The elasticity tensor of a residually stressed material

DOI10.1007/BF00044971zbMath0793.73002OpenAlexW1985353723MaRDI QIDQ1309791

Anne Hoger

Publication date: 9 January 1994

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

Full work available at URL: https://doi.org/10.1007/bf00044971

zbMATH Keywords

initial stresssmall strainslinearizingsmall displacement gradientsinhomogeneous nonpositive definite tensor

Mathematics Subject Classification ID

Vector and tensor algebra, theory of invariants (15A72) Theory of constitutive functions in solid mechanics (74A20) Elastic materials (74B99)

Related Items

A Theory of Volumetric Growth for Compressible Elastic Biological Materials ⋮ Wave-propagation in an incompressible hollow elastic cylinder with residual stress ⋮ Thermo-mechanically coupled constitutive equations for soft elastomers with arbitrary initial states ⋮ Homogenization-based constitutive models for magnetorheological elastomers at finite strain ⋮ The elasticity tensor of a transversely isotropic hyperelastic material with residual stress ⋮ Initial stresses in elastic solids: constitutive laws and acoustoelasticity ⋮ Reflection of plane waves from the boundary of an initially stressed incompressible half-space ⋮ Propagation of Rayleigh wave in initially-stressed compressible hyperelastic materials ⋮ On the numerical treatment of initial strains in biological soft tissues ⋮ The tensor equation \(AX +XA = \Phi (A,H)\), with applications to kinematics of continua ⋮ Positive definiteness of the elasticity tensor of a residually stressed material ⋮ A curvature-dependent interfacial energy-based interface stress theory and its applications to nano-structured materials. I. General theory ⋮ The constitutive equation for finite deformations of a transversely isotropic hyperelastic material with residual stress ⋮ The dependence of the elasticity tensor on residual stress

Cites Work

• On the residual stress possible in an elastic body with material symmetry
• On the derivative of the square root of a tensor and Guo's rate theorems
• On the existence of an elastic potential for a simple material without memory
• On the stress in an internally constrained elastic material
• On universal solutions in initially stressed bodies
• Residual stress in an elastic body: A theory for small strains and arbitrary rotations
• On the determination of residual stress in an elastic body
• An introduction to continuum mechanics
• On constitutive inequalities for simple materials. I
• Material symmetry and thermostatic inequalities in finite elastic deformations
• General theory of small elastic deformations superposed on finite elastic deformations
• Unnamed Item
• Unnamed Item
• Unnamed Item