Difference between revisions of "Isotropic Material"
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This [[Material Models|material]] is a [[Material Models|small strain, linear elastic material]]. The components stress are related to components of strain by | This [[Material Models|material]] is a [[Material Models#Linear Elastic Small Strain Materials|small strain, linear elastic material]]. The components stress are related to components of strain by | ||
<math>\sigma_{ij} = \bigl(\lambda\varepsilon_{ii} - 3K(\alpha \Delta T+\beta c)\bigr)\delta_{ij} + 2G\varepsilon_{ij}</math> | <math>\sigma_{ij} = \bigl(\lambda\varepsilon_{ii} - 3K(\alpha \Delta T+\beta c)\bigr)\delta_{ij} + 2G\varepsilon_{ij}</math> | ||
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where λ is the Lame, K is bulk modulus, α is thermal expansion coefficient, ΔT is temperature difference, β is solvent expansion coefficient, c is solvent concentration, and G is shear modulus. Two other isotropic material properties are modulus, E, and Poisson's ratio, ν. | where λ is the Lame, K is bulk modulus, α is thermal expansion coefficient, ΔT is temperature difference, β is solvent expansion coefficient, c is solvent concentration, and G is shear modulus. Two other isotropic material properties are modulus, E, and Poisson's ratio, ν. | ||
Although an isotropic material can be defined any two of λ, K, G, E, and ν, the only properties allowed for defining this material are E and ν. | == Properties == | ||
Although an isotropic [[Material Models|material]] can be defined any two of λ, K, G, E, and ν, the only properties allowed for defining this material are E and ν. | |||
Revision as of 13:09, 27 March 2013
This material is a small strain, linear elastic material. The components stress are related to components of strain by
[math]\displaystyle{ \sigma_{ij} = \bigl(\lambda\varepsilon_{ii} - 3K(\alpha \Delta T+\beta c)\bigr)\delta_{ij} + 2G\varepsilon_{ij} }[/math]
where λ is the Lame, K is bulk modulus, α is thermal expansion coefficient, ΔT is temperature difference, β is solvent expansion coefficient, c is solvent concentration, and G is shear modulus. Two other isotropic material properties are modulus, E, and Poisson's ratio, ν.
Properties
Although an isotropic material can be defined any two of λ, K, G, E, and ν, the only properties allowed for defining this material are E and ν.