Periodic Homogenization of the Prandtl–reuss Model With Hardening

Schweizer, Ben; Veneroni, Marco

doi:10.1142/s1756973710000291

Cited by 15 publications

(15 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Proof. The proof of (2.16) is the same as in [18], Lemma 2.6. Using the definition of Ψ δ in (2.6), we choose, for every δ > 0, a function π δ ∈ L 2 (Ω; R d×d ) such that…”

Section: Convergence Propertiesmentioning

confidence: 97%

Stochastic homogenization of plasticity equations

Heida

Schweizer

2018

ESAIM: COCV

Self Cite

View full text Add to dashboard Cite

In the context of infinitesimal strain plasticity with hardening, we derive a stochastic homogenization result. We assume that the coefficients of the equation are random functions: elasticity tensor, hardening parameter and flow-rule function are given through a dynamical system on a probability space. A parameter ε > 0 denotes the typical length scale of oscillations. We derive effective equations that describe the behavior of solutions in the limit ε → 0. The homogenization limit is based on the needle-problem approach: We verify that the stochastic coefficients "allow averaging": In average, a strain evolutions . With the abstract result of [9] we obtain the stochastic homogenization limit.

show abstract

“…Proof. The proof of (2.16) is the same as in [18], Lemma 2.6. Using the definition of Ψ δ in (2.6), we choose, for every δ > 0, a function π δ ∈ L 2 (Ω; R d×d ) such that…”

Section: Convergence Propertiesmentioning

confidence: 97%

Stochastic homogenization of plasticity equations

Heida

Schweizer

2018

ESAIM: COCV

Self Cite

View full text Add to dashboard Cite

show abstract

“…While the underlying questions are similar, these contributions study a different scaling behavior in ε. Other homogenization results for the wave equation are contained in [7,19,22,23,27,28].…”

Section: Comparison With the Literaturementioning

confidence: 99%

Bloch-Wave Homogenization on Large Time Scales and Dispersive Effective Wave Equations

Dohnal¹,

Lamacz²,

Schweizer³

2014

Multiscale Model. Simul.

View full text Add to dashboard Cite

We investigate second order linear wave equations in periodic media, aiming at the derivation of effective equations in R n , n ∈ {1, 2, 3}. Standard homogenization theory provides, for the limit of a small periodicity length ε > 0, an effective second order wave equation that describes solutions on time intervals [0, T ]. In order to approximate solutions on large time intervals [0, T ε −2 ], one has to use a dispersive, higher order wave equation. In this work, we provide a well-posed, weakly dispersive effective equation and an estimate for errors between the solution of the original heterogeneous problem and the solution of the dispersive wave equation. We use Bloch-wave analysis to identify a family of relevant limit models and introduce an approach to select a well-posed effective model under symmetry assumptions on the periodic structure. The analytical results are confirmed and illustrated by numerical tests.

show abstract

“…The proof is essentially as in [25]. Since we construct solutions with a high regularity (higher than energy estimates suggest), we can use a strong solution concept for system (1.2): The relation (1.2a) is satisfied in the sense of distributions, the relations (1.2b) and (1.2c) are satisfied pointwise almost everywhere.…”

Section: Existence Results and Estimates For Plasticity Equationsmentioning

confidence: 99%

“…The latter situation, in which g is the subdifferential of an indicatrix, is also the subject in the homogenization result of [25]. In that contribution, strong solutions are obtained with a Galerkin scheme.…”

Section: Further Comparison With the Literaturementioning

confidence: 99%

Homogenization of plasticity equations with two-scale convergence methods

Schweizer

Veneroni

2014

Applicable Analysis

View full text Add to dashboard Cite

We investigate the deformation of heterogeneous plastic materials. The model uses internal variables and kinematic hardening, elastic and plastic strain are used in an infinitesimal strain theory. For periodic material properties with periodicity length scale η > 0, we obtain the limiting system as η → 0. The limiting two-scale plasticity model coincides with well-known effective models. Our direct approach relies on abstract tools from two-scale convergence (regarding convex functionals and monotone operators) and on higher order estimates for solution sequences.

show abstract

Periodic Homogenization of the Prandtl–reuss Model With Hardening

Cited by 15 publications

References 28 publications

Stochastic homogenization of plasticity equations

Stochastic homogenization of plasticity equations

Bloch-Wave Homogenization on Large Time Scales and Dispersive Effective Wave Equations

Homogenization of plasticity equations with two-scale convergence methods

Contact Info

Product

Resources

About