Computation of Cauchy heterogeneous stress field in a cruciform specimen subjected to equibiaxial tensile within parameter identification of isotropic hyperelastic materials

Abstract

Heterogeneous stress and strain fields have been investigated by Finite Element Method (FEM) in a cruciform specimen holed at the center and subjected to equibiaxial tensile. The stress field is zero at the boundary of the hole; it is a useful boundary condition to compute local stress field. Also, the heterogeneity proves out to be an advantage in order to increase the variety of deformation states. So, a digital image correlation (DIC) system could provide the local deformations, and the corresponding stress field was optimized and adapted to the specimen geometry. Indeed, on the basis of FE results, the heterogeneous Cauchy stress field has been computed analytically in a sub-core region of the s ample. As a result, the local strain and stress fields may be related; so that, the material parameters of isotropic and incompressible rubber-like materials could be identified from experimental data arising from a single heterogeneous test. Besides, the key ideas have been highlighted in order to solve the inverse problem related

to the identification procedure.