Dimensionally Reduced Modelling of Hyperelastic Coated Fabric Using Variational Asymptotic Method

The dimensional reduction of a hyperelastic coated fabric from 3D to 2D is achieved asymptotically using the Variational Asymptotic Method (VAM). This method combines constrained calculus of variations with asymptotics. VAM divides the analysis into a 1D through-the-thickness analysis and a 2D reference surface analysis. The 1D analysis results in the derivation of asymptotically accurate 3D warping functions and a 2D nonlinear constitutive relation. The 2D nonlinear reference surface analysis uses the derived 2D constitutive law to determine 2D displacements and strains via 2D nonlinear finite element analysis (FEA). The classification of 3D strain energy density into distinct orders is made possible by introducing two intrinsic small parameters: 1) a geometric small parameter, which is the ratio of thickness to characteristic length (h/L<<1), and 2) a physical small parameter, ensuring that the largest component of 3D strain is limited to 20 percent, which is less than 1. The model accounts for both geometric and material nonlinearities. This study presents preliminary results, including zeroth-order results on derived 3D warping functions and a 2D constitutive law.