Asymmetric stress-strain measures in construction of multilevel constitutive models of materials
The paper considers certain problems regarding the use of asymmetric mesoscale stress-strain measures in construction of multilevel constitutive models of inelastic deformation of materials. The use of these measures is given arguments; an asymmetric strain rate measure independent of the choice of a reference frame is introduced. The general structure of a two-level model of inelastic deformation of material is described using the proposed mesoscale stress-strain measures; the balance equation of angular momentum is used to demonstrate the necessity to pass on to symmetric measures on the macroscale. Application of the proposed model for description of inelastic deformation of a partially crystalline polymer material is considered on the example of low-density polyethylene. A series of computational experiments is performed showing a considerable discrepancy in the data that the model provides for a crystallite with an asymmetric elastic constant tensor (within the first and second pairs of indices) and with a symmetric one. The theoretical substantiation given and the calculation results obtained with the developed model demonstrate the necessity of using asymmetric stress-strain measures in construction of multilevel models of materials.