Strength design of porous materials using B-spline based level set method

Abstract

The inverse homogenization method can tailor some mechanical and physical effective properties by laying out materials in a periodic representative volume element. However, studies on strength design are yet to be developed because of the difficulties in numerically retrieving its value. Unlike traditional asymptotic homogenization, the fast Fourier transform-based homogenization method based on the augmented Lagrangian approach uses a Green operator in the frequency domain to replace time-consuming finite element analysis and inherently meet the periodic boundary conditions. Thus, it is developed in this work to retrieve material strength in terms of the von Mises yield criterion. The zero-level contour of a linear combination of cubic B-spline basis functions with repeated knots is used to represent the microstructure profile in the design of material strength. The effective strength or its squared difference with a prescribed target is minimized within the framework of the reaction diffusion-based B-spline level set method. The filtered, non-consistent discrete Green operator is adopted to avoid slow convergence of porous material. Examples of porous material demonstrate that the proposed method guarantees surface smoothness, optimization flexibility, and structural periodicity in strength design.