A mortar based approach for the enforcement of periodic boundary conditions on arbitrarily generated meshes

DOI10.1016/j.cma.2014.01.029zbMath1296.74092OpenAlexW2012827683MaRDI QIDQ459311

J. Herrera, D. Rodríguez-Gómez

Publication date: 8 October 2014

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

Full work available at URL: https://doi.org/10.1016/j.cma.2014.01.029

zbMATH Keywords

periodic boundary conditioncomputational homogenizationmortar decomposition methodnon-conform meshes

Mathematics Subject Classification ID

Finite element methods applied to problems in solid mechanics (74S05) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Homogenization and oscillations in dynamical problems of solid mechanics (74Q10)

Related Items (11)

Mesh generation for periodic 3D microstructure models and computation of effective properties ⋮ Formulation and numerical implementation of a variationally consistent multi-scale model based on second-order computational homogenisation at finite strains for quasi-static problems ⋮ A primal formulation for imposing periodic boundary conditions on conforming and nonconforming meshes ⋮ An adaptive global-local approach for phase-field modeling of anisotropic brittle fracture ⋮ Second-order homogenisation of crystal plasticity and martensitic transformation ⋮ Unified periodic boundary condition for homogenizing the thermo-mechanical properties of composites ⋮ On the computational treatment of fully coupled crystal plasticity slip and martensitic transformation constitutive models at finite strains ⋮ On the efficient enforcement of uniform traction and mortar periodic boundary conditions in computational homogenisation ⋮ Multilevel global-local techniques for adaptive ductile phase-field fracture ⋮ A mixed parallel strategy for the solution of coupled multi-scale problems at finite strains ⋮ Comparison of current methods for implementing periodic boundary conditions in multi-scale homogenisation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Mortar contact formulations for deformable-deformable contact: past contributions and new extensions for enriched and embedded interface formulations
• Computational homogenization based on a weak format of micro-periodicity for RVE-problems
• Consistent treatment of boundaries with mortar contact formulations using dual Lagrange multipliers
• On the existence of representative volumes for softening quasi-brittle materials - A failure zone averaging scheme
• Fluid-structure interaction for non-conforming interfaces based on a dual mortar formulation
• Sensitivity of the macroscopic elasticity tensor to topological microstructural changes
• A model reduction method for the post-buckling analysis of cellular microstructures
• A segment-to-segment mortar contact method for quadratic elements and large deformations
• A large deformation mortar formulation of self contact with finite sliding
• The reduced model multiscale method (R3M) for the nonlinear homogenization of hyperelastic media at finite strains
• A variational approach to the theory of the elastic behaviour of multiphase materials
• Computational micro-to-macro transitions for discretized micro-structures of heterogeneous materials at finite strains based on the minimization of averaged incremental energy.
• Two-scale kinematics and linearization for simultaneous two-scale analysis of periodic heterogeneous solids at finite strain.
• Determination of the size of the representative volume element for random composites: Statistical and numerical approach.
• A mortar segment-to-segment contact method for large deformation solid mechanics.
• Simulation of the multi-scale convergence in computational homogenization approaches
• \(FE^2\) multiscale approach for modelling the elastoviscoplastic behaviour of long fibre SiC/Ti composite materials
• Computational micro-to-macro transitions of discretized microstructures undergoing small strains
• Automated modeling for complex woven mesostructures
• An adaptive sub-incremental strategy for the solution of homogenization-based multi-scale problems
• A local finite element implementation for imposing periodic boundary conditions on composite micromechanical models
• Frictionless 2D contact formulations for finite deformations based on the mortar method
• A mesh adaptation procedure for periodic domains
• On micro-to-macro transitions for multi-scale analysis of non-linear heterogeneous materials: unified variational basis and finite element implementation
• Novel boundary conditions for strain localization analyses in microstructural volume elements
• A dual mortar approach for 3D finite deformation contact with consistent linearization
• Computational homogenization for adhesive and cohesive failure in quasi‐brittle solids
• Unilateral non-linear dynamic contact of thin-walled structures using a primal-dual active set strategy
• Multiscale aggregating discontinuities: A method for circumventing loss of material stability
• Toward realization of computational homogenization in practice
• A Mortar Finite Element Method Using Dual Spaces for the Lagrange Multiplier
• Strain-driven homogenization of inelastic microstructures and composites based on an incremental variational formulation
• Computational Contact Mechanics
• Gaussian quadrature formulas for triangles
• Discretization methods and iterative solvers based on domain decomposition
• An approach to micro-macro modeling of heterogeneous materials

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