Two-scale homogenization of electromechanically coupled boundary value problems

DOI10.1007/s00466-012-0715-9zbMath1398.74106OpenAlexW170719365MaRDI QIDQ1933490

Jörg Schröder, Marc-André Keip

Publication date: 24 January 2013

Published in: Computational Mechanics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00466-012-0715-9

zbMATH Keywords

homogenizationeffective propertiespiezoelectricityelectromechanical couplingelectrostriction\(FE^{2}\)-method

Mathematics Subject Classification ID

Inhomogeneity in solid mechanics (74E05) Finite element methods applied to problems in solid mechanics (74S05) Effective constitutive equations in solid mechanics (74Q15) Electromagnetic effects in solid mechanics (74F15) Micromechanical theories (74A60) Homogenization in equilibrium problems of solid mechanics (74Q05)

Related Items

Unified treatment of microscopic boundary conditions and efficient algorithms for estimating tangent operators of the homogenized behavior in the computational homogenization method ⋮ Homogenization in micro-magneto-mechanics ⋮ Experimental and numerical investigations of the electro-mechanical response of particle filled elastomers. II: Continuum modeling approach ⋮ Two-scale computational homogenization of electro-elasticity at finite strains ⋮ Multi-field variational formulations and mixed finite element approximations for electrostatics and magnetostatics ⋮ An adaptive \(\mathrm{FE}^2\) approach for fiber-matrix composites ⋮ Homogenization and multiscale stability analysis in finite magneto-electro-elasticity. Application to soft matter EE, ME and MEE composites ⋮ Algorithmic two-scale transition for magneto-electro-mechanically coupled problems, FE \({}^2\)-scheme: localization and homogenization ⋮ Nonlinear modeling and finite element simulation of magnetoelectric coupling and residual stress in multiferroic composites ⋮ A multiscale approach to the computational characterization of magnetorheological elastomers ⋮ Computation of non‐linear magneto‐electric product properties of 0–3 composites ⋮ Variational modeling and homogenization in dissipative magneto‐mechanics ⋮ Coordinate‐invariant phase field modeling of ferro‐electrics, part II: Application to composites and poly‐crystals ⋮ Homogenization and multiscale stability analysis in finite magneto‐electro‐elasticity ⋮ An electro‐elastic phase‐field model for nematic liquid crystal elastomers based on Landau‐de‐Gennes theory ⋮ Computational homogenization of higher‐order continua ⋮ Homogenization of Elastic Dielectric Composites with Rapidly Oscillating Passive and Active Source Terms ⋮ Electro-mechanical actuation modulates fracture performance of soft dielectric elastomers ⋮ A representative volume element model to evaluate the effective properties of flexoelectric nanocomposite ⋮ Scale transition and residual fields in modeling of polycrystalline ferroelectrics based on the internal energy potential and a Voigt-Reuss approximation ⋮ Mixed virtual element formulations for incompressible and inextensible problems ⋮ FEM-CM as a hybrid approach for multiscale modeling and simulation of ferroelectric boundary value problems ⋮ Efficient multiscale modeling of heterogeneous materials using deep neural networks ⋮ On the two-potential constitutive modeling of dielectric elastomers ⋮ Computation of effective piezoelectric properties of stratified composites and application to wave propagation analysis ⋮ Computational homogenization in dissipative electro-mechanics of functional materials ⋮ Multi-physics computational grains (MPCGs) for direct numerical simulation (DNS) of piezoelectric composite/porous materials and structures ⋮ Computational stability analysis of periodic electroactive polymer composites across scales ⋮ A multiscale FE-FFT framework for electro-active materials at finite strains ⋮ Product properties of a two-phase magneto-electric composite: synthesis and numerical modeling ⋮ Numerical homogenisation of gradient materials ⋮ Computational homogenization of fibrous piezoelectric materials

Cites Work

• Unnamed Item
• A sub-stepping scheme for multi-scale analysis of solids
• Multi-scale computational homogenization: trends and challenges
• Two-scale kinematics and linearization for simultaneous two-scale analysis of periodic heterogeneous solids at finite strain.
• Invariant formulation of the electromechanical enthalpy function on transversely isotropic piezoelectric materials
• Computational micro-to-macro transitions of discretized microstructures undergoing small strains
• Effective properties of composite materials with periodic microstructure: A computational approach
• Computational homogenization analysis in finite plasticity. Simulation of texture development in polycrystalline materials
• Prediction of the mechanical behavior of nonlinear heterogeneous systems by multi-level finite element modeling
• An analytical and numerical approach for calculating effective material coefficients of piezoelectric fiber composites
• Elastic properties of reinforced solids: Some theoretical principles
• Multi‐scale constitutive modelling of heterogeneous materials with a gradient‐enhanced computational homogenization scheme
• Multi‐scale modeling of heterogeneous structures with inelastic constitutive behaviour
• A class of general algorithms for multi-scale analyses of heterogeneous media