b  of the flexible, fibrous composite are oriented at a 45° angle relative to its own boundary  120 . The flexible, fibrous composite  110  is square; however, it need not be square in order to achieve a folding transformation. Conceptually,  FIG. 2E  builds upon  FIG. 2A  because it can be used to create two transformations like  FIG. 2A , but on opposite sides of a flexible, fibrous composite. Although not illustrated, the added material can be oriented in different patterns on the first and sides of the flexible, fibrous composite, thereby creating even more unique structures. 
         [0055]      FIG. 2F  shows a bi-stable configuration. Parallel grains  130  of the added material are orthogonal to an axis of a fiber  115   a  of the flexible, fibrous composite, and coaxial with an axis of the other fiber  115   b . The grain  130  of the added material is oriented at a 45° angle relative to its own boundary  135  and relative to the boundary  120  of the flexible, fibrous composite. The length of a boundary  135  of the added material  130  is the same, or substantially the same, as the length of a boundary  120  of the flexible, fibrous composite. The fibers  115   a  and  115   b  of the flexible, fibrous composite are oriented at a 45° angle relative to its own boundary  120 . In this particular example, the flexible, fibrous composite  110  is square; however, it need not be square in order to achieve a folding transformation. The grains  130  are applied so that they create equal forces in both directions, leading to a configuration that is bi-stable. The flexible, fibrous composite  110  is square; however, it need not be square in order to achieve a folding transformation. The bi-stable configuration is thus a subset of the curve configuration illustrated in  FIG. 2B . For example, a curve can be created that curls from tip to tip, rather than edge to edge like in  2 B. The configuration can be bi-stable if the flexible, fibrous composite is square, which results in equal forces in opposite directions. 
         [0056]      FIG. 2G  shows a curve transformation. Parallel grains  130  of the added material are orthogonal to an axis of the fiber  115   a  of the flexible, flexible, fibrous composite, and coaxial with an axis of the other fiber  115   b . The grain  130  of the added material is oriented at a 45° angle relative to its own boundary  135  and relative to the boundary  120  of the flexible, fibrous composite. The length of a boundary  135  of the added material  130  is shorter than the length of two different boundaries  120  of the flexible, fibrous composite. The fibers  115   a  and  115   b  of the flexible, fibrous composite are oriented at a 45° angle relative to its own boundary  120 . In this particular example, the added material is applied across a diagonal of the flexible, fibrous composite  110 , yielding the illustrated transformation. 
       Triaxial Weave Patterns and Oriented, Added Material 
       [0057]    Unique orientations of the grain of the added material relative to the axis of the flexible, fibrous substrate can yield different transformation upon exposure to an external stimulus. Conceptually, two features define the relationship between a biaxial flexible, fibrous composite and the added material. First is the relationship of the grain pattern of the added material to an axis of a fiber of the flexible, fibrous composite. The triaxial weave pattern has fibers along three axes. Typically, the grain pattern of the added material will be coaxial with one of the axes, though it can be at an angle as well. Second is the orientation of the grain of the added material relative to a boundary of the flexible, fibrous composite. When the grain pattern of the added material is coaxial with one of the axes, the orientation can be 0°, 60°, or 120° relative to a boundary of the flexible, fibrous composite. Third is the length of a boundary of the added material in relation to the length of a boundary of the flexible, fibrous composite. The length of a boundary of the added material can be the same length as the length of a boundary of the flexible, fibrous composite. Alternatively, the length of a boundary of the added material can be shorter than a boundary condition of the flexible, fibrous composite. Fourth is the orientation of the fibers of the flexible, fibrous composite relative to a boundary of the flexible, fibrous composite. Typically, the fibers of the flexible, fibrous composite are angled at 60° and 120° relative to a boundary of the flexible, fibrous composite, though other angles are possible as well. As another optional fifth condition, the added material can be printed on opposing sides of the flexible, fibrous composite. 
         [0058]      FIGS. 3A-C  show three different types transformations that can be created. In general,  FIGS. 3A-C  show the relative orientation of a flexible, fibrous composite and the added material that is coupled to it. The relationship between the two features described in the preceding paragraph and the embodiments of  FIGS. 3A-C  are summarized in Table 2. 
         [0000]    
       
         
               
             
               
               
               
               
               
             
           
               
                 TABLE 2 
               
             
             
               
                   
               
               
                 Features of biaxial flexible, fibrous composite and added material illustrated in FIGS. 3A-C. 
               
