Micro-crack interactions and shape design optimization problems: A boundary element approach.

Abstract

Most materials contain micro-scale features e.g., cracks, inclusions, secondary phases and their interfaces. The strength and life of macro-scale components fabricated from these materials essentially depend on the interactions and evolutions of associated micro-features. In the first part of this dissertation, a hybrid micro-macro Boundary Element Method (BEM) formulation is developed to capture the micro-scale effects, effectively and efficiently, within the context of a macro-scale analysis. The micro-scale effects are introduced through an augmented fundamental solution, and the effects of macro-scale design considerations on micro-scale evolutions are investigated through the hybrid BEM approach. A unit cell model in conjunction with the hybrid BEM approach is also developed to obtain effective homogenized material properties for these heterogeneous materials. Numerical results obtained from the proposed hybrid BEM scheme are compared to existing analytical and numerical results. Investigation of design sensitivities and optimization with respect to various geometric, material and process parameters is the focus of the second part of this dissertation. A direct differentiation approach is pursued for this purpose and numerical results are presented for small strain elasto-viscoplastic problems. Shape optimization is carried out by coupling the standard and sensitivity analyses with an optimizer. Numerical results are presented for various homogenized media and are also compared to known solutions for this class of problems.