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.

Continuous semigroup theory is applied to proof the existence and uniqueness of a solution to a fluid-structure interaction (FSI) problem of non-stationary Stokes flow in two bulk domains, separated by a 2D elastic, permeable plate. The plate's curvature is proportional to the jump of fluid stresses across the plate and the flow resistance is modeled by Darcy's law. In the weak formulation of the considered physical problem, a linear operator in space is associated with a sum of two bilinear forms on the fluid and the interface domains, respectively. One attains a system of equations in operator form, corresponding to the weak problem formulation. Utilizing the sufficient conditions in the Lumer-Phillips theorem, we show that the linear operator is a generator of a contraction semigroup, and give the existence proof to the FSI problem.

A design optimization task in the setting of fluid–structure interaction (FSI) with a periodic filter medium is considered. On the microscale, the thin filter has a small in-plane period and thickness $$\varepsilon $$ ε and consist of flexural yarns in contact. Its topology, as well as its linear material properties, are dependent on a discrete design variable. A desired flow-induced displacement profile of the filter in steady-state is to be obtained by optimal choice of this variable. The governing state system is a one-way coupled, homogenized and dimension reduced FSI model, attained by the scale limit $$\varepsilon \rightarrow 0$$ ε → 0 . The design variable enters in the arising macroscopic model parameters, namely the filter’s homogenized stiffness tensors and its permeability tensor. The latter are attained by the solution of cell-problems on the smallest periodic unit of the filter. The existence of optimal solutions is verified by proving the continuous dependence of these macroscopic model parameters, as well as the design-to-state operator, on changes of the design. A numerical optimization example is provided.

This paper covers the mechanical simulation of woven textiles on the yarn level with an investigation of the influence of the sliding between yarns and changing yarn cross-sections under loading. An experimental validation of the simulation tools for a range of chosen woven structures with different weaving types and thicknesses of multifilament glass fibre yarns is provided. The main focus of the paper is the classification of the folding mechanisms in textiles.

Spacer fabrics are 3D technical textiles, consisting of two parallel textile layers, which are connected by a series of monofils. In many industrial applications, such as the deployment as a distance holder, the compression properties of spacer fabrics play a crucial role. The article experimentally investigates the potential of influencing these compression properties by the incorporation of parallel seams into the fabric. Moreover, an efficient simulation-based finite-element approach is presented, that allows the a-priori estimation of effective compression resistance. For this purpose, a dimension reduction approach is employed, that reduces the arising highly complex multi-contact problems to simulations on the yarn and monofil centerlines. Input for the simulation are known mechanical properties of the yarns and the general lapping plan of the spacer fabric. The proposed model is applicable to the linear compression regime, i.e., before buckling and large bending arises. As a proof-of-concept, the compression experiment for a plane, circular punch on the spacer fabric with and without added seams is simulated and afterwards validated by experiments. The good agreement of the attained compression curves demonstrates the applicability of the numerical approach