Coupled damage–plasticity model for cyclic loading: Theoretical formulation and numerical implementation

► We model the original formulation for residual deformation. ► We show the change of elastic response. ► Stress based finite element interpolation leads to robust implementation. ► We examine different hardening phenomena for cyclic loading effects. In this work we present a phenomenological constitutive model which is capable of coupling two basic inelastic behavior mechanisms, plasticity and damage. The model is targeting cyclic loading applications. Thus, in either plasticity or damage part, both isotropic and linear kinematic hardening effects are taken into account. The main advantage of the model is the use of independent plasticity versus damage criteria for describing the inelastic mechanisms. Another advantage concerns the numerical implementation of such model provided in hybrid-stress variational framework, resulting with very enhanced accuracy and efficient computation of stress and internal variables in each element. Several illustrative examples are presented in order to confirm the accuracy and efficiency of the proposed formulation in application to cyclic loading.