Clamped Neo-Hookean Material - Revision history

Nairnj: /* Dissipated Energy */

2020-12-03T20:42:13Z

Dissipated Energy

← Older revision		Revision as of 20:42, 3 December 2020
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	=== Dissipated Energy ===		=== Dissipated Energy ===

	Note that deformation within the clamped region may maintain constant J<sub>E</sub> meaning that J<sub>P</sub> will increase or decrease as J increases or decreases. Because a decrease in J<sub>P</sub> corresponds to an increase in energy, the material is a non-physical implementation of plasticity methods. As a result, ~~not~~ attempt was made to track dissipated energy. The only consequence of this fact is that you cannot use this material to simulate heating caused by plastic deformation (<i>i.e.</i>, calculations in [[Thermal Calculations#Conduction\|"Adiabatic" mode]] will not result in particle temperature changes). Except for this simulation option, the dissipated energy plays no role in MPM results.		Note that deformation within the clamped region may maintain constant J<sub>E</sub> meaning that J<sub>P</sub> will increase or decrease as J increases or decreases. Because a decrease in J<sub>P</sub> corresponds to an increase in energy, the material is a non-physical implementation of plasticity methods. As a result, no attempt was made to track dissipated energy. The only consequence of this fact is that you cannot use this material to simulate heating caused by plastic deformation (<i>i.e.</i>, calculations in [[Thermal Calculations#Conduction\|"Adiabatic" mode]] will not result in particle temperature changes). Except for this simulation option, the dissipated energy plays no role in MPM results.

	In brief, this material was developed for animation simunlations and likely should be limited to such simulations.		In brief, this material was developed for animation simunlations and likely should be limited to such simulations.

Nairnj: /* Dissipated Energy */

2019-12-20T05:05:11Z

Dissipated Energy

← Older revision		Revision as of 05:05, 20 December 2019
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	=== Dissipated Energy ===		=== Dissipated Energy ===

	~~Although plastic material will dissipate energy whenever~~ the ~~elongations are~~ clamped in ~~tension, it will gain~~ energy ~~when clamped in compression. In other words~~, ~~this~~ material is ~~does not satisfy thermodynamic requirements for~~ plasticity ~~modeling~~. ~~Furhtermore~~, ~~the code does~~ not ~~calculate~~ dissipated ~~(or created~~ energy). ~~A work-around to~~ this ~~issue~~ is ~~to set critical compression extension to 1 such~~ that ~~no clamping ever occurs in compression. The~~ material ~~can still soften in tension and that process should only occur~~ by ~~dissipating energy and increasing in J~~<~~sub~~>P</~~sub~~>.		Note that deformation within the clamped region may maintain constant J<sub>E</sub> meaning that J<sub>P</sub> will increase or decrease as J increases or decreases. Because a decrease in J<sub>P</sub> corresponds to an increase in energy, the material is a non-physical implementation of plasticity methods. As a result, not attempt was made to track dissipated energy. The only consequence of this fact is that you cannot use this material to simulate heating caused by plastic deformation (<i>i.e.</i>, calculations in [[Thermal Calculations#Conduction\|"Adiabatic" mode]] will not result in particle temperature changes). Except for this simulation option, the dissipated energy plays no role in MPM results.

	~~Whether compression clamping is allowed or omitted~~, ~~the current implementation of this model does not calculate dissipated energy. The only consequence of this fact is that you cannot use~~ this material to simulate heating caused by plastic deformation (i.e. calculations in [[Thermal Calculations#Conduction\|"Adiabatic" mode]] will not result in particle temperature changes). Except for this simulation option, the dissipated energy plays no role in MPM results.		In brief, this material was developed for animation simunlations and likely should be limited to such simulations.

	=== Residual Stress ===		=== Residual Stress ===

Nairnj: /* Dissipated Energy */

2019-12-20T04:03:45Z

Dissipated Energy

← Older revision		Revision as of 04:03, 20 December 2019
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	=== Dissipated Energy ===		=== Dissipated Energy ===

	Although plastic material will dissipate energy whenever the elongations are clamped in tension, it will gain energy when clamped in compression. In other words, this material is does not satisfy thermodynamic requirements for plasticity modeling. Furhtermore, the code does not calculate dissipated (or created energy). A work-around to this issue		Although plastic material will dissipate energy whenever the elongations are clamped in tension, it will gain energy when clamped in compression. In other words, this material is does not satisfy thermodynamic requirements for plasticity modeling. Furhtermore, the code does not calculate dissipated (or created energy). A work-around to this issue is to set critical compression extension to 1 such that no clamping ever occurs in compression. The material can still soften in tension and that process should only occur by dissipating energy and increasing in J<sub>P</sub>.

