On the Multiplicative Logarithmic Strain Space Formulation

Abstract

A new constitutive approach to finite-deformation formulations of elasto-plasticity (with isotropic thermal expansion) is presented, which is well-suited to a broad range of metals used for industrial applications. The constitutive equations are formulated within the logarithmic strain space. The coupling of elasticity, plasticity and thermal expansion is based on a multiplicative approach of commutative-symmetric stretch tensor products with symmetrizing rotation tensors in the middle of two symmetric stretch tensors. It is essential for finite-deformation formulations to refer to an appropriate reference configuration K₀ in order to model material orthotropy correctly (and not to mix up material / physical anisotropy with deformation-induced / geometrical anisotropy). Furthermore, it is essential to define proper stretch and strain tensors which are geometrical interpretable, i.e. which only depend on a current  K and a reference K₀ configuration (and not on the geometrical deformation path between these configurations). Therefore, all stretch and strain tensors are defined with respect to the same reference configuration K₀, the total stretches and strains as well as the partial ones: the elastic, plastic and thermal stretches and strains. And these reference configurations should be the appropriate ones, where—in the case of fiber-reinforced (metal) bodies—the fibers are placed orthogonal to each other or where Walter Noll’s symmetry group considerations characterize the physical nature of materials with their most specificity as: orthotropic, transversal isotropic or fully isotropic.