Time and rate dependent constitutive model coupled with nonlocal damage at finite strains for semi-crystalline polymers

Many constitutive models were developed in the literature to model the complex behaviour of polymer materials. These models can be sorted in two categories: the physical based models where the microstructure of the material is taken into account for representing the macroscopic behaviour [1,2] and the phenomenological based models where the material discontinuities, in the microstructural scale, are homogenised in a representative volume element. In this way, elasto-plastic constitutive models based on the 3RYHUVWUHVV ́ FRQFHSW 9%2 > @ Xsing the unified state variable theory were extended for polymeric materials [4,5]. The addition of mineral fillers in the semi-crystalline matrix increases the cavitation phenomenon. In this case, the viscoelastic-viscoplastic deformation of the material is accompanied by damage in the form of nucleation, growth and coalescence of cavities. Many damage model were developed for polymer application in order to represent this phenomenon [6,7,8,9]. The damage present in this kind of material induces a softening behaviour which leads to the localisation of the strain in a narrow zone of the structure accompanied by numerical solutions depending of the finite element mesh. The nonlocal model where introduced in the literature in this way, in order to overcome the mesh dependency phenomenon [10,11]. In this work, a non-associated viscoelastic-viscoplastic model coupled with nonlocal damage is developed in order to model a mineral filled semi-crystalline polymer used in the automotive industry. The constitutive equations of the model are stated under finite strain framework by using a hypoelastic formulation. The interesting properties of the logarithmic tensor linking the work conjugate pair Cauchy stress and Henky strain are used in the proposed model. In order to obtain a mesh independent solution with the material exhibiting softening, an integral-type nonlocal damage is developed in this work.