A hyperelastic material model considering biaxial coupling of tension–compression and shear for the forming simulation of woven fabrics

In the past decades, numerous material models have been developed to describe the forming behavior of fabrics, allowing for modeling of complex forming processes. Especially under constrained forming conditions, distinct multiaxial stress states can occur, which need to be captured by macroscopic material models. In this paper, a nonlinear hyperelastic constitutive model is presented and implemented in an Abaqus/Explicit user subroutine Vumat, considering biaxial coupling and normal-shear coupling of the interwoven fiber bundles in a woven fabric. The couplings are formulated for positive and negative normal strains. Exemplary forming studies on the generic double dome geometry are performed to investigate the influence of the couplings on the forming result. The results show that the biaxial coupling should be considered under highly constrained boundary conditions in thickness direction. The normal-shear coupling affects the forming behavior only under very high draping angles and appears to be of less relevance in these conditions.