Fraunhofer ISC
(Source: Fraunhofer ISC)
As part of the Fraunhofer Cluster of Excellence Programmable Materials CPM, the Application Center Textile Fiber Ceramics (AWZ TFK) is developing innovative auxetic folded structures in knitted fabrics. The aim is to implement auxetic unit cells as the smallest building unit in a programmable material with textile manufacturing processes.
Everyday experience teaches us: if you stretch a material, it becomes thinner – if you squeeze it, it becomes thicker. Auxetic materials, however, behave atypically to our everyday perception and experience in this respect. They are special, paradoxical materials that differ fundamentally from normal materials in their cross-deformation properties. However, auxetic properties are not based on the material properties of the raw material, but on the internal structure of the material, thus any material or composite can behave auxetically if it has the appropriate structure. As part of the Fraunhofer Cluster of Excellence Programmable Materials CPM, the AWZ TFK has set itself the task of developing textile structures that exhibit auxetic transverse deformation properties. The central question is how a textile unit cell must be designed in order to exhibit auxetic transverse deformation as a single smallest structural unit as well as in the surface composite of the unit cells.
Auxetics – how does it work?
Even though the cross-stretch properties of auxetic materials sound like science fiction, they originate from nature. There are natural materials that have auxetic macro or micro-structures. For example, calves suck on auxetic materials every day because cows’ teats have skin that expands transversely when stretched. If the calf sucks on the teat, the tissue widens, and the milk can flow freely. Another example is the pomelo fruit, which has an auxetic skin. If it falls from the tree, it does not burst open but remains undamaged. A highly effective impact protection that is also very light. These 2 examples from nature give an idea of the wide field of applications for auxetic materials.
Since it is a geometric structural property that can be designed in a variety of ways, there is the possibility of introducing a flexible structure into solid materials and creating new types of material properties by combining molecular and macrostructural characteristics. Scientifically, 5 classes of geometric structures that exhibit auxetic behavior have been identified to date. The common feature of the models of all classes is the internal geometric structure, which includes an elastic and an inelastic part. The elastic part allows rotation or displacement of the basic structure. The inelastic part, on the other hand, constrains the elastic part and provides the framework for maintaining structural stability. The multitude of geometric structures within the classes are ideal structures and can only in the rarest cases be directly transferred to materials. Especially in the development of auxetic textiles, the challenge arises to reconcile the structural bonds of auxetic motion with the limiting binding structure of textiles.
The auxetic expansion is measured by means of the Poisson's ratio v, which as an elastic constant defines the transverse contraction behavior of a material (Fig. 1). The Poisson's ratio for auxetic materials is negative, because the change in thickness and length is simultaneously positive and materials usually cannot propagate. However, Poisson's ratio is not readily applicable to auxetic materials, because it is defined only for basic materials in their natural form. If the basic materials are now brought into an auxetic structure, this has a negative Poisson's ratio, but the basic material still has a neutral or positive Poisson's ratio.
Fig. 1: Cross-contraction behavior (Source: Fraunhofer ISC)
The cross-contraction property of auxetic materials opens a wide range of potential uses. The special property of such materials can positively influence various mechanical parameters and improve performance on different dimensions that would otherwise not be possible. Structural parameters such as energy absorption capacity or durability can be positively influenced to an above-average extent and this at the same weight. The same applies to stiffness as well as thermal and vibration behavior. For example, if normal materials are hit by an object, the material "flows" away from the impact zone. This greatly weakens the area and makes it more unstable. In the case of an auxetic material, the impact zone compresses, and it "flows" into the zone. The zone is not weakened, but strengthened. Furthermore, in a textile context, auxetic materials could potentially improve the comfort of clothing. Conventional garments become tighter when stretched to length. Auxetic textiles can adapt optimally to body shapes and offer more comfort.Auxetics in textiles
The research objective of the AWZ is the production of textiles with a suitable structure to achieve auxetic cross-expansion. This is a particular challenge in the textile field because textiles are subject to process as well as material-dependent constraints and internal stresses as well as forces. The overall character of a textile is determined by the raw materials used, the manufacturing process and the respective techniques. This is particularly the case with knitted, warp-knitted and woven fabrics, since these flat or 3-dimensional textiles are manufactured by suitable weaves from linear units, e.g. yarns or monofilaments. The properties of the knitted or woven textile are influenced by the basic material processed, the weaves used or their combination, and the respective manufacturing parameters. Each individual element brings specific properties and conditions, which in turn interact with the other elements. These multilayered and complex internal structures represent a particular challenge in the development of auxetic textiles.
To introduce auxetic structures into a textile, the research focus has been on the development of auxetic knitted fabrics of the left-left and right-right binding groups (Fig. 2). Knitted fabrics consist of interlaced yarn loops of right and/or left stitches arranged according to the binding group. With each stitch, the yarn is placed in a state of tension by the loop formation. This stored force of the loop can be called the torque of the stitch.
