Abstract: Modelling Anisotropy in Plastic Deformation and Damage, Recent Advances and Open Questions
Theory of plasticity is the name given to the mathematical study of stress-strain relationships in solids undergoing permanent/irrecoverable deformation. The task of the theory is two-fold: first, to derive explicit relations in agreement with observations at the macroscopic scale, and second to predict the response for any combinations of loadings. Given that data are generally 1-D and the locus of states defining the onset of plastic deformation is a 6-D manifold, the task is extremely difficult. Moreover, for metallic materials due to their intrinsic symmetries associated to their crystalline structure or preferential orientations induced by processing, the response is strongly anisotropic. In this lecture is presented a rigorous framework for modelling plastic anisotropy and very recent constitutive models developed in this framework. New interpretations and explanations of ubiquitous features of the mechanical response of titanium and magnesium materials based on these models for a variety of loadings including bending, torsion and combined axial-torsional are provided. Key contributions towards the fundamental understanding of plasticity-damage couplings are briefly presented. We conclude with a presentation of open research questions and discussion of possible directions of study.