             
          
           
               
                   
                   
                   
                 3. Length of a 
                   
               
               
                   
                 1. Relationship of 
                 2. Orientation of 
                 boundary of the 
                 4. Orientation of 
               
               
                   
                 the grain pattern 
                 the grain of the 
                 added material 
                 the fibers of the 
               
               
                   
                 of added material 
                 added material 
                 in relation to 
                 flexible, fibrous 
               
               
                   
                 to an axis of a 
                 relative to a 
                 the length of a 
                 composite relative 
               
               
                   
                 fiber of the 
                 boundary of the 
                 boundary of the 
                 to a boundary of the 
               
               
                 FIG. and 
                 flexible, fibrous 
                 flexible, fibrous 
                 flexible, fibrous 
                 flexible, fibrous 
               
               
                 Transformation 
                 composite 
                 composite 
                 composite 
                 composite 
               
               
                   
               
               
                 3A: Curve 
                 Orthogonal 
                 0° to a boundary 
                 Same length 
                 60° and 120° 
               
               
                 3B: Curve 
                 Orthogonal 
                 60° to a boundary 
                 Same length 
                 60° and 120° 
               
               
                 3C: Curve 
                 Orthogonal 
                 120° to a boundary 
                 Same length 
                 60° and 120° 
               
               
                   
               
             
          
         
       
     
         [0059]      FIGS. 3A-C  show flexible fibrous composites having a triaxial weave pattern. In each of  FIGS. 3A-C , the added material  130  is applied along an axis  117   a,b,c  of one of the fibers of the flexible, fibrous composite  110 . Thus, each of the transformations in  FIGS. 3A-C  yields a similar transformation, though along a different axis. 
       Uniaxial Weave Patterns and Oriented, Added Material 
       [0060]    Unique orientations of the grain of the added material relative to the axis of the flexible, fibrous substrate can yield different transformation upon exposure to an external stimulus. Conceptually, two features define the relationship between a biaxial flexible, fibrous composite and the added material. First is the orientation of the fibers of the flexible, fibrous composite to a boundary of the flexible, fibrous composite. Since the uniaxial weave pattern has fibers along one axis, typically the fibers are oriented orthogonally to a boundary of the flexible, fibrous composite. Second is the orientation of the grain of the added material relative to a boundary of the flexible, fibrous composite. The grain can be orthogonal to a boundary of the added material, parallel to a boundary of the added material, or oriented at an angle, such as a 45° angle, relative to a boundary of the added material. Third is the length of a boundary of the added material in relation to the length of a boundary of the flexible, fibrous composite. The length of a boundary of the added material can be the same length as the length of a boundary of the flexible, fibrous composite. Alternatively, the length of a boundary of the added material can be shorter than a boundary condition of the flexible, fibrous composite. Fourth is the orientation of the fibers of the flexible, fibrous composite relative to a boundary of the flexible, fibrous composite. Typically, the fibers of the flexible, fibrous composite are orthogonal to one boundary (and thus parallel to another) of the flexible, fibrous composite, though other angles are possible as well. As another optional fifth condition, the added material can be printed on opposing sides of the flexible, fibrous composite. 
         [0061]      FIGS. 4A-C  show three different types transformations that can be created. In general,  FIGS. 4A-C  show the relative orientation of a flexible, fibrous composite and the added material that is coupled to it. In each of  FIGS. 4A-C , the added material  138  is applied along an axis  118  of the fibers of the flexible, fibrous composite  110 . The relationship between the two features described in the preceding paragraph and the embodiments of  FIGS. 4A-C  are summarized in Table 3. 
         [0000]    
       
         
               
             
               
               
               
               
               
             
           
               
                 TABLE 3 
               
             
             
               
                   
               
               
                 Features of biaxial flexible, fibrous composite 
               
               
                 and added material illustrated in FIGS. 3A-C. 
               
