An explicit, direct simulation of multiaxial finite strain inelastic behavior for polymeric solids

Abstract

In contrast with the widely known elastoplastic behavior of hard solids with very small elastic deformations, we study elastoplastic behavior of soft solids dominated by very large elastic deformations. Toward this goal, thermo-coupled rate-independent and rate-dependent elastoplastic J2-flow models with evolving rubberlike elasticity are established for the first time in a sense of identically meeting the Clausius–Duhem inequality. Novel results are presented for coupling effects in three respects: (i) how finite strain elastic behavior may evolve with development of plastic flow; (ii) how plastic flow may be induced in a process of pure heating; and (iii) how strain rate effects may be characterized to ensure smooth transitions to the rate-independent case. It is demonstrated that complex inelastic deformation features observed in soft solids such as elastomers, including the Mullins effect, the permanent set, the induced anisotropy, the thermal recovery and the rate effect etc., may be derived as direct, natural consequences of the proposed model. In particular, explicit expressions for the constitutive functions incorporated are derivable from the uniaxial data for the purpose of achieving an explicit, exact simulation of the foregoing inelastic features, thus bypassing usual complexities both in choosing suitable forms of constitutive functions and in identifying unknown parameters in an approximate sense.