Size Dependent Failure Constrained Topology Optimization Approaches

Vincenzo G Vernacchio, Purdue University

Abstract

New approaches in topology optimization and manufacturing techniques are generating multi-scale, physically realized mechanical components from advanced materials. Current optimization formulations do not consider the dependence of strength on feature size. By failing to account for the mechanical models of this behavior, sub-optimal structures are generated.A currently available academic density-based topology optimization code is extended to incorporate strength constraints. A continuum theory of failure novel to the optimization field is implemented to account for both general yielding and fracture dominated failure. The fracture limit is then formulated in terms of well-established models of brittle and quasi-brittle size dependence. Additional models of size dependence based on assumed flaw sizes are considered using the theory of linear elastic fracture mechanics. To unify the optimized topology and the empirical geometric-scaling models used, a novel geometric measure of local size is proposed. This measure interprets the evolving density field using a consistent domain of support and maintains consistency with gradient-based methods of optimization. The geometric measure is evaluated using test-problems which consider a minimum compliance objective under geometric constraints.The resulting optimized structures are presented for the geometric and size-dependent strength constrained formulations. The geometrically constrained results illustrate the flexibility and robustness of the proposed local size measure. The various models of size-dependent strength illustrate the impact and necessity of considering physical models of material within the topology optimization formulation. Results which exhibit clear ”micro-structural” features and scale transitioning architectures are presented for limited multi-scale optimization studies.An attempt at physical validation considering a single model of quasi-brittle material failure is made. Existing approaches for generating 3D volumetric meshes from image data are leveraged to yield CAD interpretations of optimized structures. Structures are then printed using a 3D printing PolyJet process with a previously established size-dependent material. Structures are destructively evaluated under displacement controlled load testing. The resulting tests indicate that the stress states in the structure fail to induce the expected size-dependent material characteristics. Furthermore, the testing results indicate the difficulty in properly accounting for boundary conditions in the topology optimization approach.

Degree

M.Sc.

Advisors

Siegmund, Purdue University.

Subject Area

Mathematics|Mechanics

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