Minimizers of nonlocal polyconvex energies in nonlocal hyperelasticity
DOI10.1515/ACV-2022-0089zbMATH Open1546.74009MaRDI QIDQ6566022
Javier Cueto, Carlos Mora-Corral, José Carlos Bellido
Publication date: 3 July 2024
Published in: Advances in the Calculus of Variations (Search for Journal in Brave)
Euler-Lagrange equationsperidynamicsnonlocal gradientminimizer existenceRiesz fractional gradientnonlocal Piola identity
Nonlinear elasticity (74B20) Energy minimization in equilibrium problems in solid mechanics (74G65) Fractional derivatives and integrals (26A33) PDEs in connection with mechanics of deformable solids (35Q74) Peridynamics (74A70)
Cites Work
- Title not available (Why is that?)
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- Title not available (Why is that?)
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- Localization of nonlocal gradients in various topologies
- Local invertibility in Sobolev spaces with applications to nematic elastomers and magnetoelasticity
- Fracture surfaces and the regularity of inverses for BV deformations
- On a new class of fractional partial differential equations
- Invertibility and weak continuity of the determinant for the modelling of cavitation and fracture in nonlinear elasticity
- Functional analysis, Sobolev spaces and partial differential equations
- Regularity properties of deformations with finite energy
- Null Lagrangians, weak continuity, and variational problems of arbitrary order
- Convexity conditions and existence theorems in nonlinear elasticity
- On a new class of fractional partial differential equations. II
- Quasistatic crack growth in nonlinear elasticity
- An existence theory for nonlinear elasticity that allows for cavitation
- On a new class of elastic deformations not allowing for cavitation
- Revisiting brittle fracture as an energy minimization problem
- Reformulation of elasticity theory for discontinuities and long-range forces
- Fractional vector analysis based on invariance requirements (critique of coordinate approaches)
- Quasiconvexity in the fractional calculus of variations: characterization of lower semicontinuity and relaxation
- Fractional Piola identity and polyconvexity in fractional spaces
- Bond-based peridynamics does not converge to hyperelasticity as the horizon goes to zero
- \( \Gamma\)-convergence of polyconvex functionals involving \(s\)-fractional gradients to their local counterparts
- A distributional approach to fractional Sobolev spaces and fractional variation: existence of blow-up
- Singularities and computation of minimizers for variational problems
- Some Open Problems in Elasticity
- Lusin's condition and the distributional determinant for deformations with finite energy
- Discontinuous equilibrium solutions and cavitation in nonlinear elasticity
- A NONLOCAL VECTOR CALCULUS, NONLOCAL VOLUME-CONSTRAINED PROBLEMS, AND NONLOCAL BALANCE LAWS
- Direct methods in the calculus of variations
- Failure of the local chain rule for the fractional variation
- Non-local gradients in bounded domains motivated by continuum mechanics: fundamental theorem of calculus and embeddings
- A variational theory for integral functionals involving finite-horizon fractional gradients
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