On spatial and material covariant balance laws in elasticity
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Publication:3441714
DOI10.1063/1.2190827zbMath1111.74004OpenAlexW2084887554MaRDI QIDQ3441714
Arash Yavari, Jerrold E. Marsden, Michael Ortiz
Publication date: 16 May 2007
Published in: Journal of Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://authors.library.caltech.edu/4639/
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Cites Work
- Unnamed Item
- On spatial and material settings of hyperelastostatic crystal defects
- On the driving traction acting on a surface of strain discontinuity in a continuum
- The energy-momentum tensor and material uniformity in finite elasticity
- Mass, internal energy, and Cauchy's equations in frame-indifferent thermodynamics
- On the rotated stress tensor and the material version of the Doyle- Ericksen formula
- The force on a lattice defect in an elastic body
- The Hamiltonian structure of nonlinear elasticity: The material and convective representations of solids, rods, and plates
- Pseudomomentum and material forces in nonlinear elasticity: Variational formulations and application to brittle fracture
- The elastic energy-momentum tensor
- On the dissipation associated with equilibrium shocks in finite elasticity
- On nonlinear elasticity theory for crystal defects
- Asynchronous variational integrators
- Referential Doyle-Ericksen formulae for the Eshelby tensor in nonlinear elasticity
- A covariant constitutive description of anisotropic nonlinear elasticity
- Dislocation microstructures and the effective behavior of single crystals
- Kinetic relations and the propagation of phase boundaries in solids
- On spatial and material settings of thermo-hyperelastodynamics
- The nature of configurational forces
- Inverse deformation results in finite elasticity
- Discrete crystal elasticity and discrete dislocations in crystals
- On Cauchy's equations of motion
- Material forces and configurational forces in the interaction of elastic singularities
- Special Topics in Elastostatics
- Relativistic elasticity
- From Saturated Elasticity to Finite Evolution, Plasticity and Growth
- Elastic-Plastic Deformation at Finite Strains
- The force on an elastic singularity
