A Newton solver for micromorphic computational homogenization enabling multiscale buckling analysis of pattern-transforming metamaterials

DOI10.1016/j.cma.2020.113333zbMath1506.74332arXiv2008.12850OpenAlexW3082546758MaRDI QIDQ2020909

Martin Doškář, S. E. H. M. van Bree, Marc G. D. Geers, Ondřej Rokoš, Ron H. J. Peerlings

Publication date: 26 April 2021

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2008.12850

zbMATH Keywords

Newton methodbifurcation analysiscomputational homogenizationmicromorphic continuummechanical metamaterials

Mathematics Subject Classification ID

Nonlinear elasticity (74B20) Bifurcation and buckling (74G60) Homogenization and oscillations in dynamical problems of solid mechanics (74Q10)

Related Items (1)

Second-order computational homogenisation enhanced with non-uniform body forces for non-linear cellular materials and metamaterials

Uses Software

• PLCP
• SQPlab

Cites Work

• Study of efficient homogenization algorithms for nonlinear problems
• Mechanics of deformation-triggered pattern transformations and superelastic behavior in periodic elastomeric structures
• Multi-scale computational homogenization: trends and challenges
• Computational micro-to-macro transitions for discretized micro-structures of heterogeneous materials at finite strains based on the minimization of averaged incremental energy.
• Appropriate number of unit cells in a representative volume element for micro-structural bifurcation encountered in a multi-scale modeling
• Microscopic symmetric bifurcation condition of cellular solids based on a homogenization theory of finite deformation
• Computational micro-to-macro transitions of discretized microstructures undergoing small strains
• Post-buckling analysis of elastic honeycombs subject to in-plane biaxial compression.
• Multi-scale second-order computational homogenization of multi-phase materials: a nested finite element solution strategy
• Micromorphic computational homogenization for mechanical metamaterials with patterning fluctuation fields
• Generalized continua and non-homogeneous boundary conditions in homogenisation methods
• On multiscale FE analyses of heterogeneous structures: from homogenization to multigrid solvers
• Numerical optimization. Theoretical and practical aspects. Transl. from the French
• An approach to micro-macro modeling of heterogeneous materials

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