An efficient monolithic solution scheme for FE${}^2$ problems

Abstract

The FE${}^2$ method is a very flexible but computationally expensive tool for multiscale simulations. In conventional implementations, the microscopic displacements are iteratively solved for within each macroscopic iteration loop, although the macroscopic strains imposed as boundary conditions at the micro-scale only represent estimates. In order to reduce the number of expensive micro-scale iterations, the present contribution presents a monolithic FE${}^2$ scheme, for which the displacements at the micro-scale and at the macro-scale are solved for in a common Newton-Raphson loop. In this case, the linear system of equations within each iteration is solved by static condensation, so that only very limited modifications to the conventional, staggered scheme are necessary. The proposed monolithic FE${}^2$ algorithm is implemented into the commercial FE code Abaqus. Benchmark examples demonstrate that the monolithic scheme saves up to ~60% of computational costs.

References in corpus (2)

• A hybrid approach to simulate the homogenized irreversible elastic-plastic deformations and damage of foams by neural networks
• Micromorphic Computational Homogenization for Mechanical Metamaterials with Patterning Fluctuation Fields

Cited by in corpus (4)

• FE${}^{\text{ANN}}$ $-$ An efficient data-driven multiscale approach based on physics-constrained neural networks and automated data mining
• Moving window techniques to model shock wave propagation using the concurrent atomistic-continuum method
• Micromorphic FE${}^2$ Simulation of Plastic Deformations of Foam Structures
• Empirical Hyper Element Integration Method (EHEIM) with Unified Integration Criteria for Efficient Hyper Reduced FE${}^2$ Simulations