Conservation laws in nonlinear elastodynamics

DOI10.1016/0020-7225(89)90134-1zbMath0702.73032OpenAlexW2147256169MaRDI QIDQ915534

Elsie Sterbin Gottlieb

Publication date: 1989

Published in: International Journal of Engineering Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0020-7225(89)90134-1

zbMATH Keywords

closed idealexterior differential forms19-dimensional differentiable manifold4-dimensional sectioning of proper differential formsarbitrary strain energy functionCartan's exterior calculus of formsconservation of canonical (material) momentumEshelby's energy-momentum tensorfull set of basic balance lawsring of formssmooth solution submanifoldsurface elements patched together

Mathematics Subject Classification ID

Nonlinear elasticity (74B20) Exterior differential systems (Cartan theory) (58A15) Generalities, axiomatics, foundations of continuum mechanics of solids (74Axx)

Related Items

Symmetry groups for arbitrary motions of hyperelastic solids, Pseudomomentum and material forces in nonlinear elasticity: Variational formulations and application to brittle fracture, Equivalence groups for second order balance equations, On dual conservation laws in planar elasticity, On conservation laws in geometrically nonlinear elasto-dynamic field of non-homogeneous materials

Cites Work

• Conservation laws in elasticity. II: Linear homogeneous isotropic elastostatics
• Aspects of variational arguments in the theory of elasticity: fact and folklore
• Conservation laws in linear elasto-dynamics
• Conservation laws in linear elasticity based upon divergence transformations
• Conservation laws in elasticity. I: General results
• On a class of conservation laws in linearized and finite elastostatics
• Invariant variation problems
• Prolongation structures of nonlinear evolution equations
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