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The level set method has been widely applied in topology optimization of mechanical structures, primarily for linear materials, but its application to nonlinear hyperelastic materials, particularly for compliant mechanisms, remains largely unexplored. This paper addresses this gap by developing a comprehensive level set-based topology optimization framework specifically for designing compliant mechanisms using neo-Hookean hyperelastic materials. A key advantage of hyperelastic materials is their ability to undergo large, reversible deformations, making them well-suited for soft robotics and biomedical applications. However, existing nonlinear topology optimization studies using the level set method mainly focus on stiffness optimization and often rely on linear results as preliminary approximations. Our framework rigorously derives the shape sensitivity analysis using the adjoint method, including crucial higher-order displacement gradient terms often neglected in simplified approaches. By retaining these terms, we achieve more accurate boundary evolution during optimization, leading to improved convergence behavior and more effective structural designs. The proposed approach is first validated with a mean compliance problem as a benchmark, demonstrating its ability to generate optimized structural configurations while addressing the nonlinear behavior of hyperelastic materials. Subsequently, we extend the method to design a displacement inverter compliant mechanism that fully exploits the advantages of hyperelastic materials in achieving controlled large deformations. The resulting designs feature smooth boundaries and clear structural features that effectively leverage the material's nonlinear properties. This work provides a robust foundation for designing advanced compliant mechanisms with large deformation capabilities, extending the reach of topology optimization into new application domains where traditional linear approaches are insufficient. The developed methodology is expected to provide a timely solution to computational design for soft robotics, flexible mechanisms, and other emerging technologies that benefit from hyperelastic material properties. 

Abstract Intracranial aneurysm rupture causes life-threatening sub-arachnoid hemorrhage. Current endovascular devices like coils, flow diverters, and intravascular implants aim to thrombose the aneurysm but have limitations and varying success rates depending on aneurysm characteristics. We propose a new computational framework integrating CFD and topology optimization to design personalized aneurysm implants. The optimization problem aims to reduce blood flow velocity within the aneurysm while ensuring adequate structural integrity of the implant. The fluid dynamics are governed by the Navier-Stokes equations, while the solid mechanics are described by the linear elasticity equations. A Darcy-Brinkman model is employed to simulate flow through the porous implant in the fluid domain, while the Solid Isotropic Material with Penalization (SIMP) method is used to interpolate between solid and void regions in the structural domain during topology optimization. The objective combines fluid energy dissipation ratio and solid strain energy with spatially varying weights. Global and local volume constraints generate personalized implants with porosity and flow-diverting architectures. The approach is demonstrated on patient-specific aneurysm geometries from rotational angiography. This CFD-driven topology optimization method enables personalized aneurysm implant design to potentially improve occlusion rates and reduce complications compared to current devices. Further studies will validate the optimized designs and investigate their efficacy in vitro and in vivo.