	~~The consequences of this observation~~ is ~~that this material should not be used for~~ , the ~~currently implemented~~ model does not calculate ~~that~~ energy. The only consequence of this fact is that you cannot use this material to simulate heating caused by plastic deformation (i.e. calculations in [[Thermal Calculations#Conduction\|"Adiabatic" mode]] will not result in particle temperature changes). Except for this simulation option, the dissipated energy plays no role in MPM results.		Whether compression clamping is allowed or omitted, the current implementation of this model does not calculate dissipated energy. The only consequence of this fact is that you cannot use this material to simulate heating caused by plastic deformation (i.e. calculations in [[Thermal Calculations#Conduction\|"Adiabatic" mode]] will not result in particle temperature changes). Except for this simulation option, the dissipated energy plays no role in MPM results.

	=== Residual Stress ===		=== Residual Stress ===

Nairnj: /* Dissipated Energy */

2019-12-20T03:56:32Z

Dissipated Energy

← Older revision		Revision as of 03:56, 20 December 2019
Line 35:		Line 35:
	=== Dissipated Energy ===		=== Dissipated Energy ===

	Although ~~this~~ plastic material will dissipate energy whenever the elongations are clamped, the currently implemented model does not calculate that energy. The only consequence of this fact is that you cannot use this material to simulate heating caused by plastic deformation (i.e. calculations in [[Thermal Calculations#Conduction\|"Adiabatic" mode]] will not result in particle temperature changes). Except for this simulation option, the dissipated energy plays no role in MPM results.		Although plastic material will dissipate energy whenever the elongations are clamped in tension, it will gain energy when clamped in compression. In other words, this material is does not satisfy thermodynamic requirements for plasticity modeling. Furhtermore, the code does not calculate dissipated (or created energy). A work-around to this issue

			The consequences of this observation is that this material should not be used for , the currently implemented model does not calculate that energy. The only consequence of this fact is that you cannot use this material to simulate heating caused by plastic deformation (i.e. calculations in [[Thermal Calculations#Conduction\|"Adiabatic" mode]] will not result in particle temperature changes). Except for this simulation option, the dissipated energy plays no role in MPM results.

	=== Residual Stress ===		=== Residual Stress ===

Nairnj: /* Neo-Hookean Option */

2019-12-13T20:01:54Z

Neo-Hookean Option

← Older revision		Revision as of 20:01, 13 December 2019
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	=== Neo-Hookean Option ===		=== Neo-Hookean Option ===

	If either <tt> CritComp</tt> or <tt> CritTens</tt> are less than zero, the elongation will never be clamped. As a consequence, the material will be a hyperlastic, Neo-hookean material. This mode is normally used when <tt>Elastic</tt> is 0 to use the corotated elasticity model described above. There is no point to using this mode when <tt>Elastic</tt> is 1 because that material is better done by using the regular [[Neo-Hookean Material\|neo-Hookean material]]. See [[Comparison of Neo-Hookean Materials]] for details on available neo-Hookean materials.		If either <tt> CritComp</tt> or <tt> CritTens</tt> are less than zero, the elongation will never be clamped. As a consequence, the material will be a hyperlastic, Neo-hookean material. This mode is normally used when <tt>Elastic</tt> is 0 to use the modified, corotated elasticity model described above. There is no point to using this mode when <tt>Elastic</tt> is 1 because that material is better done by using the regular [[Neo-Hookean Material\|neo-Hookean material]]. See [[Comparison of Neo-Hookean Materials]] for details on available neo-Hookean materials.

	== History Data ==		== History Data ==

Nairnj: /* Constitutive Law */

2019-12-13T20:00:25Z

Constitutive Law

← Older revision		Revision as of 20:00, 13 December 2019
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	<math>\Phi\bigl(\mathbf{F}_E,G(J_P),\lambda(J_P)\bigr) = G(J_P)\sum_k (\lambda_k-1)^2 + {\lambda(J_P)\over 2}(J_E-1)^2</math>		<math>\Phi\bigl(\mathbf{F}_E,G(J_P),\lambda(J_P)\bigr) = G(J_P)\sum_k (\lambda_k-1)^2 + {\lambda(J_P)\over 2}(J_E-1)^2</math>

	where <math>\lambda_k</math> are the principal elongations and J<sub>E</sub> is the determinant of <math>\mathbf{F}_E</math>. This potential is a modified, co-rotated energy function; the modification changed the Lamé term for improved stability at large deformation<ref name="MCR">A. Stomakhin, R. Howes,C. Schroeder, and J.M. Teran (2012). "Energetically consistent invertible elasticity." In Eurographics/ACM SIGGRAPH Symposium on Computer Animation.</ref>~~. the~~ The Cauchy stress by this law is		where <math>\lambda_k</math> are the principal elongations and J<sub>E</sub> is the determinant of <math>\mathbf{F}_E</math>. This potential is a modified, co-rotated energy function; the modification changed the Lamé term for improved stability at large deformation.<ref name="MCR">A. Stomakhin, R. Howes,C. Schroeder, and J.M. Teran (2012). "Energetically consistent invertible elasticity." In Eurographics/ACM SIGGRAPH Symposium on Computer Animation.</ref> The Cauchy stress by this law is

