As part of the activities dedicated to the internationalization of research, the Department of Continuum Mechanics and Structural Analysis in the University Carlos III of Madrid will host throughout October the internationally recognized Professor Miles B. Rubin, from the Faculty of Mechanical Engineering of the Israel Institute of Technology (TECHNION). Professor Miles Rubin is one of the world’s recognized authorities in the Continuum Mechanics community.
- Professor Rubin will give two open lectures on 5th and 14th October:
Unphysical arbitrariness in constitutive equations for elastically anisotropic nonlinear lastic-viscoplastic solids:
Constitutive equations for elastically anisotropic nonlinear elastic-viscoplastic solids are often formulated assuming that the strain energy function depends on an elastic deformation gradient. Also, dependence on a triad of vectors can be introduced to characterize directions of material anisotropy. The elastic deformation gradient is usually written in terms of the total deformation gradient and a plastic deformation gradient, together with a specification of the reference configuration. Alternatively, it is possible to introduce a triad of microstructural vectors which are determined by integrating evolution equations and which characterize the elastic response and orientations of directions of anisotropy. The objective of this paper is to demonstrate that the elastic, total and plastic deformation measures and the vectors used to characterize directions of material anisotropy contain unphysical arbitrariness which prevents them from being measured. In contrast, the microstructural vectors used in the alternative formulation can be measured and are not sensitive to this arbitrariness.
Modeling a smooth elastic-inelastic transition with a strongly objective numerical integrator needing no iteration:
Large deformation evolution equations for elastic distortional deformation and isotropic hardening/softening have been developed that model a smooth elastic-inelastic transition for both rate-independent and rate-dependent response with no need for loadingunloading conditions. A novel special case is a rate-independent overstress model. Specific simplified constitutive equations are proposed that capture the main effects of elastic-plastic and elastic-viscoplastic materials with only a few material parameters. Moreover, a robust and strongly objective numerical integrator for these simplified evolution equations has been developed which needs no iteration. Examples show the influence of the various parameters on the predicted material response. The smoothness of the elastic-inelastic transition in the proposed model, with the associated overstress, tends to spread the inelastic region. This side effect prevents severe deformation from being localized in an element region that continues to reduce in size with mesh refinement. However, preliminary calculations indicate the need for additional modeling of a material characteristic length that independently controls the size of a localized severely deformed region.