Optimizing heterogeneous elastic material distributions on 3D models

Optimizing heterogeneous elastic material distribution on a 3D part to achieve desired deformation behavior is an important task in computer-aided design and additive manufacturing. This paper presents a solution to this problem, which involves interactive design, automatic deformation generation, and optimization of spatial distribution of heterogeneous elastic materials. Our method improves previous techniques in three aspects. First, we incorporates a geometric deformation-based interactive design into FEM-based optimization, which makes the solution less dependent of initial guesses of Young’s modulus values and it more likely to produce the target design even with sparse user input of displacements and forces at a limited set of mesh vertices. Second, we formulate the problem as an $L_2$- or $L_0$-optimization problem. The $L_2$ formulation outputs smoothly varying heterogeneous material distribution that accommodates multiple functions within a single part. The $L_0$ formulation achieves the computation of sparse material distribution in one step, which is beneficial for additive manufacturing with multi-material printers. Third, we utilize the adjoint method to derive formulae for efficiently computing the gradient of the objective functions, making it possible to quickly solve the optimization problem in the full-dimensional space of materials, which was previously infeasible. The experiments demonstrate the robustness and efficiency of our approach.