The Convexity Properties of a Class of Constitutive Models for Biological Soft Issues

DOI10.1177/108128602027726zbMath1072.74052OpenAlexW2028323374MaRDI QIDQ4812734

J. Patrick Wilber, Jay R. Walton

Publication date: 23 August 2004

Published in: Mathematics and Mechanics of Solids (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1177/108128602027726

zbMATH Keywords

strong ellipticity conditionLegendre-Hadamard conditionFung model

Mathematics Subject Classification ID

Nonlinear elasticity (74B20) Biomechanics (92C10) Biomechanical solid mechanics (74L15)

Related Items (12)

Data-driven tissue mechanics with polyconvex neural ordinary differential equations ⋮ A continuum constitutive model for the active behaviour of skeletal muscle ⋮ Determination of material models for arterial walls from uniaxial extension tests and histological structure ⋮ On strong ellipticity for implicit and strain-limiting theories of elasticity ⋮ Dependence of the frequency spectrum of small amplitude vibrations superimposed on finite deformations of a nonlinear, cylindrical elastic body on residual stress ⋮ A composites-based hyperelastic constitutive model for soft tissue with application to the human annulus fibrosus ⋮ Efficient evaluation of the material response of tissues reinforced by statistically oriented fibres ⋮ A linearized and incompressible constitutive model for arteries ⋮ Convex Fung-type potentials for biological tissues ⋮ A Universal Model for the Elastic, Inelastic and Active Behaviour of Soft Biological Tissues ⋮ On the deformation of orthotropic Cosserat elastic cylinders ⋮ On monotonicity for strain-limiting theories of elasticity

Cites Work

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• On copositive matrices and strong ellipticity for isotropic elastic materials
• Ordinary and strong ellipticity in the equilibrium theory of incompressible hyperelastic solids
• Ellipticity and deformations with discontinuous gradients in finite elastostatics
• On stability and uniqueness in finite elasticity
• On the failure of ellipticity of the equations for finite elastostatic plane strain
• A reformulation of the strong ellipticity conditions for unconstrained hyperelastic media
• Nonlinear problems of elasticity
• Direct methods in the calculus of variations
• A new constitutive framework for arterial wall mechanics and a comparative study of material models

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