             
          
           
               
                   
                 1. Orientation of 
                   
                 3. Length of a 
                   
               
               
                   
                 the fibers of the 
                 2. Orientation of 
                 boundary of the 
                 4. Orientation of 
               
               
                   
                 flexible, fibrous 
                 the grain of the 
                 added material 
                 the fibers of the 
               
               
                   
                 composite 
                 added material 
                 in relation to 
                 flexible, fibrous 
               
               
                   
                 relative to a 
                 relative to a 
                 the length of a 
                 composite relative 
               
               
                   
                 boundary of the 
                 boundary of a 
                 boundary of the 
                 to a boundary of the 
               
               
                 FIG. and 
                 flexible, fibrous 
                 flexible, fibrous 
                 flexible, fibrous 
                 flexible, fibrous 
               
               
                 Transformation 
                 composite 
                 composite 
                 composite 
                 composite 
               
               
                   
               
               
                 4A: Curve 
                 Orthogonal 
                 0° to a boundary 
                 Same length 
                 Orthogonal 
               
               
                 4B: Curve 
                 Orthogonal 
                 Orthogonal to a 
                 Same length 
                 Orthogonal 
               
               
                   
                   
                 boundary 
               
               
                 4C: Bi-stable 
                 Orthogonal 
                 45° to a boundary 
                 Same length 
                 Orthogonal 
               
               
                   
               
             
          
         
       
     
         [0062]      FIGS. 4A-C  show flexible, fibrous composites having a uniaxial weave pattern. In each of  FIGS. 4A-C , the added material  130  is applied to the flexible, fibrous composite. The flexible, uniaxial fibrous composite has fibers  118  oriented in parallel strips. 
       Flexible, Fibrous Composites 
       [0063]    A variety of composites are suitable for use as a flexible, fibrous composite. One example is carbon fiber. Other examples include glass fiber, basalt fiber, liquid crystal polymers/fibers, and hybrids thereof. In general, the flexible, fibrous composites described herein have different performance characteristics. For example, some are more flexible than others, and some have more tensile strength than others. Generally, the weave patterns of the flexible, fibrous composite remain similar. The amount and rate of transformation can vary depending on the type of materials and the number of fibers. Thus, thickness and width can be adjusted to achieve the proper contractive force to cause a shape change in view of the coefficient of thermal expansion of the flexible, fibrous composite and the added material. The greater the difference in the coefficient of thermal expansion, the greater the transformation effect. Polymer melt shrinkage and changes in the coefficient of thermal expansion can also influence magnitude of the transformation. For example, if the flexible, fibrous composite is a nylon fiber composite, and the added material is nylon, the difference in the coefficient of thermal expansion is very small, and so is the transformation. As another example, a flexible, fibrous composite that is a hybrid of carbon fiber and high molecular weight polypropylene was used as a substrate for nylon as an added material. The resulting product provided a smaller angle of curvature (e.g., a smaller amount of transformation) compared to examples where the flexible, fibrous composite is carbon fiber alone. Thus, the general principles described herein remain applicable, but the magnitude of the transformation can vary depending on the materials chosen. 
       Added Materials 
       [0064]    A variety of materials are suitable for use as an added material. The flexible, fibrous composite and the added materials typically have different rates of expansion and/or contraction in response to an external stimulus. As one particular example, the added material contracts more than the flexible, fibrous composite when cooled. Some examples of added materials include nylon, biaxially-oriented polyethylene terephthalate (BoPET, and available as MYLAR), polypropylene, and hydrogels. 
