2024/01/29 by P. Areias, Charles dos Santos, Areias, Pedro +5
Engineering · Physics and Astronomy · #FOS: Mathematics #Fluid Dynamics Simulations and Interactions #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Numerical methods in engineering
paper · pdf · doi:10.48550/arxiv.2401.15962
openalex publication_date 2024/01/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we introduce an implicit staggered algorithm for crystal plasticity finite element method (CPFEM) which makes use of dynamic relaxation at the constitutive integration level. An uncoupled version of the constitutive system consists of a multi-surface flow law complemented by an evolution law for the hardening variables. Since a saturation law is adopted for hardening, a sequence of nonlinear iteration followed by a linear system is feasible. To tie the constitutive unknowns, the dynamic relaxation method is adopted. A Green-Nagdhi plasticity model is adopted based on the Hencky strain calculated using a [ 2/2 ] Padé approximation. For the incompressible case, the approximation error is calculated exactly. A enhanced-assumed strain (EAS) element technology is adopted, which was found to be especially suited to localization problems such as the ones resulting from crystal plasticity plane slipping. Analysis of the results shows significant reduction of drift and well defined localization without spurious modes or hourglassing.