The micromorphic approach for plasticity, damage and evolution of microstructures

A unifying thermomechanical framework is presented that reconciles several classes of gradient elastoviscoplasticity and damage models proposed in the literature during the last 40 years. It is based on the introduction of the micromorphic counterpartχφ of a selected state or internal variable φ in a standard constitutive model. In addition to the classical balance of momentum equation, a balance of micromorphic momentum is derived that involves generalized stress tensors. The corresponding additional bound-ary conditions are also deduced from the procedure. The power of generalized forces is assumed to contribute to the energy balance equation. The free energy density function is then chosen to depend on the relative generalized strain φ−χφ and the microstrain gradient ∇χφ. When applied to the deformation gradient itself, φ ≡ F ∼ , the method yields the micromorphic theory according to Eringen and Mindlin, together with its extension to finite deformation elastoviscoplasticity [1, 2]. If the selected variable is the cumulative plastic strain, the theory reduces to the so–called “nonlocal implicit gradient–enhanced elastoplasticity model ” provided that simplified linear relationship