Simulating hyperelastic materials with anisotropic stiffness models in a particle-based framework.

We present a particle-based smoothed particle hydrodynamics (SPH) framework for simulating hyperelastic materials with anisotropic stiffness models. While most elastic simulations predominantly rely on mesh-based approaches, such as the Finite Element method, the relationship between Lamé's first parameter and Poisson's ratio complicates the strict enforcement of volume conservation, making it challenging to stabilize simulations for common biological tissues like fat and muscle. In this paper, we couple an implicit divergence-free SPH solver with particle-based deformation gradient computation and apply various elastic energy functions to achieve incompressible elastic simulations. The incompressibility of elastic objects and collisions between different bodies are managed by the implicit SPH algorithm. We further incorporate anisotropic energy functions, constructed from the extrapolation of Cauchy–Green invariants, to introduce anisotropic properties to the objects. By integrating activation and contraction coefficients into the energy functions, particles can simulate muscle contractions and lift heavy objects. Our method can effectively represent elastic objects with varying mechanical properties across different directions and be further employed to mimic muscle contractions. Experiments demonstrate that our approach provides realistic simulations for a wide range of animal and human body movements. [Display omitted] • Leveraging a Lagrangian-based approach for the simulation of anisotropic elasticity. • Integration of Smoothed Particle Hydrodynamics with anisotropic energy functions for advanced modeling. • Adaptable simulation of muscle contraction, effectively mimicking a diverse range of movement behaviors. • Enforcing strict incompressibility in the simulation of muscle-like tissues, ensuring highly accurate representations. [ABSTRACT FROM AUTHOR]