Topology optimization of energy absorbing structures with maximum damage constraint

Abstract

A novel density-based topology optimization framework for plastic energy absorbing structural designs with maximum damage constraint is proposed. This framework enables topologies to absorb large amount of energy via plastic work before failure occurs. To account for the plasticity and damage during the energy absorption, a coupled elastoplastic ductile damage model is incorporated with topology optimization. Appropriate material interpolation schemes are proposed to relax the damage in the low-density regions while still ensuring the convergence of Newton-Raphson solution process in the nonlinear finite element analyses. An effective method for obtaining path-dependent sensitivities of the plastic work and maximum damage via adjoint method is presented, and the sensitivities are verified by the central difference method. The effectiveness of the proposed methodology is demonstrated through a series of numerical examples.to the recent review studies [12,14]. Among these available methods, the density-based method is perhaps the most popular one, which is also the subject of this study.Most of the studies concerning density-based topology optimization are based on linear or nonlinear elastic material, with applications to stiffness designs, compliant mechanisms, and fundamental frequency designs [10,13,[22][23][24][25]. Energy absorption is an irreversible process and is accompanied by various inelastic material dependent mechanisms. To account for such inelastic material response, inelastic constitutive models should be considered in topology optimization for designing energy absorbing structures. However, there are limited studies in topology optimization considering material nonlinearities. An attempt to include von Mises elastoplasticity in topology optimization was first made by Swan and Kosaka [26], wherein interpolation schemes based on Voigt-Reuss type mixing rules were used. Maute et al. [27] and Schwarz et al.[28] considered a Solid Isotropic Material with Penalization (SIMP)-like interpolation [29] with von Mises plasticity for maximizing ductility in topology optimization and an approximate sensitivity analysis was utilized. Later on, Bogomolny and Amir [30] combined the Drucker-Prager elastoplasticity with topology optimization for conceptual maximum stiffness reinforced concrete structure designs and the adjoint method proposed by Michaleris et al. [31] was used for the sensitivity analysis. Kato et al. [32] eliminated the simplifications used in references [27,28] to obtain more accurate analytical sensitivities for multiphase material topology optimization with von Mises elastoplasticity. Nakshatrala and Tortorelli [33] proposed a topology optimization framework for energy dissipation maximization subjected to impact loadings wherein the material response was modeled with von Mises plasticity. Wallin et al. [34] extended the von Mises plasticity to finite strain scenario for maximum plastic work designs. Recently, the authors also incorporated anisotropic Hoffmann plasticity model in topology o...

Design of dissipative multimaterial viscoelastic‐hyperelastic systems at finite strains via topology optimization

“…Extending the topology optimization formulations using time‐domain analysis with inelastic materials is not trivial due to the challenges in obtaining consistent path‐dependent response sensitivities. Although the recipes for path/time‐dependent sensitivity analysis of inelastic structures can be traced back to the 1990s, the successful incorporation of these methods in topology optimization was not achieved until recent years . In applications with viscoelastic materials, James and Waisman examined the structural topology optimization considering the time‐dependent creep behavior of viscoelastic materials while optimizing structural stiffness.…”

“…Although the recipes for path/time-dependent sensitivity analysis of inelastic structures can be traced back to the 1990s, 13 the successful incorporation of these methods in topology optimization was not achieved until recent years. [14][15][16][17] In applications with viscoelastic materials, James and Waisman 18 examined the structural topology optimization considering the time-dependent creep behavior of viscoelastic materials while optimizing structural stiffness. Yun and Youn 19 carried out a multimaterial topology optimization in the time domain for energy dissipation designs by combining linear viscoelastic and elastic materials.…”

A unified framework for nonlinear path‐dependent sensitivity analysis in topology optimization

“…12,13 In these cases, the design sensitivity calculation is simplified, as the system behavior is path independent. In recent years, there has been an increased effort to include advanced inelastic material behavior within topology optimization in order to allow for the consideration of design applications such as plastic energy dissipation, [21][22][23] damage/fracture mitigation, [24][25][26][27] constraints on plastic yielding, 28 viscoelastic creep response, 29 and inelastic wave propagation, 30 among others. Unlike with linear elastic or hyperelastic solids, however, when using inelastic material models, the calculation of design sensitivity is a nontrivial task.…”

“…An alternative sensitivity analysis method was proposed by Kato et al 44 for elastoplastic multiphase composite topology optimization and was also demonstrated to be accurate as well as efficient. However, this method is not general and is limited to certain special cases as described in the work of Kato et al 44 More recent topology optimization studies utilizing inelastic materials and dynamics perform sensitivity analysis within the adjoint framework proposed by Michaleris et al 38 (see, eg, other works [21][22][23][25][26][27][28]30,45,46 ). However, these studies present sensitivity calculations on a case-by-case basis for the problems considered therein and often approach and implement sensitivity analyses in different ways.…”

Topology optimization with incompressible materials under small and finite deformations using mixed u/p elements

“…Topology optimization is a powerful design tool that has been used in numerous applications, including stiffness design, frequency design, and design for energy dissipation, among many others. [1][2][3][4][5][6][7][8][9][10] Many engineering materials exhibit nearly incompressible behavior when undergoing deformation, including rubber-like materials, biological soft tissues, metals undergoing plastic flow, etc. [11][12][13][14][15] Incompressibility is manifested as an inability to undergo volumetric deformations, and neglecting material incompressibility during analysis can lead to large discrepancies between predicted and measured behaviors.…”