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Marcusyoder (talk | contribs) Added the actual formula for isotropic linear material properties. |
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</math>
For linear isotropic materials the strain energy density function specializes to:
<math>U = frac{1}{2}\sum_{i=1}^{3}\sum_{j=1}^{3}\sigma_{ij}\epsilon_{ij} = frac{1}{2}(\sigma_x\epsilon_x+\sigma_y\epsilon_y+\sigma_z\epsilon_z+\tau_{xy}\gamma_{xy}+\tau_{yz}\gamma_{yz}+\tau_{xz}\gamma_{xz})</math>
A strain energy density function is used to define a [[hyperelastic material]] by postulating that the [[stress (physics)|stress]] in the material can be obtained by taking the [[derivative]] of <math>W</math> with respect to the [[strain (physics)|strain]]. For an isotropic, hyperelastic material the function relates the [[energy]] stored in an [[Elasticity (physics)|elastic material]], and thus the stress-strain relationship, only to the three [[strain (materials science)|strain]] (elongation) components, thus disregarding the deformation history, heat dissipation, [[stress relaxation]] etc.
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