Multimaterial topology optimization for finite strain elastoplasticity: theory, methods, and applications

2025-02-04

AI Summary

This study addresses the multi-objective performance customization of plastically deformable metallic materials under finite-strain elastoplastic large deformations. Method: We propose a topology optimization framework that concurrently optimizes structural configuration and multimaterial distribution. A novel multiphase material interpolation model is introduced—first to accommodate isochoric plastic flow and history dependence. An adjoint-based inverse method, integrated with automatic differentiation, is developed to efficiently compute complex design sensitivities, thereby elucidating toughening mechanisms associated with hardening-mode transitions and stress-rotation zones. The framework is rigorously grounded in finite-strain elastoplastic constitutive theory and gradient-based optimization. Results: Validated on 2D/3D energy-dissipating dampers, load-bearing beams, impact-resistant bumpers, and cold-formed panels, the method significantly enhances the synergy of stiffness, strength, and structural toughness across diverse material combinations and hardening behaviors.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

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Abstract

Plasticity is inherent to many engineering materials such as metals. While it can degrade the load-carrying capacity of structures via material yielding, it can also protect structures through plastic energy dissipation. To fully harness plasticity, here we present the theory, method, and application of a topology optimization framework that simultaneously optimizes structural geometries and material phases to customize the stiffness, strength, and structural toughness of designs experiencing finite strain elastoplasticity. The framework accurately predicts structural responses by employing a rigorous, mechanics-based elastoplasticity theory that ensures isochoric plastic flow. It also effectively identifies optimal material phase distributions using a gradient-based optimizer, where gradient information is obtained via a reversed adjoint method to address history dependence, along with automatic differentiation to compute the complex partial derivatives. We demonstrate the framework by optimizing a range of 2D and 3D elastoplastic structures, including energy-dissipating dampers, load-carrying beams, impact-resisting bumpers, and cold working profiled sheets. These optimized multimaterial structures reveal important mechanisms for improving design performance under large deformation, such as the transition from kinematic to isotropic hardening with increasing displacement amplitudes and the formation of twisted regions that concentrate stress, enhancing plastic energy dissipation. Through the superior performance of these optimized designs, we demonstrate the framework's effectiveness in tailoring elastoplastic responses across various spatial configurations, material types, hardening behaviors, and combinations of candidate materials. This work offers a systematic approach for optimizing next-generation multimaterial structures with elastoplastic behaviors under large deformations.

Problem

• Optimizes structural geometries and material phases
• Customizes stiffness, strength, and structural toughness
• Addresses finite strain elastoplasticity in engineering materials

Innovation

• Multimaterial topology optimization
• Finite strain elastoplasticity theory
• Gradient-based optimizer with adjoint method