Anisotropic hyperelastic model of SiC twill fabrics considering biaxial coupling effects

SiC woven fabrics used in flexible thermal protection systems for hypersonic morphing vehicles exhibit significant large-deformation mechanical responses. To characterize this nonlinear behavior, a physically based macroscopic anisotropic hyperelastic constitutive model is proposed. Unlike traditional constitutive models that rely on polynomial or piecewise functions, this approach constructs a continuous tangent stiffness function with smooth transition characteristics to describe the typical J-shaped stress–strain curves of woven fabrics. The stress–strain relationships and strain energy density functions are derived through mathematical integration. This method mathematically guarantees model continuity and the zero-stress boundary condition, while integrating both tensile and shear responses into a consistent constitutive framework. Furthermore, the model introduces specific coupling terms to characterize the significant biaxial stiffening effect of unbalanced SiC twill fabrics. The model is implemented in Abaqus/Explicit via the VFABRIC user subroutine and validated against uniaxial tension, picture frame shear, and equibiaxial tension experiments. A macroscopic hemispherical punch simulation is also conducted to evaluate the model’s robustness. Results show that the hyperelastic model accurately reproduces the nonlinear hardening behavior and anisotropic characteristics of SiC fabrics under various loading paths, thereby providing a robust tool for evaluating mechanical responses and designing flexible thermal protection structures.