2021/01/31 by Nils Lange, Geralf Hütter, Bjöern Kiefer +1 · 1 citation
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Algorithm #Applied mathematics #Benchmark (surveying) #Boundary (topology) #Boundary value problem #Code (set theory) #Composite Material Mechanics #Computational science #Computer science #Mathematical analysis #Mathematical optimization #Mathematics #Newton's method #Nonlinear system #Numerical methods in engineering #Physics #Scale (ratio) #Scheme (mathematics) #cs.CE #cs.NA #math.NA #physics.comp-ph
paper · pdf · doi:10.1016/j.cma.2021.113886
published as Computer Methods in Applied Mechanics and Engineering 382 (2021), 113886
arxiv created 2021/04/06 · openalex publication_date 2021/05/06 · arxiv updated 2021/05/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The FE2 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 FE2 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 FE2 algorithm is implemented into the commercial FE code Abaqus. Benchmark examples demonstrate that the monolithic scheme saves up to ~60% of computational costs.