Design of fracture resistant energy absorbing structures using elastoplastic topology optimization

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

“…However, as long as the numerical differentiation is consistent with the underlying numerical implementation, the errors in sensitivity analyses are minimal. As has been shown in previous studies by Zhang et al, 22 Li et al, 25 and Li and Khandelwal, 27 in the sensitivity verification above, and as will be shown throughout this section, high accuracy is preserved during the adjoint sensitivity analysis.…”

“…Thus, damage is an important physical phenomenon to be considered in the analysis and design of elastoplastic structures. 25,27 This phenomenon can be considered by using coupled damage models, which describe the evolution of both plasticity and damage. 56 However, if a local description of damage is used in simulating material softening, the numerical solution obtained from FEA using these models reveals pathological dependence on the size and orientation of the underlying finite element mesh.…”

“…Finally, the length scale parameter is subject to interpolation following e = l e , whereas the local accumulated plastic strain in F e int, (see Equation (A.8) in Appendix A) is scaled by e , with p = p l = 3. The total plastic work W p (Equations (27) and (28)) is maximized, and all problems are subject to a volume fraction constraint, which limits the volume of material in the domain to a fraction V f = 0.5. Initial designs consist of a Figure 15 shows the optimized topologies and convergence plots for each of the four problem types considered.…”

“…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.…”