Nairnj: /* Constitutive Law */

2019-12-13T19:58:35Z

Constitutive Law

← Older revision		Revision as of 19:58, 13 December 2019
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	<math>\Phi\bigl(\mathbf{F}_E,G(J_P),\lambda(J_P)\bigr) = G(J_P)\sum_k (\lambda_k-1)^2 + {\lambda(J_P)\over 2}(J_E-1)^2</math>		<math>\Phi\bigl(\mathbf{F}_E,G(J_P),\lambda(J_P)\bigr) = G(J_P)\sum_k (\lambda_k-1)^2 + {\lambda(J_P)\over 2}(J_E-1)^2</math>

	where <math>\lambda_k</math> are the principal elongations and J<sub>E</sub> is the determinant of <math>\mathbf{F}_E</math>. The Cauchy stress by this law is		where <math>\lambda_k</math> are the principal elongations and J<sub>E</sub> is the determinant of <math>\mathbf{F}_E</math>. This potential is a modified, co-rotated energy function; the modification changed the Lamé term for improved stability at large deformation<ref name="MCR">A. Stomakhin, R. Howes,C. Schroeder, and J.M. Teran (2012). "Energetically consistent invertible elasticity." In Eurographics/ACM SIGGRAPH Symposium on Computer Animation.</ref>. the The Cauchy stress by this law is

Nairnj: /* Constitutive Law */

2019-12-13T19:54:24Z

Constitutive Law

← Older revision		Revision as of 19:54, 13 December 2019
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	<math>G(J_P)= G(1)e^{\xi(1-J_P)} \qquad {\rm and} \qquad \lambda(J_P)= \lambda(1)e^{\xi(1-J_P)}</math>		<math>G(J_P)= G(1)e^{\xi(1-J_P)} \qquad {\rm and} \qquad \lambda(J_P)= \lambda(1)e^{\xi(1-J_P)}</math>

	where <math>\xi</math> is a hardening parameter and <math>G(1)</math> and <math>\lambda(1)</math> are the initial shear and Lamé moduli (''i.e''., before any plasticity). Note that in tension, the material softens, which can emulate ~~fracture~~. In compression, the material hardens.		where <math>\xi</math> is a hardening parameter and <math>G(1)</math> and <math>\lambda(1)</math> are the initial shear and Lamé moduli (''i.e''., before any plasticity). Note that in tension, the material softens, which can emulate damage propagation and failure. In compression, the material hardens.

	The plasticity is implemented as follows:		The plasticity is implemented as follows:

Nairnj: /* Constitutive Law */

2019-12-13T19:51:50Z

Constitutive Law

← Older revision		Revision as of 19:51, 13 December 2019
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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 neo-Hookean material. Plasticity occurs when the elongation in either tensile of compressive elongation reaches a critical value. This material is based on the material used 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 that model was based on engineering analysis of snow, it was simplified for efficiency in animation and for ease it creating a variety of responses.		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 the material modeling used 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 that 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 uses an isotropic, neo-Hookean material potential energy:		The elastic regime of the material uses an isotropic, neo-Hookean material potential energy:

Nairnj: /* Neo-Hookean Option */

2017-11-16T22:44:23Z

Neo-Hookean Option

← Older revision		Revision as of 22:44, 16 November 2017
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	=== Neo-Hookean Option ===		=== Neo-Hookean Option ===

	If either <tt> CritComp</tt> or <tt> CritTens</tt> are less than zero, the elongation will never be clamped. As a consequence, the material will be a hyperlastic, Neo-hookean material. This mode is normally used when <tt>Elastic</tt> is 0 to use the corotated elasticity model described above. There is no point to using this mode when <tt>Elastic</tt> is 1 because that material is better done by using the regular [[Neo-Hookean Material\|neo-Hookean material]]. ~~A third neo-Hookean material is a~~ [[~~Mooney Material\|Mooney~~-~~Rivilin material~~]].		If either <tt> CritComp</tt> or <tt> CritTens</tt> are less than zero, the elongation will never be clamped. As a consequence, the material will be a hyperlastic, Neo-hookean material. This mode is normally used when <tt>Elastic</tt> is 0 to use the corotated elasticity model described above. There is no point to using this mode when <tt>Elastic</tt> is 1 because that material is better done by using the regular [[Neo-Hookean Material\|neo-Hookean material]]. See [[Comparison of Neo-Hookean Materials]] for details on available neo-Hookean materials.

	== History Data ==		== History Data ==