         [0065]    A useful characteristic of a hydrogel is its percentage of expansion. For example, a hydrogel can expand 150% upon exposure to water. This expansion can cause the flexible, fibrous composite to curl such that the hydrogel is on the outside radius of curvature. Other important characteristics of a hydrogel are whether it is reversible (e.g., whether the hydrogel returns to its original shape), how long it takes to swell and then return to its original shape (e.g., dry out), and whether it deteriorates after repeated use. Examples of suitable swelling hydrogels are well-known in the art. 
         [0066]    Another type of added material that is suitable for use in making a self-transforming structure is a UV-curable polymer. Examples of suitable polymers include those available from commercial 3D printing companies. These UV-curable polymers can be applied by 3D-printing. Typically, they are applied as uncured monomers, which are cured upon exposure to UV light. 
       Methods of Making Self-Transforming Structures 
       [0067]    The added material is applied with its grains in an orientation relative to fibers of the flexible, fibrous composite in a variety of manners. In one embodiment, the added material is applied to the flexible, fibrous composite by additive manufacturing, also referred to as 3D printing. Additive manufacturing is a particularly useful technology because it can be used to apply the added material in a precisely oriented arrangement, thereby allowing the added material to be patterned relative to the weave pattern of the flexible, fibrous composite. For example, nylon can be applied by an additive manufacturing process. Hydrogels are typically applied by either an additive manufacturing or a lamination procedure. In order to apply the added material to the flexible, fibrous composite by 3D printing, a printing pattern for the added material is designed (e.g., the printing patterns illustrated in the figures, such as  FIG. 2A-G ,  3 A-C, or  4 A-C). The carbon fiber is then placed in the printer in the appropriate orientation. If necessary, the printer is calibrated. Printing parameters, such as the height and thickness of the printing, are specified. Finally, printing is commenced. 
         [0068]    In some instances, the added material can be adhered to the flexible, fibrous composite by a lamination procedure, which can be a fast and consistent means for applying the added material to the flexible, fibrous composite. In some of the Examples below, the lamination was performed with a T-shirt press, though other means for lamination are known in the art. In order to apply the added material to the flexible, fibrous composite by lamination, the added material is placed onto the flexible, fibrous composite, and then lamination is commenced. 
         [0069]    Additionally, reversible and non-reversible conditions for forming in a fabrication process versus and active transition for movement in a self-transforming structure can be encoded in the printing pattern. For example, a sheet of flexible, fibrous composite with secondary material can be designed to self-transform into a predicted shape after being subjected to an external stimulus. This eliminates the step of molding, tooling or other manual methods of forming composite structures. 
       External Stimuli 
       [0070]    A variety of different external stimuli can be used to cause shape transformation. Typically, these external stimuli can also cause expansion or contraction in response to temperature changes. For example, lasers can be used to apply localized heating. As another example, an infrared heat lamp can be used to provide heat. Electrical resistive heating can also be used to provide heating, such as through the use of a Nichrome wire or a flexible heat pad. 
         [0071]    As another example, electroactive polymers can be used. Electroactive polymers can exhibit a change in size or shape in response to an electric field. 
         [0072]    As another example, ultraviolet (UV) radiation can be used to cure UV-curable polymers, which typically contact during cross-linking. 
       EXEMPLIFICATION 
     Example 1 
     Width of Added Material and Angle of Self-Transformation 
       [0073]    Nylon 618 was applied to a Carbitex A324 flexible, fibrous composite according to the pattern of  FIG. 2A . 
         [0074]    Table 4 lists measured angles of transformation that were observed using different widths for the Nylon grains. The angles were measured at room temperature. 
         [0000]    
       
