Abstract: Macroscopic constitutive modeling and Process Optimization through integration of mathematics, mechanics and computational materials sciences: new advances, challenges and opportunities
Constitutive plasticity modeling refers 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. Available data are sparse and generally limited to 1-D conditions whereas the locus of states defining the onset of irreversible deformation is a 6-D manifold. Therefore, the task of a modeler is extremely difficult.
Moreover, most metallic materials and some ceramic materials due to the intrinsic symmetries associated to their crystalline structure or preferential orientations induced by processing, display a strongly anisotropic behavior.
In this lecture are presented the various approaches developed in our group towards creating new knowledge while tackling very challenging and important technological issues. Since the research being conducted in our group integrates mathematics, mechanics and computational sciences, we discuss the overall approach and give a gist of the new research and projects on three inter-related topics.
After a brief presentation of a recent analytical single-crystal model, developed such as to satisfy automatically the invariance requirements with respect to any proper orthogonal transformation belonging to the cubic crystalline system, advances, challenges and opportunities in bridging scales and implementing homogenization schemes in the context of finite-elements are discussed.
We conclude with a presentation of work being done on the use of machine learning techniques capable of learning from sparse simulation data to generate efficient real-time results and integration of Active Learning AI-driven approaches.