Fig. 2: Basic knitting bindings (Source: Fraunhofer ISC)
In the right-left basic binding (single jersey), only right stitches are knitted; here, the release of energy from the stitch loops shows up as a curling effect at the edges. In the left-left basic binding (double jersey), this state of tension is balanced by alternating left and right stitches. The same applies to the left-left basic binding with an alternation of left and right rows of stitches. Due to the stitch tension, both sides of the stitches in the left-left knit in basic binding show exclusively left stitches in the unstretched state. In the case of left-left knits, instead of alternating left and right rows of stitches with a design of flat sections of left and right stitches, a 3D deformation can be designed by using the torque. With regard to the production of an auxetic material structure, the tension in the stitches offers the possibility of actively using them for auxetic deformation.Research design
The research design included a preliminary study with origami paper folds and 3 series of experiments in flat knitting technology. In the preliminary study, the principle of the stretching behavior of auxetic materials was made comprehensible on the basis of folded paper structures. This haptic-visual understanding was obligatory, because without suitable, defined 3D structures, such as folds, hinges etc., auxetic behavior cannot develop. The preliminary study formed the basis for the integration of a structure into a 2D textile fabric, which enables a 3D auxetic construction of the textile.
In the first series of experiments on the flat knitting machine, the roll-up behavior of right and left stitches in left-to-left knits with flat designs was investigated experimentally to establish a solid foundation for understanding the forces and their interactions in the smallest unit stitch. Foundations for the specific study of the curl-up behavior of the transition lines from left to right stitches were postulated, which were specified in a second series of experiments. The research focus was placed on the systematic investigation of the roll-up effect of the transition lines from left to right stitches in the left-to-left knitted fabric. The research results show that the roll-up effect depends in strength and direction on the angle of the transition line of right and left stitches. The findings obtained from the first 2 series of experiments were summarized in a structural model for the development of auxetic knits. This structural model forms the foundation for the design of auxetic pattern structures in left-hand knits and creates the basis for further research in this field.
Auxetic folds in knitted fabric
In terms of weave technology, it is not possible to create an actual origami fold structure in knitted fabrics of the left-left weave group, since these folds have 3 different structural elements. These structural elements are mountain and valley folds as elastic elements and geometric areas as fixed components (Fig. 3). In order to realize this in the knitted fabric, 3 groups of binding elements are required per se, which can mechanically represent the elastic structural elements with folding direction as well as the inelastic, stabilizing structural elements.
Fig. 3: Structural elements of the Miura-Ori folding (Source: Fraunhofer ISC)
As the most important folding in nature, Miura-Ori folding was the focus of the third research series. It was investigated whether the structural model can be used purposefully for the development of foldable knitted fabrics based on the Miura-Ori principle. The Miura-Ori fold exhibits auxetic cross expansion, and its unit cell is equally subject to distortion in the knitted fabric due to the equal angles of the mountain and valley folds. Thus, due to the folding geometry of the Miura-Ori fold, a fold can be created at any angle and the distortion can be neglected. 
Fig. 4: Right-right knitted fabric with Miura-Ori folding (Source: Fraunhofer ISC)
By integrating the structural model into the folding geometry, the production of foldable right-right knitted fabrics with left-left sections as folding elements could be realized (Fig. 4). As expected from the auxetic Miura-Ori structure, the folded knits showed a negative Poisson's ratio v (Fig. 5). In addition to the implementation of variations and combinations of single cells of the Miura-Ori folds in the horizontal and vertical direction, the implementation of the diamond fold structure was also examined. Here, a distortion of 55 % in the longitudinal direction was found, which prevented the folding due to the lack of folding geometry. To prevent the distortion of the weave design of the diamond fold structure, further investigations are required for the further development of the design system of auxetic and foldable knits.
Fig. 5: Auxetic behavior right-right knit (v=-0.4118) (Source: Fraunhofer ISC)
The potential applications of foldable auxetic knitted fabrics are versatile. For example, it is conceivable to use them in interior design concepts for visual screening, thermal insulation or sound absorption. The porous structure of the knitted fabric, coupled with the folding, has the potential to improve the acoustic room situation. To verify its suitability, measurements have already been conducted with regard to the sound-reducing effect. These showed that the sound reduction of the opened knitted fabric is comparable to that of a conventional acoustic foam. Weaknesses were found in the area of stability of the textile, resulting in a need for further research to stiffen the solid structural elements. In addition to functional potential, the knitted system offers a wide range of aesthetic possibilities for designers. Obligatory for progression of the application possibilities of the folded knits is the integration of material variations. Knitting with multiple threads gives the possibility to combine different materials and integrate different functionalities. Therefore, it is also necessary to examine to what extent the results with the yarn used can be transferred to other materials and with which material the properties can be further improved. 
