Lie point symmetries, conservation and balance laws in linear gradient elastodynamics

DOI10.1007/s10659-007-9105-5zbMath1115.74026OpenAlexW2010242050MaRDI QIDQ2642370

Markus Lazar, Charalampos Anastassiadis

Publication date: 20 August 2007

Published in: Journal of Elasticity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10659-007-9105-5

zbMATH Keywords

Conservation lawsSymmetriesGradient elasticityPath-independent integrals

Mathematics Subject Classification ID

Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of dynamical problems in solid mechanics (74H10) Elastic materials (74B99)

Related Items (6)

Rotational invariance conditions in elasticity, gradient elasticity and its connection to isotropy ⋮ Semi-analytical solution for the Lamb's problem in second gradient elastodynamics ⋮ Mathematical modeling of the elastic properties of cubic crystals at small scales based on the toupin-Mindlin anisotropic first strain gradient elasticity ⋮ Wave momentum in models of generalized continua ⋮ Reprint of: ``Wave momentum in models of generalized continua ⋮ Conservation and balance laws in linear elasticity of grade three

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Lie point symmetries and conservation laws in microstretch and micromorphic elasticity
• Symmetries and conversation laws in micropolar elasticity
• Conservation laws in elasticity. II: Linear homogeneous isotropic elastostatics
• Pseudomomentum and material forces in nonlinear elasticity: Variational formulations and application to brittle fracture
• The elastic energy-momentum tensor
• Conservation laws in linear elasto-dynamics
• Energy-momentum tensors in nonsimple elastic dielectrics
• On material equations in second-gradient electroelasticity
• Dispersive Rayleigh-wave propagation in microstructured solids characterized by dipolar gradient elasticity
• Invariant relations in Boussinesq-type equations
• The Eshelby stress tensor, angular momentum tensor and dilatation flux in gradient elasticity
• Energy theorems and the \(J\)-integral in dipolar gradient elasticity
• On first strain-gradient theories in linear elasticity
• On a class of conservation laws in linearized and finite elastostatics
• Micro-structure in linear elasticity
• On conservation and balance laws in micromorphic elastodynamics
• The Mode III Crack Problem in Microstructured Solids Governed by Dipolar Gradient Elasticity: Static and Dynamic Analysis
• Mechanics in Material Space
• Conservation Laws and Energy-Release Rates
• Symmetries and differential equations
• Anti-plane shear Lamb's problem treated by gradient elasticity with surface energy.

This page was built for publication: Lie point symmetries, conservation and balance laws in linear gradient elastodynamics