A constitutive framework based on elastic and internal energy degradation

Abstract

A general constitutive framework is presented capable of representing different irreversible deformation modes, like plasticity, elastic damage, complex evolution of the hardening properties and the induced coupling effects. The formulation can be framed in the generalized standard material models with internal variables and multiple dissipative activation functions. The formulation is thermodynamically consistent and the state laws, the structure of the dissipation and of the activation functions are all derived complying with the principles of thermodynamics. The generalized flow rules are derived under the hypothesis of generalized associativity. The main aspect of the proposed model is the definition of an internal damage variable which is appended as a factor of the internal energy and is then able to describe a progressive degradation of an isotropic hardening modulus. In particular, the one-dimensional stress-strain case, for a ductile material is examined in some detail. The complex evolution of the strength which follow the first post yielding phase is modelled as an irreversible degradation of an hardening component. This case is examined neglecting the elastic damage effects, since for metals the degradation of the elastic properties is produced at large strains and can be considered a subsequent state. The discrete step problem is presented and a resolution strategy based on the Euler-backward difference scheme is proposed. The numerical results for an assigned, monotonically increasing, total strain show that the proposed model possesses the feature to represent complex hardening evolutions including the hardening saturation conditions and some unstable branches which characterize softening transition phases.