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Design of dissipative multimaterial viscoelastic‐hyperelastic systems at finite strains via topology optimization
Author(s) -
Zhang Guodong,
Khandelwal Kapil
Publication year - 2019
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.6083
Subject(s) - hyperelastic material , topology optimization , viscoelasticity , finite element method , stiffness , dissipation , dissipative system , context (archaeology) , finite strain theory , topology (electrical circuits) , computer science , materials science , mathematics , structural engineering , engineering , physics , composite material , paleontology , quantum mechanics , combinatorics , biology , thermodynamics
Summary This study focuses on the topology optimization framework for the design of multimaterial dissipative systems at finite strains. The overall goal is to combine a soft viscoelastic material with a stiff hyperelastic material for realizing optimal structural designs with tailored damping and stiffness characteristics. To this end, several challenges associated with incorporating finite‐deformation viscoelastic‐hyperelastic materials in a multimaterial design framework are addressed. This includes consideration of a thermodynamically consistent finite‐strain viscoelasticity model for simulating energy dissipation together with F‐bar finite elements for handling material incompressibility. Moreover, an effective multimaterial interpolation scheme is proposed, which preserves the physics of material mixtures in the context of density‐based topology optimization. A numerically accurate analytical design sensitivity calculation is also presented using a path‐dependent adjoint method. Furthermore, both prescribed‐load and prescribed‐displacement boundary conditions are considered in the optimization formulations, together with various strategies for controlling stiffness. As demonstrated by the numerical examples, the use of the stiffer hyperelastic material phase in a design not only improves stiffness but also increases energy dissipation capacity. Moreover, with the finite‐deformation theory, the effect of the loading magnitude on the optimized designs can be observed.