Simulation of elastic properties of spacer fabrics and its effective permeability at different compression states

We consider spacer fabrics, who are plates or shells composed of two knitted plane layers connected by vertical beams. Several small parameters occur in the structure, the period, the thickness of the fibers and the height of the spacer fabric. Our aim is to compute the effective stiffness and permeability of such spacer fabrics. In order to reduce the computational effort and simplify the computational model, homogenization and dimension reduction techniques are applied to replace the fabric by an equivalent two-dimensional plate or shell with effective elastic properties and simultaneously to keep the resolved micro-structure for the fluid simulation, to compute its effective permeability. The corresponding analysis for the scale separation and the detailed description of the algorithm can be found in [7]. The relation between the small parameters and the kind of the loading determine the dominance of the bending or tension of beams on the micro-level. This paper demonstrates the algorithm on an application example. We compute the elastic properties of a spacer fabric and its effective permeability for different stages of the compression of the spacer fabric. Numerical examples were performed by the successive application of the multi-scale simulation tools, Fiber FEM and GeoDict, developed at Fraunhofer ITWM and compared with the corresponding experimental results, based on measurements performed at the TU Dresden.