On the effective behavior of nonlinear inelastic composites: I. Incremental variational principles

By N. Lahellec, Pierre Suquet. 2007

182 citations recorded by the source corpus.

A new method for determining the overall behavior of composite materials comprised of nonlinear inelastic constituents is presented. Upon use of an implicit time-discretization scheme, the evolution equations describing the constitutive behavior of the phases can be reduced to the minimization of an incremental energy function. This minimization problem is rigorously equivalent to a nonlinear thermoelastic problem with a transformation strain which is a nonuniform field (not even uniform within the phases). In this first part of the study the variational technique of Ponte Castaneda is used to approximate the nonuniform eigenstrains by piecewise uniform eigenstrains and to linearize the nonlinear thermoelastic problem. The resulting problem is amenable to simpler calculations and analytical results for appropriate microstructures can be obtained. The accuracy of the proposed scheme is assessed by comparison of the method with exact results.

Subfields: Biomedical Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/c1448510b592a520d5df9de18132042507e79cf8

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In Biomedical Engineering

1. J. Michel
2. X. Martínez
3. F. Otero
4. S. Oller
5. Pierre Suquet
6. I. Doghri
7. L. Brassart
8. Laurent Stainier

In Mechanics of Materials

1. L. Brassart
2. L. Delannay
3. Laurent Stainier
4. J. Michel
5. X. Martínez
6. F. Otero
7. I. Doghri
8. Pierre Suquet

Citations in the corpus

• On the two-potential constitutive modeling of rubber viscoelastic materials (2016, unknown): “Because of its derivation from two thermodynamic potentials that are functions of the deformation gradient tensor F and an internal variable Fv grounded in the undeformed configuration, the constitutive relation (36)–(37) is well suited for use in boundary-value problems, particularly in homogenizat”
• Nonlinear reduced order homogenization of materials including cohesive interfaces (2015, unknown): “[17–19]).”
• Multiscale Computational Homogenization: Review and Proposal of a New Enhanced-First-Order Method (2016, methodology): “The geometry of the RVE is meshed with finite elements to solve the microscale Boundary Value Problem (BVP), then through homogenization rules the micro-results are linked to macro-scale properties [34, 35, 63, 107, 120].”
• Homogenization of elasto-(visco) plastic composites based on an incremental variational principle (2012, background): “…JDðx; enþ1;Dp;NÞ ð41Þ with JDðx; enþ1;Dp;NÞ ¼ wðx; e; ep; pÞ # wnðxÞ þ Dt/ (ðx; _p;pÞ: ð42Þ The local problem (40) can be restated into the following equivalent variational representation (Miehe, 2002; Lahellec and Suquet, 2007a): WD !enþ1ð Þ ¼ inf enþ12Kð!enþ1Þ WD x; enþ1ð Þh i ¼ inf enþ12K…”
• A model-reduction approach in micromechanics of materials preserving the variational structure of constitutive relations (2016, methodology): “After time-discretization, the overall stress σ at time tn+1 derives from the effective potential w̃∆ (Lahellec and Suquet, 2007a,b) (deduced from the local variational principle (10)), σ = ∂w̃∆ ∂ε (ε), w̃∆(ε) = Inf ε∈K(ε) 〈 Inf α J(ε,α) 〉 , (21) where ε is the prescribed macroscopic strain at time…”