Topology optimization of finite strain viscoplastic systems under transient loads. (25th March 2018)

• Record Type: Journal Article
• Authors: Ivarsson, Niklas; Wallin, Mathias; Tortorelli, Daniel
• Is Part Of: International journal for numerical methods in engineering. Volume 114:Number 13(2018)
• Page Start: 1351
• Page End: 1367
• Publication Date: 2018-03-25
• Subjects: crashworthiness -- discrete adjoint sensitivity analysis -- finite strain -- rate‐dependent plasticity -- topology optimization; Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 620.001518
• DOI: 10.1002/nme.5789
• Languages: English
• ISSNs: 0029-5981

Abstract

Summary: A transient finite strain viscoplastic model is implemented in a gradient‐based topology optimization framework to design impact mitigating structures. The model's kinematics relies on the multiplicative split of the deformation gradient, and the constitutive response is based on isotropic hardening viscoplasticity. To solve the mechanical balance laws, the implicit Newmark‐beta method is used together with a total Lagrangian finite element formulation. The optimization problem is regularized using a partial differential equation filter and solved using the method of moving asymptotes. Sensitivities required to solve the optimization problem are derived using the adjoint method. To demonstrate the capability of the algorithm, several protective systems are designed, in which the absorbed viscoplastic energy is maximized. The numerical examples demonstrate that transient finite strain viscoplastic effects can successfully be combined with topology optimization.