A constitutive model for describing decoupled material behavior in thickness and in‐plane directions

Abstract

An increasing demand for paper and paperboard in engineering applications has emerged throughout the years. This leads to a growing interest in simulation tools to predict the material behavior, which is challenging due to the anisotropic structure of the material. It can be divided into in‐plane and out‐of‐plane behavior, which is mostly independent of each other resulting from the microstructure. Thus, a constitutive material model that captures in‐plane and out‐of‐plane behavior in a consistent manner is desired to simulate complex deformation states. The decoupling will be incorporated by a decomposition of the kinematics and the energy formulation into in‐plane and out‐of‐plane terms by use of structural tensors. This approach is flexible and can easily be extended to inelastic material behavior. In this work, the introduction of the decoupling into a constitutive material model for inelastic behavior is described. Visco‐elasticity is included through inelastic potentials. Three different potential formulations are given where focus is on the third, novel formulation, which defines inelastic strain evolution only in out‐of‐plane directions. The capabilities of this formulation are compared to the remaining potentials by simulations of a pinched cylinder that is loaded in the out‐of‐plane direction.