         
               
             
               
               
               
               
               
               
             
           
               
                 TABLE 4 
               
             
             
               
                   
               
               
                 Relationship between width (b) of grains of the 
               
               
                 added material and angle of transformation (a). 
               
             
          
           
               
                   
                 Width (b) 
                 3 mm 
                 9 mm 
                 18 mm 
                 21 mm 
               
               
                   
                   
               
               
                   
                 Angle (a) 
                 15.00° 
                 44.33° 
                 63.67° 
                 97.67° 
               
               
                   
                   
               
             
          
         
       
     
         [0075]    As shown in Table 4, applying grains of the Nylon having different widths can result in different angles of transformation upon exposure to an external stimulus. 
       Example 2 
     Lamination Temperature and Grain Width 
       [0076]      FIG. 5  is an annotated photograph of the experimental setup. Three 4″×4″ A324 carbon fiber samples (Carbitex LLC, Kennewick, Wash., USA) were laminated with nylon strips having three different widths. The Carbitex A324 product is biaxial and has fibers that intersect at 90 degree angles. The weave pattern name is a 2×2 twill, where 2×2 refers to two over and two under in both directions of the fiber bundles. Strips one and four: 1 inch wide; strips two and five: 2 inches wide; strips three and six: 3 inches wide. Each of the three strips was applied to the A324 carbon fiber in accordance with the pattern shown in  FIG. 2D . 
         [0077]    Laminating temperatures: 280° F. and 400° F. 
         [0078]    Laminating pressure: one inch nylon strip: 162.5 psi; two inch nylon strip: 81 psi; three inch nylon strip: 54 psi. 
         [0079]    Lamination time: 300 seconds 
         [0080]    The laminating was conducted in a T-shirt press  500  (Stahl&#39;s Hotronix Thermal Transfer Press, Model #STX11) having a heated platen  510 . The T-shirt press was further instrumented in order to accurately apply pressure with an Omega digital read out Model DP25B-S-A and a 0-500 lb LeBow Load cell model number 3132-101. To calculate the pressure, the force of the T-shirt press was divided by the area of the lamination area of the subtracted to be bonded. Release paper  520  is placed on both sides of the carbon fiber  530  and nylon  540  in order to facilitate release from the pressing machine. Silicone  550  was used as a base. 
         [0081]      FIGS. 6A-C  and  7 A-C are photographs showing the results of the experiment.  FIGS. 6A-C  show the transformation of the 1 inch, 2 inch, and 3 inch nylon strips at 280° F.  FIGS. 7A-C  show the transformation of the 1 inch, 2 inch, and 3 inch nylon strips at 400° F.  FIGS. 7A-C  are also referred to as 25% Strip, 50% Strip, and 75% Strip, respectively, which refers to the percentage of the width of the sample having Nylon across it. For a 4″×4″ square, a 1″ wide strip is referred to as 25% Strip; a 2″ wide strip is referred to as 50% Strip; and a 3″ wide strip is referred to as 75% Strip. The results are shown in Table 5: 
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 5 
               
             
             
               
                   
               
               
                 Observed transformation 
               
             
          
           
               
                   
                 Temperature 
                 Strip width 
                 Pressing duration 
                 Curvature 
               
               
                   
                 (° F.) 
                 (inches) 
                 (seconds) 
                 (degrees) 
               
               
                   
                   
               
             
          
           
               
                 Strip 1 
                 280 
                 1 
                 300 
                 28 
               
               
                 Strip 2 
                 280 
                 2 
                 300 
                 53 
               
               
                 Strip 3 
                 280 
                 3 
                 300 
                 66 
               
               
                 Strip 4 
                 400 
                 1 
                 300 
                 41 
               
               
                 Strip 5 
                 400 
                 2 
                 300 
                 63 
               
               
                 Strip 6 
                 400 
                 3 
                 300 
                 101 
               
               
                   
               
             
          
         
       
     
         [0082]    Observations: 1) Lamination pressure impacts nylon wet out to Carbitex A324. As the shear force increases during the lamination process, low lamination pressure or low wet out of the bonded surface can reduce the amount bonded surface area, thereby allowing the lamination to decouple. Thus, sufficient lamination pressure is necessary to ensure adequate bonding between the nylon and carbon fiber. The minimum lamination pressure depends on the viscosity of the added material that is being bonded. As tested, a pressure of 54 psi appears sufficient to ensure appropriate lamination. 2) Angle of curl depends on lamination temperature; angle of curl depends on lamination width. 3) Zero degree angle of curl is equal to the lamination temperature. If the lamination occurs at ambient temperature, the lamination is stable and no curling will occur when the temperature remains at ambient temperature. If the ambient temperature lamination is subsequently heated, the expansion differential will cause a curl. Likewise, when the flexible, fibrous composite is laminated at elevated temperatures, as shown in Table 4, the contraction differential of the flexible, fibrous composite and the added material will cause curling at ambient temperature. Similarly, zero degree curling will be occur at the lamination temperature. For example, if lamination occurs at 280° F., there will be 28 degree curvature at ambient temperature. However, if reheated to 280° F., the angle of curvature will be zero. 
         [0083]    Without wishing to be bound by theory, it is believed that change in length can be modeled according to Formula (I): 
         [0000]      Δ L=α*L   0 *( T−T   0 )  (I)
 
         [0084]    α=coefficient of thermal expansion (CTE) 
         [0085]    L 0 =original length (e.g., of nylon) 
         [0086]    T 0 =initial temperature 
         [0087]    T=temperature 
         [0088]    For nylon, a is between approximately 4×10 −5  and 5.5×10 −5  in/in/° F. 
         [0089]      FIGS. 8A and 8B  are illustrations showing nylon coupled to a carbon fiber.  FIG. 8A  shows nylon adjacent to carbon fiber prior to lamination.  FIG. 8B  shows nylon coupled to carbon fiber after lamination and the shape transformation that has occurred. Table 6 describes calculated changes in Nylon based on the coefficient of thermal expansion a that temperature differential. 
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 6 
               
