A stretching behavior of knitted and woven textiles is modeled. In our work, the yarns are modeled as one-dimensional hyperelastic strings with frictional contact. Capstan law known for Coulomb's friction of yarns is extended to an additional adhesion due to gluing of filaments on the yarn surface or some chemical reaction. Two-step Newton's method is applied for the solution of the large stretching with sliding evolution in the contact nodes. The approach is illustrated on a hysteresis of knitted textile and on the force-strain curve for a woven pattern and both compared with experimental effective curves.

In many textiles and fiber structures, the behavior of the material is determined by the structural arrangements of the fibers, their thickness and cross-section, as well as their material properties. Textiles are thin plates made of thin long yarns in frictional contact with each other that are connected via a rule defined by a looping diagram. The yarns themselves are stretchable or non-stretchable. All these structural parameters of a textile define its macroscopic behavior. Its folding is determined by all these parameters and the kind of the boundary fixation or loading direction. The next influencing characteristic is the value of the loading. The same textile can behave similar to a shell and work just for bending, or behave as a membrane with large tension deformations under different magnitudes of the loading forces. In our research, bounds on the loading and frictional parameters for both types of behavior are found. Additionally, algorithms for the computation of effective textile properties based on the structural information are proposed. Further focus of our research is the nature of folding, induced by pre-strain in yarns and some in-plane restriction of the textile movements, or by the local knitting or weaving pattern and the yarn’s cross-sections. Further investigations concern different applications with spacer fabrics. Structural parameters influencing the macroscopic fabric behavior are investigated and a way for optimization is proposed. An overview of our published mathematical and numerical papers with developed algorithms is given and our numerical tools based on these theoretical results are demonstrated.

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Simulation-based prediction of mechanical properties is highly desirable for optimal choice and treatment of leather. Nowadays, this is state-of-the-art for many man-made materials. For the natural material leather, this task is however much more demanding due to the leather’s high variability and its extremely intricate structure. Here, essential geometric features of the leather’s meso-scale are derived from 3D images obtained by micro-computed tomography and subsumed in a parameterizable structural model. That is, the fiber-bundle structure is modeled. The structure model is combined with bundle properties derived from tensile tests. Then the effective leather visco-elastic properties are simulated numerically in the finite element representation of the bundle structure model with sliding contacts between bundles. The simulation results are validated experimentally for two animal types, several tanning procedures, and varying sample positions within the hide. Finally, a complete workflow for assessing leather quality by multi-scale simulation of elastic and visco-elastic properties is established and validated.