A Particle-Driven Nonlinear Design Framework for Hyperelastic Structures with Large-Scale Migration Using an Implicit Isogeometric Material Point Method

Qixuan Zhong; Liang Gao; Jie Gao

doi:10.1016/j.eng.2026.07.034

Engineering ›› :202607034 DOI: 10.1016/j.eng.2026.07.034

research-article

A Particle-Driven Nonlinear Design Framework for Hyperelastic Structures with Large-Scale Migration Using an Implicit Isogeometric Material Point Method

Qixuan Zhong ^a
, Liang Gao ^a^,^*
, Jie Gao ^b^,^c^,^*

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Abstract

The topology optimization of hyperelastic structures undergoing large deformation has attracted increasing attention in emerging fields such as soft robotics, flexible electronics, and biotechnology. However, strong geometric and material nonlinearities often cause numerical instability, mesh distortion, and convergence failure during optimization. This study develops a particle-driven topology optimization framework for hyperelastic structures based on large-scale particle migration. In this framework, particle positions serve as the primary design variables that govern material aggregation and the formation of load-bearing members, whereas material densities are treated as secondary variables. This position-driven mechanism enables material redistribution through large spatial migration rather than through density updates with limited particle movement, making it well suited to hyperelastic large-deformation problems. To improve nonlinear solution stability, an implicit isogeometric material point method coupled with the Newton–Raphson scheme and an isogeometric fictitious-domain interpolation scheme are introduced to enhance convergence under severe deformation. The optimization formulation is then derived by backward sensitivity transfer with respect to particle positions and material densities, together with an adaptive particle update strategy. Several two- and three-dimensional numerical examples demonstrate the effectiveness and robustness of the proposed framework and clarify the role of large-scale particle migration in hyperelastic topology optimization.

Keywords

Hyperelastic structures / Topology optimization / Nonlinear design / Isogeometric material point method / Particle migration

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Qixuan Zhong, Liang Gao, Jie Gao. A Particle-Driven Nonlinear Design Framework for Hyperelastic Structures with Large-Scale Migration Using an Implicit Isogeometric Material Point Method. Engineering 202607034 DOI:10.1016/j.eng.2026.07.034

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