On the use of the upper triangular (or QR) decomposition for developing constitutive equations for Green-elastic materials
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Publication:1659894
DOI10.1016/J.IJENGSCI.2012.05.003zbMath1423.74110OpenAlexW1978413364MaRDI QIDQ1659894
Publication date: 23 August 2018
Published in: International Journal of Engineering Science (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.ijengsci.2012.05.003
Classical linear elasticity (74B05) Nonlinear elasticity (74B20) Linear constitutive equations for materials with memory (74D05)
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Cites Work
- Unnamed Item
- Constitutive framework optimized for myocardium and other high-strain, laminar materials with one fiber family
- Kinematics and elasticity framework for materials with two fiber families
- Further results on the strain-energy function for anisotropic elastic materials
- On implicit constitutive theories.
- An adaptive method for homogenization in orthotropic nonlinear elasticity
- Material symmetry restrictions on non-polynomial constitutive equations
- A new representation theorem for elastic constitutive equations of cubic crystals
- On universal relations in continuum mechanics
- Invariant formulation of hyperelastic transverse isotropy based on polyconvex free energy functions.
- The elasticity of elasticity
- Physically motivated invariant formulation for transversely isotropic hyperelasticity
- Material symmetry restrictions on constitutive equations
- Physically based invariants for nonlinear elastic orthotropic solids
- Additional Universal Relations for Transversely Isotropic Elastic Materials
- The Strain-Energy Function for Anisotropic Elastic Materials
- A Microstructurally Based Orthotropic Hyperelastic Constitutive Law
- On a class of non-dissipative materials that are not hyperelastic
- On the response of non-dissipative solids
- An invariant basis for natural strain which yields orthogonal stress response terms in isotropic hyperelasticity
- Physically based strain invariant set for materials exhibiting transversely isotropic behavior
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