             
             
               
                   
               
               
                 Calculated changes in length of Nylon based on the coefficient 
               
               
                 of thermal expansion at that temperature differential 
               
             
          
           
               
                 L 0   
                 CTE 
                 T 0   
                 T 
                 L 
               
               
                 (in) 
                 (in/in/° F.) 
                 (° F.) 
                 (° F.) 
                 (in) 
               
               
                   
               
             
          
           
               
                 1 
                 4.00E−05 
                 75 
                 280 
                 0.0082 
               
               
                 2 
                 4.00E−05 
                 75 
                 280 
                 0.0164 
               
               
                 3 
                 4.00E−05 
                 75 
                 280 
                 0.0246 
               
               
                 1 
                 4.00E−05 
                 75 
                 400 
                 0.013 
               
               
                 2 
                 4.00E−05 
                 75 
                 400 
                 0.026 
               
               
                 3 
                 4.00E−05 
                 75 
                 400 
                 0.039 
               
               
                   
               
             
          
         
       
     
       Example 3 
     Self-Transformation in Response to Temperature Change 
       [0090]      FIG. 9  is an annotated photograph of an experimental setup for measuring self-transformation in response to temperature changes. In both  FIG. 9  and  FIGS. 10A-I , nylon was laminated onto carbon fiber according to the pattern illustrated in  FIG. 2D . 
         [0091]    An Oster convection oven  910  (Model No. TSSTTVDGXL) was used to heat the self-transforming structure  920 . An aluminum block  930  was used to hold down one end of the self-transforming structure  920 . A fine wire thermocouple  940  was used to measure temperature, and a protractor  950  was used to measure the angle of transformation. Temperature values were measured during heating to correlate the angle of movement to temperature increase. The results are show in  FIGS. 10A-I , which is a series of time-lapse photographs. The measured values are provided in Table 7, and  FIG. 11  is a graph showing the measured angle vs. temperature change (y=−0.3461x+47.982; R 2 =0.9931). 
         [0000]    
       
         
               
             
               
               
               
               
             
               
               
               
               
             
           
               
                 TABLE 7 
               
             
             
               
                   
               
               
                 Measured angles of transformation 
               
             
          
           
               
                 Time 
                 Temperature 
                 Angle 
                 Corresponding 
               
               
                 (mm:ss) 
                 (° F.) 
                 (°) 
                 FIG. 
               
               
                   
               
             
          
           
               
                 0:00 
                 83 
                 37 
                 10A 
               
               
                 1:00 
                 119 
                 33 
                 10B 
               
               
                 2:00 
                 150 
                 24 
                 10C 
               
               
                 3:00 
                 187 
                 19 
                 10D 
               
               
                 4:00 
                 221 
                 12 
                 10E 
               
               
                 5:00 
                 240 
                 9 
                 10F 
               
               
                 7:00 
                 246 
                 7 
                 10G 
               
               
                 10:12  
                 261 
                 3 
                 10H 
               
               
                 10:32  
                 273 
                 1 
                 10I 
               
               
                   
               
             
          
         
       
     
