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

This article 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 operator, instead of deformation gradient tensor and tensor, fewer computational operations at run-time. Owing to this proposed formulation, expressions developed strain invariants constant components, which also based on operator. Results show that DJ-TLED consumed between 0.70× 0.88× CPU solution times compared state-of-the-art TLED achieved up 121.72× 94.26× speed improvements in tetrahedral hexahedral meshes, respectively, GPU acceleration. Compared TLED, most notable difference is notions stress not explicitly visible but embedded implicitly formulation forces. Such can be beneficial fast computation particularly useful if displacement field primary interest, demonstrated neurosurgical simulation brain deformations image-guided neurosurgery. present work contributes towards comprehensive concerning isotropic anisotropic hyperelastic constitutive models implementation.