Topology optimization of multiscale elastoviscoplastic structures

Abstract

Summary This paper extends current concepts of topology optimization to the design of structures made of nonlinear microheterogeneous materials. The objective is to maximize the macroscopic structural stiffness for a prescribed material volume usage while accounting for the nonlinearity and the microstructure of the material. The resulting design problem considers two scales: the macroscopic scale at which the optimization is performed and the microscopic scale at which the material heterogeneities and the nonlinearities are observed. The topology optimization at the macroscopic scale is performed by means of the bi‐directional evolutionary structural optimization method. The solution of the macroscopic boundary value problem requires as inputs the effective constitutive response with full consideration of the microstructure. While computational homogenization methods such as the FE2 method could be used to solve the nonlinear multiscale problem, the associated numerical expense (CPU time and memory) is highly unacceptable. In order to regain the computational feasibility of the computational scale transition, a recent model reduction technique of the authors is employed: the potential‐based reduced basis model order reduction with graphics processing unit acceleration. Numerical examples show the efficiency of the resulting nonlinear two‐scale designs. The impact of different load amplitudes on the design is examined. Copyright © 2015 John Wiley & Sons, Ltd.

Topology Optimization Applications on Engineering Structures

“…Wang et al [118] used to optimize constrained damping layer structure. Fritzen et al [119] taken nonlinear elastoviscoplastic microscopic RVE into account at all points of the macroscopic design domain by using BESO. Later, Xia et al [120] introduced a damping scheme on sensitivity numbers to the same approach.…”

Current and future trends in topology optimization for additive manufacturing

“…More recently, Xia et al proposed a BESO based fracture resistant topology optimization that accounts for the complete fracturing process in quasi-brittle composites [205]. For the ones dealing with viscoelasticity and viscoplasticity, the readers are referred to the references [206][207][208][209][210][211][212]. The optimization of discrete structures, like trusses or beams, considering material and geometric nonlinearities were discussed in Choi and Santos [213], Ohsaki and Arora [214], and Ohsaki and Ikeda [215].…”

Topology optimization for maximizing the fracture resistance of quasi-brittle composites

“…The extended bi-directional evolutionary structural optimization (BESO) method developed in [32,33] for the design of elastoplastic structures is adopted in this work to carry out topology optimization. Composites made of two material phases, matrix phase and inclusion phase, are considered.…”

“…In this work, the extended bi-directional evolutionary structural optimization (BESO) method recently developed by the first author and his collaborators in [32,33] for the design of elastoplastic structures is adopted to carry out topology optimization. As compared to continuously defined density-based methods, the ESO-type methods [34][35][36][37][38] naturally avoid the definition of supplementing pseudo-relationships between fictitious materials and fracture toughness for the sake of their discrete nature, resulting in clear physical interpretation and algorithmic advantages.…”