Parallel Finite Element Algorithm for Large Elastic Deformations: Program Development and Validation

Abstract

A comprehensive understanding of large elastic deformation, characterized by its nonlinear strain and stress properties, is vital for examining tectonic deformation across geological timescales. We employ the PFELAC software 2.2 platform to automate the generation of parallel elastic large deformation finite element codes. By writing only a minimal amount of fundamental finite element language rooted in the principle of virtual work, we significantly enhance the program development efficiency. The accuracy of the finite element method is rigorously validated through comparisons with analytical solutions from two idealized models. Furthermore, we investigate the influences of mesh density and CPU core count on computational performance. As the number of cores increases, the parallel speedup ratio rises, but the parallel efficiency decreases. For 16 cores, the speedup ranges from 11.36 to 12.24, with a parallel efficiency between 0.71 and 0.77. In contrast, for 64 cores, the speedup is between 24.70 and 34.78, while the parallel efficiency drops to between 0.39 and 0.43. The program’s application to simulate crustal fold deformation reveals marked distinctions between large and small deformation theories, emphasizing the critical importance of large deformation theory in tectonic studies.

Keywords

• large deformation theory
• small deformation theory
• parallel finite element program
• fold deformation
• green strain
• Cauchy stress