Anisotropic hyperelastic/plastic behavior on stress-constrained thin structures by iterating on the elastic Cauchy

Anisotropic hyperelastic/plastic behavior on stress-constrained thin structures by iterating on the elastic Cauchy–Green tensor

Areias, P. / de Melo, F.Q. / Sikta, J.N.

Abstract

Abstract Thin-walled structures impose zero-stress constraints at free faces. These are in general nonlinear functions of strain and, in the elasto-plastic case, non-smooth. Under these circumstances, the conjugate strain components become constitutive unknowns. By iterating for the elastic Cauchy–Green tensor in the $6 -$ dimensional space, we directly obtain a system that includes the zero-stress constraints. Coupling of the stress and strain constitutive unknowns is possible due to the use of a convenient equation arrangement. This contrasts with the standard decoupling schemes. Herein, we use the Kröner–Lee decomposition of the deformation gradient to obtain a differential–algebraic system which includes stress constraints in analogous form to additional yield conditions. The source is the right Cauchy–Green tensor. The main contribution is the development of a thin-walled implicit integrator for any hyperelastic case and any yield function. Integration is based on a backward-Euler method for the flow law complemented by the solution of a yield condition and the stress constraints. We make use of the elastic Mandel stress construction, which is power-consistent with the plastic strain rate. Two complete fully orthotropic worked examples are presented.

Highlights • Kröner–Lee formulation with fully anisotropic hyperelastic and plastic behavior. • Yield function based on Mandel stress, non-symmetric flow law. • Replacement of some flow-law equations by stress constraints. • Analysis of error and stability for the implicit integrator. • Application to the pinched cylinder and the fully anisotropic plate inflation.