Difference between revisions of "Clamped Neo-Hookean Material"
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== Constitutive Law == | == Constitutive Law == | ||
This [[Material Models|MPM Material]] is an isotropic, elastic-plastic material in large strains using a hyperelastic formulation. The elastic part is a | This [[Material Models|MPM Material]] is an isotropic, elastic-plastic material in large strains using a hyperelastic formulation. The elastic part is a neo-Hookean material. Plasticity occurs when the elongation in either tensile of compressive elongation reaches a critical value. This material is based on similar material using in a paper to animate snow mechanics<ref name="DIZ">A. Stomakhin, C. Schroeder, L. Chai, J. Teran, and A. Selle, "A material point method for snow simulation," ACM Trans. Graph., Vol. 32, No. 4, Article 102, July 2013.</ref>. Although the model was based on engineering analysis of snow, it was simplified for efficiency in animation and for ease it creating a variety of responses. | ||
The elastic regime of the material using a neo-Hookean material: | The elastic regime of the material using a neo-Hookean material: | ||
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<math>W = \Phi\bigl(F,G(J_P),\lambda(J_P)\bigr) </math> | <math>W = \Phi\bigl(\mathbf{F}_E,G(J_P),\lambda(J_P)\bigr) </math> | ||
where <math>\Phi()</math> is a neo-Hookean potential energy function that depends on the current elastic deformation gradient (<math>\mathbf{F}_E</math>) and shear and Lamé moduli <math>G(J_P)</math> and <math>\lambda(J_P)</math>. The implementation hear allows two different neo-Hookean law. The first uses the law proposed in Stomakhin ''et al.''<ref name="DIZ"/>. The second use the law defined for the standard [[Neo-Hookean Material|neo-Hookean material]]. | |||
== Material Properties == | == Material Properties == | ||
Revision as of 12:40, 7 February 2015
Constitutive Law
This MPM Material is an isotropic, elastic-plastic material in large strains using a hyperelastic formulation. The elastic part is a neo-Hookean material. Plasticity occurs when the elongation in either tensile of compressive elongation reaches a critical value. This material is based on similar material using in a paper to animate snow mechanics[1]. Although the model was based on engineering analysis of snow, it was simplified for efficiency in animation and for ease it creating a variety of responses.
The elastic regime of the material using a neo-Hookean material:
[math]\displaystyle{ W = \Phi\bigl(\mathbf{F}_E,G(J_P),\lambda(J_P)\bigr) }[/math]
where [math]\displaystyle{ \Phi() }[/math] is a neo-Hookean potential energy function that depends on the current elastic deformation gradient ([math]\displaystyle{ \mathbf{F}_E }[/math]) and shear and Lamé moduli [math]\displaystyle{ G(J_P) }[/math] and [math]\displaystyle{ \lambda(J_P) }[/math]. The implementation hear allows two different neo-Hookean law. The first uses the law proposed in Stomakhin et al.[1]. The second use the law defined for the standard neo-Hookean material.
Material Properties
The material properties are given in the following table.
| Property | Description | Units | Default |
|---|---|---|---|
| CritComp | Critical compression extension | none | 0.025 |
| CritComp | Critical tensile extension | none | 0.0075 |
| xihard | Hardening coefficient | none | 10 |
| Elastic | Enter 0 to basic elastic stresses on the model in Ref. [1]. Enter 1 to base elastic stresses on the neo-Hookean material. | none | 0 |
| (other) | Properties to define underlying neo-Hookean material (note that UJOption is always 1 when Elastic is 0, but can be any option when Elastic is 1) | varies | varies |
Examples
These commands model snow: