A direct Jacobian total Lagrangian explicit dynamics finite element algorithm for real-time simulation of hyperelastic materials

TL;DR

This paper introduces a novel explicit finite element algorithm for real-time hyperelastic material simulation that uses Jacobian-based formulations to reduce computational cost and improve speed, especially with GPU acceleration.

Contribution

The paper presents a Jacobian-based explicit dynamics finite element algorithm that simplifies force calculations and enhances computational efficiency for real-time nonlinear mechanics simulations.

Findings

Achieved up to 121.72x speedup in tetrahedral meshes with GPU.

Reduced CPU solution times to 70-88% of existing methods.

Demonstrated application in neurosurgical brain deformation simulation.

Abstract

This paper presents a novel direct Jacobian total Lagrangian explicit dynamics (DJ-TLED) finite element algorithm for real-time nonlinear mechanics simulation. The nodal force contributions are expressed using only the Jacobian operator, instead of the deformation gradient tensor and finite deformation tensor, for fewer computational operations at run-time. Owing to this proposed Jacobian formulation, novel expressions are developed for strain invariants and constant components, which are also based on the Jacobian operator. Results show that the proposed DJ-TLED consumed between 0.70x and 0.88x CPU solution times compared to state-of-the-art TLED and achieved up to 121.72x and 94.26x speed improvements in tetrahedral and hexahedral meshes, respectively, using GPU acceleration. Compared to TLED, the most notable difference is that the notions of stress and strain are not explicitly visible in the proposed DJ-TLED but embedded implicitly in the formulation of nodal forces. Such a force formulation can be beneficial for fast deformation computation and can be particularly useful if the displacement field is of primary interest, which is demonstrated using a neurosurgical simulation of brain deformations for image-guided neurosurgery. The present work contributes towards a comprehensive DJ-TLED algorithm concerning isotropic and anisotropic hyperelastic constitutive models and GPU implementation. The source code is available at https://github.com/jinaojakezhang/DJTLED.