Model reduction by mean-field homogenization in viscoelastic composites. I. Primal theory

DOI10.1098/rspa.2020.0407zbMath1472.74181OpenAlexW3095640695WikidataQ102325411 ScholiaQ102325411MaRDI QIDQ5161127

Martín I. Idiart, Pierre Suquet, Noël Lahellec

Publication date: 29 October 2021

Published in: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences (Search for Journal in Brave)

Full work available at URL: https://europepmc.org/articles/pmc7655739

zbMATH Keywords

compositesthermodynamicshomogenizationvariational methodsviscoelasticitymathematical modellingmechanics

Mathematics Subject Classification ID

Linear constitutive equations for materials with memory (74D05) Homogenization in equilibrium problems of solid mechanics (74Q05)

Related Items

The elastic properties of dilute solid suspensions with imperfect interfacial bonding: variational approximations versus full-field simulations ⋮ Mean-field descriptions for the viscoelastic response of thermorheologically complex reinforced solids ⋮ Model reduction by mean-field homogenization in viscoelastic composites. II. Application to rigidly reinforced solids ⋮ Application of the variational EIV approach to linear viscoelastic phases governed by several internal variables -- examples with the generalized Maxwell law

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Optimization of the collocation inversion method for the linear viscoelastic homogenization
• Effective properties of linear viscoelastic heterogeneous media: internal variables formulation and extension to ageing behaviours
• On the effective behavior of nonlinear inelastic composites. I: Incremental variational principles
• On the effective behavior of nonlinear inelastic composite. II: A second-order procedure
• Homogenization and mechanical dissipation in thermoviscoelasticity
• Nonuniform transformation field analysis
• Structural morphology and relaxation spectra of viscoelastic heterogeneous materials
• Application of the incremental variational approach (EIV model) to the linear viscoelastic homogenization of different types of microstructures: long fiber-, particle-reinforced and strand-based composites
• The variational formulation of viscoplastic constitutive updates
• Estimates for the overall linear properties of pointwise heterogeneous solids with application to elasto-viscoplasticity
• Effective behavior of linear viscoelastic composites: A time-integration approach
• Complex moduli of viscoelastic composites. I: General theory and application to particulate composites
• Inelastic constitutive relations for solids: An internal-variable theory and its application to metal plasticity
• A model-reduction approach in micromechanics of materials preserving the variational structure of constitutive relations
• Continuum Thermodynamics
• Transformation field analysis of inelastic composite materials
• Variational second-order estimates for nonlinear composites
• The Theory of Composites
• Effective potentials in nonlinear polycrystals and quadrature formulae
• Strain-driven homogenization of inelastic microstructures and composites based on an incremental variational formulation
• Field statistics in nonlinear composites. I. Theory
• Variational linear comparison bounds for nonlinear composites with anisotropic phases. I. General results