Diagonal Hessian Proxy for Efficient Elastic Simulation Using Peridynamics.

Area of Science:

• Computational physics
• Computer graphics
• Materials science

Background:

• Meshless methods are crucial for deformable simulation, but existing techniques like shape matching struggle with generic elastic models.
• Peridynamics offers versatility for material behavior but faces challenges with Hessian matrix size, leading to inefficiency and accuracy loss.

Purpose of the Study:

• To develop an efficient and robust peridynamics-based solver for simulating generic elastic models in meshless integration.
• To overcome the limitations of existing meshless solvers in handling complex material behaviors.

Main Methods:

• Proposed an efficient first-order Hessian proxy using stress tensor decomposition for stable and parallelizable computations.
• Introduced strain limiting between peridynamics bonds to enhance stability, especially for hyperelastic models.
• Developed a GPU-implementable algorithm with nested iteration loops for strain limiting and elastic Jacobians.

Main Results:

• The proposed solver demonstrates superior efficiency and faster convergence compared to alternative numerical methods.
• Achieved robust simulation of a wide range of elastic constitutive models in various scenarios.
• The method proved effective in preventing tensile instability in meshless integration.

Conclusions:

• The developed peridynamics solver offers a practical and effective solution for simulating elasticity using meshless integration.
• The approach significantly enhances computational performance and stability for complex deformable simulations.
• This work advances the capabilities of meshless simulation for generic elastic materials.