Gurson–Tvergaard–Needleman model guided fracture‐resistant structural designs under finite deformations

Abstract

A finite strain shear modified Gurson–Tvergaard–Needleman (GTN) model based on multiplicative elastoplasticity, together with its implementation details, is presented. This GTN model which can simulate the loss of load‐carrying capacity of porous metals through nucleation, growth, shearing, and coalescence of voids is incorporated in an optimization framework for designing structures with optimal plastic energy dissipation capacity while satisfying prescribed constraints on material usage and damage. An adjoint method‐based analytical path‐dependent sensitivity analysis is presented that can be used with gradient‐based optimization algorithms. Using the proposed topology optimization formulations, the optimized designs exhibit well‐constrained fracture at the design displacements. Ultimate performance analyses of the optimized designs demonstrate that the fracture‐resistant designs can have higher ductility, ultimate strength as well as improved energy dissipation, as compared to the designs guided by von Mises plasticity where no fracture mechanisms are modeled. Moreover, due to finite deformations, a fracture can initiate at multiple locations and critical fracture locations can change during the loading process. In addition, different failure modes are revealed from different optimized designs under large deformations.

Topology Optimization to Fracture Resistance: A Review and Recent Developments

“…Similar approaches were developed by the same authors in [153] where the plastic work was maximized under damage and volume constraints, and in [154] using a nonlocal damage model. More recently, Zhang and Khandelwal [155] extended such strategy to a finite strains Gurson-Tvergaard-Needleman plasticity model within a SIMP TO framework, where the plastic work was maximized under damage and volume constraints (see Fig. 11)…”

Geotechnical Characteristic Assessments of Floodplain Soils Using SCPTU Data in Nanjing, China

“…Moreover, the meaning of failure can be quite diverse depending on the context. For example, the failure can be related to the loss of structural stability [10], the emergence of plasticity in the material [11], and the degradation of the material mechanical properties [12,13], among others. In this study, attention is focused on structures with hyperelastic materials that can sustain large strains within the elastic domain.…”

“…This study focuses on the topology optimization of structures with minimized end compliance while satisfying material volume and nonlinear stability constraints. The main contributions of this work are: (a) A novel strategy for removing spurious buckling modes based on the construction of a pseudo-mass matrix is proposed; (b) A new formulation of nonlinear stability analysis in topology optimization is considered by directly computing the eigenvalues of the tangent stiffness matrix where no other approximations are made; (c) The optimization problem is formulated to incorporate a fixed number of clusters of eigenvalues rather than a fixed number of eigenvalues so that it can handle arbitrary multiplicities of eigenvalues during the optimization process; (d) the adaptive linear energy interpolation proposed in Zhang et al [16] which has shown robust performance in handling mesh distortions in the previous studies [13,43,44] is incorporated in the proposed framework; and (e) Finally, the post-analysis on the B-spline fitted optimized topologies is carried out to evaluated the stability performance of the optimized structures.…”