A Neo-Yeoh hyperelastic interpolation model for stable multi-material topology optimization under geometric nonlinearity

Current mainstream methods for addressing numerical instability in geometrically nonlinear topology optimization typically require mesh duplication and manual manipulation of the tangent stiffness matrix. Mesh duplication significantly hinders computing efficiency, while manual manipulation restricts their applicability in commercial solvers. To address these limitations, this study proposes a Neo-Yeoh hyperelastic interpolation (NYHI) material model to address numerical instability in geometrically nonlinear topology optimization. Integrating Neo-Hookean and second-order Yeoh hyperelastic materials with a Heaviside function, the model selectively enhances shear resistance in low-density regions while maintaining accurate deformation modeling in solid elements. The topology optimization framework for multi-material problems considering geometric nonlinearity is proposed. Numerical tests on single- and multi-material structures, including cantilever and two-side clamped beams, demonstrate the model's efficacy in suppressing distortion in low-density regions and enabling stable optimization under large deformations. Key parameters in the NYHI material model are systematically analyzed, revealing their critical roles in balancing optimization stability and structural performance. The proposed model successfully addresses numerical instability issues with a single mesh, leading to a significant simplification of the topology optimization formulation.