A new thermodynamical framework for finite strain multiplicative elastoplasticity coupled to anisotropic damage

• Multiplicative elastoplasticity coupled to anisotropic damage.
• Novel definition of the effective Mandel-like stress tensor.
• Proposed framework thermodynamically consistent.
• Constitutive model using the proposed framework.

The thermodynamical framework of an elastoplastic model coupled to anisotropic damage is presented in this paper. In the finite strain context, the proposed model is based on the multiplicative decomposition of the strain gradient into elastic and plastic parts. The anisotropic degradation is introduced by means of a second order tensor and another intermediate configuration is introduced by fictitiously removing this degradation from the plastic intermediate configuration. To enhance the physical meaning of the Mandel-like stress measure work conjugated to the inelastic flow stated in this fictitious configuration, i.e. the “effective stress”, a new damage rate tensor is defined with its associated push-forward and pull-back operations. The emphasis in this paper is placed on the description of the interesting properties of the novel definitions of the push-forward and pull-back operations which are discussed through a thermodynamical framework. Furthermore, a specific constitutive model with the plastic and damage flow rules deduced from the restrictions imposed by the second law of thermodynamics is discussed with an application on an asphalt concrete material where the anisotropic evolution of the damage is highlighted.