Mappings of Lp-integrable distortion: regularity of the inverse

Onninen, Jani; Tengvall, Ville

doi:10.1017/s0308210515000530

Cited by 5 publications

(5 citation statements)

References 15 publications

(22 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We shall make use of the following equiintegrability result for inverse Jacobians of mappings of integrable distorsion, which is inspired by the work of Onninen and Tengvall [25].…”

Section: Existence Of Minimizers: Proof Of Theorem 23mentioning

confidence: 99%

A Phase-Field Approach to Eulerian Interfacial Energies

Grandi

Kružík

Mainini

et al. 2019

Arch Rational Mech Anal

View full text Add to dashboard Cite

We analyze a phase-field approximation of a sharp-interface model for twophase materials proposed by M.Šilhavý [32,33]. The distinguishing trait of the model resides in the fact that the interfacial term is Eulerian in nature, for it is defined on the deformed configuration. We discuss a functional frame allowing for existence of phasefield minimizers and Γ-convergence to the sharp-interface limit. As a by-product, we provide additional detail on the admissible sharp-interface configurations with respect to the analysis in [32,33].By checking the Γ-convergence of F ε to F 0 we essentially deliver a version of the Modica-Mortola Theorem [24] in the deformed configuration. Instrumental to this is the discussion of the interplay of deformations and perimeters in deformed configurations, which constitutes the main technical contribution of our paper (Theorem 2.2).Let us mention that variational formulations featuring both Lagrangian and Eulerian terms are currently attracting increasing attention. A prominent case is that of magnetoelastic materials [16], where Lagrangian mechanical terms and Eulerian magnetic effects combine [6,7,23,29]. Mixed Lagrangian-Eulerian formulations arise in the modeling of nematic polymers [5,6], where the Eulerian variable is the nematic director orientation, and in piezoelectrics [28], involving the Eulerian polarization instead. An interplay of Lagrangian and Eulerian effects occurs already in case of space dependent forcings, like

show abstract

“…We shall make use of the following equiintegrability result for inverse Jacobians of mappings of integrable distorsion, which is inspired by the work of Onninen and Tengvall [25].…”

Section: Existence Of Minimizers: Proof Of Theorem 23mentioning

confidence: 99%

A Phase-Field Approach to Eulerian Interfacial Energies

Grandi

Kružík

Mainini

et al. 2019

Arch Rational Mech Anal

View full text Add to dashboard Cite

show abstract

“…Thanks to the results in [33], the uniform bound on K y k L q (Ω) yields the equi-integrability of the family (det ∇y −1 k ) k , as proven in [18,Lemma 5.1]. Since |Ω y k \ Ω y | → 0 as k → ∞ by Lemma 5.1, the statement follows.…”

Section: Convergence Of the Phasesmentioning

confidence: 63%

Equilibrium for multiphase solids with Eulerian interfaces

Grandi¹,

Kružík²,

Mainini³

et al. 2020

Preprint

View full text Add to dashboard Cite

We describe a general phase-field model for hyperelastic multiphase materials. The model features an elastic energy functional that depends on the phase-field variable and a surface energy term that depends in turn on the elastic deformation, as it measures interfaces in the deformed configuration. We prove existence of energy minimizing equilibrium states and Γ-convergence of diffuse-interface approximations to the sharp-interface limit.

show abstract

“…The uniform bound on K y k L q ( ) yields the equi-integrability of the family (det ∇y −1 k ) k , as proven in [21, Lemma 5.1] (making use of results in [36]). Since | y k \ y | → 0 as k → ∞ by Lemma 5.1, the statement follows.…”

Section: Lemma 52 Let P ≥ N and Qmentioning

confidence: 93%

Equilibrium for Multiphase Solids with Eulerian Interfaces

Grandi

Kružík

Mainini

et al. 2020

J Elast

View full text Add to dashboard Cite

We describe a general phase-field model for hyperelastic multiphase materials. The model features an elastic energy functional that depends on the phase-field variable and a surface energy term that depends in turn on the elastic deformation, as it measures interfaces in the deformed configuration. We prove existence of energy minimizing equilibrium states and -convergence of diffuse-interface approximations to the sharp-interface limit.

show abstract

Mappings of L^p-integrable distortion: regularity of the inverse

Cited by 5 publications

References 15 publications

A Phase-Field Approach to Eulerian Interfacial Energies

A Phase-Field Approach to Eulerian Interfacial Energies

Equilibrium for multiphase solids with Eulerian interfaces

Equilibrium for Multiphase Solids with Eulerian Interfaces

Contact Info

Product

Resources

About