Difference between revisions of "Isotropic Material"
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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 | This [[Material Models|material]] is a [[Material Models#Linear Elastic Small Strain Materials|small strain, linear elastic material]]. The components of 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> | ||
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 coefficient, 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. | ||
== Material Properties == | == Material 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. Those two and other properties are: | Although elastic properties of 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. Those two and other properties for isotropic [[Material Models|materials]] are: | ||
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| Property !! Description !! Units !! Default | |||
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<E>0.1</E> | <E>0.1</E> | ||
Revision as of 08:20, 28 March 2013
This material is a small strain, linear elastic material. The components of 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 coefficient, 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.
Material Properties
Although elastic properties of 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. Those two and other properties for isotropic materials are:
| Property !! Description !! Units !! Default
}| <E>0.1</E> The material modulus (in MPa) <nu>0.33</nu> The material Poisson's ratio <alpha>60</alpha> The material thermal expansion coefficient (in ppm/C) <beta>60</beta> The material concentration expansion coefficient (in strain/wt fraction) <D>400</D> Diffusion constant (in mm2/sec). Only used when doing diffusion calculations. NairnMPM only. <kCond>400</kCond> Thermal conductivity (in W/(m-K)). Only used when doing conduction calculations. NairnMPM only. Other Properties See the properties common to all materials for NairnMPM only. History DataNone |