The dependence of the elasticity tensor on residual stress

DOI10.1007/BF00705803zbMath0812.73024MaRDI QIDQ1319379

Anne Hoger, Byron E. Johnson

Publication date: 14 May 1995

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

zbMATH Keywords

hyperelastic materialgeneral strain energy functionMooney materiallinearized stress-strain relationself-equilibrated inhomogeneous finite pre-deformationshell eversion

Mathematics Subject Classification ID

Nonlinear elasticity (74B20) Theory of constitutive functions in solid mechanics (74A20)

Related Items (22)

Wave-propagation in an incompressible hollow elastic cylinder with residual stress ⋮ The Use of Strain Energy to Quantify the Effect of Residual Stress on Mechanical Behavior ⋮ Reconstruction of nonuniform residual stress for soft hyperelastic tissue via inverse spectral techniques ⋮ Mathematical Modeling of Morphogenesis in Living Materials ⋮ Extension, inflation and torsion of a residually stressed circular cylindrical tube ⋮ The use of a virtual configuration in formulating constitutive equations for residually stressed elastic materials ⋮ Thermo-mechanically coupled constitutive equations for soft elastomers with arbitrary initial states ⋮ The elasticity tensor of a transversely isotropic hyperelastic material with residual stress ⋮ The exponentiated Hencky-logarithmic strain energy. I: Constitutive issues and rank-one convexity ⋮ Hyperelastic constitutive relations for soft elastomers with thermally-induced residual stress ⋮ Mechanobiology and morphogenesis in living matter: a survey ⋮ Initial stresses in elastic solids: constitutive laws and acoustoelasticity ⋮ Derivation of the linear elastic string model from three-dimensional elasticity ⋮ Reflection of plane waves from the boundary of an initially stressed incompressible half-space ⋮ Anticavitation and differential growth in elastic shells ⋮ Dependence of the frequency spectrum of small amplitude vibrations superimposed on finite deformations of a nonlinear, cylindrical elastic body on residual stress ⋮ Derivation of a linear prestressed elastic rod model from three-dimensional elasticity ⋮ Positive definiteness of the elasticity tensor of a residually stressed material ⋮ Stability of plane Couette flow past an initially stressed solid ⋮ On the existence of elastic minimizers for initially stressed materials ⋮ On the inflation of residually stressed spherical shells ⋮ The constitutive equation for finite deformations of a transversely isotropic hyperelastic material with residual stress

Cites Work

• On the residual stress possible in an elastic body with material symmetry
• On the stress in an internally constrained elastic material
• Residual stress in an elastic body: A theory for small strains and arbitrary rotations
• The elasticity tensor of a residually stressed material
• On the determination of residual stress in an elastic body
• Material symmetry and thermostatic inequalities in finite elastic deformations
• General theory of small elastic deformations superposed on finite elastic deformations
• Inversion of a perfectly elastic spherical shell
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