Difference between revisions of "Bistable Isotropic Material"
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== Constitutive Law == | == Constitutive Law == | ||
This [[Material Models|MPM material]] (or [[FEA Material Models|FEA material]]) is | This [[Material Models|MPM material]] (or [[FEA Material Models|FEA material]]) is two small-strains materials (each with same constitutive law as an [[Isotropic Material|isotropic material]]). The two material states are linked by transition rules and the transition between the two states can be reversible or irreversible. | ||
The transition between the two states is determined either by a "dilation" rule, a "distortion" rule, or a "Von Mises" stress rule (as determined by the <tt>transition</tt> property). With a dilation rule, the transition occurs when the volumetric strain | |||
| |||
<math>{\Delta V\over V} = \varepsilon_{xx}+\varepsilon_{yy}+\varepsilon_{zz}</math> | |||
reaches the entered critical value. WIth a distortion rule, the transition occurs when the second strain invariant: | |||
| |||
<math>I_2 = \sqrt{{1\over 2}\sum_{i,j}\varepsilon_{ij}'\varepsilon_{ij}'}</math> | |||
where <math>\varepsilon_{ij}'</math> is deviatoric strain tensor, reaches a critical value. By a Von Mises stress rule, the transition occurs when the Von Mises stress | |||
| |||
<math>\sigma_{VM} = \sqrt{\sum_{i,j}\sigma_{ij}'\sigma_{ij}'}</math> | |||
where <math>\sigma_{ij}'</math> is is deviatoric stress, reaches a critical value. When using a dilation rule, the new stress-strain relation can include a changed offset in volumetric strain corresponding to stress-free conditions at a non-zero dilation relative to the initial state (see <tt>DeltaVOffset</tt> property). This change normally leads to an instantaneous change in stress upon transition. When using a distortion or Von Mises stress rule, the offset is ignored and the change is only a change in slope of mechanical properties. | |||
== Material Properties == | == Material Properties == | ||
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! Property !! Description !! Units !! Default | ! Property !! Description !! Units !! Default | ||
|- | |- | ||
| | | K0 || Bulk modulus for initial state || MPa || none | ||
|- | |||
| G0 || Shear modulus for initial state || MPa || none | |||
|- | |- | ||
| a0 || Shear modulus for initial state || MPa || none | |||
|} | |} | ||
Revision as of 10:07, 28 December 2013
Constitutive Law
This MPM material (or FEA material) is two small-strains materials (each with same constitutive law as an isotropic material). The two material states are linked by transition rules and the transition between the two states can be reversible or irreversible.
The transition between the two states is determined either by a "dilation" rule, a "distortion" rule, or a "Von Mises" stress rule (as determined by the transition property). With a dilation rule, the transition occurs when the volumetric strain
[math]\displaystyle{ {\Delta V\over V} = \varepsilon_{xx}+\varepsilon_{yy}+\varepsilon_{zz} }[/math]
reaches the entered critical value. WIth a distortion rule, the transition occurs when the second strain invariant:
[math]\displaystyle{ I_2 = \sqrt{{1\over 2}\sum_{i,j}\varepsilon_{ij}'\varepsilon_{ij}'} }[/math]
where [math]\displaystyle{ \varepsilon_{ij}' }[/math] is deviatoric strain tensor, reaches a critical value. By a Von Mises stress rule, the transition occurs when the Von Mises stress
[math]\displaystyle{ \sigma_{VM} = \sqrt{\sum_{i,j}\sigma_{ij}'\sigma_{ij}'} }[/math]
where [math]\displaystyle{ \sigma_{ij}' }[/math] is is deviatoric stress, reaches a critical value. When using a dilation rule, the new stress-strain relation can include a changed offset in volumetric strain corresponding to stress-free conditions at a non-zero dilation relative to the initial state (see DeltaVOffset property). This change normally leads to an instantaneous change in stress upon transition. When using a distortion or Von Mises stress rule, the offset is ignored and the change is only a change in slope of mechanical properties.
Material Properties
| Property | Description | Units | Default |
|---|---|---|---|
| K0 | Bulk modulus for initial state | MPa | none |
| G0 | Shear modulus for initial state | MPa | none |
| a0 | Shear modulus for initial state | MPa | none |
| Property | Description | Units | Default |
|---|---|---|---|
| beta | Solvent expansion coefficient | 1/(wt fraction) | 0 |
| D | Solvent diffusion constant | mm2/sec | 0 |
| kCond | Thermal conductivity | W/(m-K) | 0 |
| (other) | Properties common to all materials | varies | varies |
History Variables
None