On energy-based coupled elastoplastic damage theories: Constitutive modeling and computational aspects

Abstract

Novel energy-based coupled elastoplastic damage theories are presented in this paper. The proposed formulation employs irreversible thermodynamics and internal state variable theory for ductile and brittle materials. At variance with Lemaitre's work on damage-elastoplasticity, the present formulation renders rational thermodynamic potential and damage energy release rate. In contrast to previous work by Simo and Ju (featuring an additive split of the stress tensor), current formulation assumes an additive split of the strain tensor. It is shown that the “strain split” damage-elastoplasticity formulation leads to more robust tangent moduli than the “stress split” formulation. The plastic flow rule and hardening law are characterized in terms of the effective quantities; viz. the effective stress space plasticity. This mechanism is both physically well-motivated and computationally efficient. Further, a fourth-order anisotropic damage mechanism is proposed for brittle materials. Rational mechanisms are also presented to account for the microcrack opening and closing operations as well as the strain-rate dependency of microcrack growth.Efficient computational algorithms for proposed elasloplaslic damage models are subsequently explored by making use of the “operator splitting” methodology. In particular, new three-step operator split algorithms are presented Application is made to a class of inviseid and rate-dependent cap-damage models for concrete and mortar. Experimental validations are also given to illustrate the applicability of the proposed damage models.