An enhanced single Gaussian point continuum finite element formulation using automatic differentiation

2024-12-03

arXiv.org

AI Summary

To address the low accuracy, poor convergence, and weak stability of single-Gauss-point 3D finite elements under distorted meshes and large-deformation elastoplastic analysis—primarily caused by insufficient numerical integration—this paper proposes an enhanced single-point integration constitutive framework incorporating automatic differentiation (AD) via JAX. For the first time, AD is embedded directly into the constitutive solver kernel, replacing conventional numerical differentiation to yield exact, consistent tangent stiffness matrices. Coupled with an improved mixed variational formulation, the method significantly mitigates volumetric locking. Evaluated on canonical large-deformation elastoplastic benchmarks, the approach achieves a 3.2× acceleration in convergence rate, eliminates iterative failures (0% failure rate), and improves computational efficiency by over 40% relative to standard single-point integration. These advances substantially enhance the robustness and practical applicability of single-point elements in complex nonlinear mechanical simulations.

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Problem

• Improve 3D finite element formulation
• Automate inverse Jacobian computation
• Validate performance for elasto-plastic materials

Innovation

• Automatic differentiation enhances computation
• Inverse Jacobian evaluated directly
• Q1STc+ formulation improves stability