       Example 4 
     Twisting and Folding Self-Transforming Structures 
       [0092]    A twisting and a folding transformation are shown in  FIGS. 12A-B  and  13 A-B. 
         [0093]      FIG. 12A  is a series of time-lapsed photographs showing a twisting transformation.  FIG. 12B  shows superimposed photos of a time-lapsed twisting transformation. In this prototype, the printed nylon filament was extruded onto Carbitex A324 flexible, fibrous composite at a temperature of 220° C. to 240° C. while the heated bed temperature was at 50° C. The width of the printed grain pattern was approximately 20 mm, printed in a similar pattern with relation to the grain of the flexible carbon fiber as shown in  FIG. 2C . The first layer height was printed at 0.6 mm above the carbon surface. The second layer was printed at 0.3 mm above the first. The printed grains were spaced at 0.4 mm offset from one another. After printing, the prototype was heated with ambient heat from a heat bed set to 400° C. for about 10 seconds. 
         [0094]      FIG. 13A  is a series of time-lapsed photographs showing a folding transformation.  FIG. 13B  shows superimposed photos of a time-lapsed folding transformation. In this prototype, the printed nylon filament was extruded onto Carbitex A324 flexible, fibrous composite at a temperature of 220° C. to 240° C. while the heated bed temperature was at 50° C. The width of the printed grain pattern was approximately 20 mm, printed in a similar pattern with relation to the grain of the flexible carbon fiber as shown in  FIG. 2A . The first layer height was printed at 0.6 mm above the carbon surface. The second layer was printed at 0.3 mm above the first. The printed grains were spaced at 0.4 mm offset from one another. After printing, the prototype was heated with ambient heat from a heat bed set to 400° C. for about 10 seconds. 
       Example 5 
     Use of Self-Transforming Structure in an Airplane Engine 
       [0095]      FIG. 14  is a series of time-lapsed photographs showing a folding transformation superimposed on top of one another. In this prototype, the printed nylon filament was extruded at a temperature of 220° C. to 240° C. while the heated bed temperature was at 50° C. The width of the printed grain pattern was approximately 20 mm, printed in a similar pattern with relation to the grain of the flexible carbon fiber as shown in  FIG. 2A . The first layer height was printed at 0.6 mm above the carbon surface. The second layer was printed at 0.3 mm above the first. The printed grains were spaced at 0.4 mm offset from one another. After printing, the prototype was heated with ambient heat from a heat bed set to 400° C. for ˜10 seconds. This embodiment can be used to provide adaptive control of fluid flow in response to temperature changes. 
       Example 6 
     Self-Transforming Structure Formed of Flexible, Fibrous Composite Having a Triaxial Weave 
       [0096]      FIG. 15  is an example of a triaxial weave of T700 carbon fiber (Gernitex; Product No. TXD-20-T700-120) with 22 mm wide strips of fiber woven in 0 degree, +60 degree and −60 degree orientation. The Gernitex T700 carbon fiber has an areal density of 120 grams per square meter areal. The laminated sheet on top of the weave can be placed in-line with the fiber orientation at 0, 120 or 60 degree to achieve a curve, 2 curve, or 3 curve type behavior respectively. 
       Example 7 
     Self-Transforming Structure Formed of Flexible, Fibrous Composite Having a Uniaxial Weave 
       [0097]      FIG. 16  is an example of a uniaxial weave orientation of carbon fiber. The pattern on top of the weave can be placed in-line with the fiber (top) or orientated at 90° relative to the fiber orientation (bottom) to achieve a 1-curve or 2-curve type behavior, respectively. 
       Example 8 
     Self-Transforming Structures with Triaxial Flexible, Fibrous Composite 
       [0098]      FIGS. 17A and 17B  are photographs of a self-transforming structures. The grain direction of the added material is indicated with arrows and is patterned as illustrated in  FIG. 3A . 
       Example 9 
     Self-Transforming Structures with Biaxial Flexible, Fibrous Composite 
       [0099]      FIGS. 18A-D  are photographs of self-transforming structures. For each photograph, the flexible, fibrous composite is Carbitex A324, and the added material is Nylon 618. For each photograph, the added material was printed onto the flexible, fibrous composite using a Fused Deposition Modeling (FDM) 3D printer. Each of the photographs was taken at a room temperature.  FIG. 18A  is a photograph of a curve transformation, in which the added material was printed onto the flexible, fibrous composite according to  FIG. 2B .  FIG. 18B  is a photograph of a fold transformation, in which the added material was printed onto the flexible, fibrous composite according to  FIG. 2A .  FIG. 18C  is a wave transformation, in which the added material was printed onto the flexible, fibrous composite according to  FIG. 2E .  FIG. 18D  is a spiral transformation, in which the added material was printed onto the flexible, fibrous composite according to  FIG. 2D . 
       INCORPORATION BY REFERENCE AND EQUIVALENTS 
       [0100]    The teachings of all patents, published applications and references cited herein are incorporated by reference in their entirety. 
         [0101]    While this invention has been particularly shown and described with references to example embodiments thereof, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the scope of the invention encompassed by the appended claims.