Orthotropic Softening Material - Revision history

Nairnj: /* Constitutive Law */

2026-03-29T17:39:17Z

Constitutive Law

← Older revision		Revision as of 17:39, 29 March 2026
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	where '''C''' is stiffness tensor for the underlying orthotopic material and '''D''' is an anisotropic 4<sup>th</sup> rank damage tensor appropriate for damage in orthotropic materials, and <math>\mathbf{\varepsilon}_{res}</math> is any residual strain (such as thermal or solvent induced strains).		where '''C''' is stiffness tensor for the underlying orthotopic material and '''D''' is an anisotropic 4<sup>th</sup> rank damage tensor appropriate for damage in orthotropic materials, and <math>\mathbf{\varepsilon}_{res}</math> is any residual strain (such as thermal or solvent induced strains).

	The MPM implementation of softening isotropic materials is described in Nairn, Hammerquist, and Aimene.<ref name="dmref"/> The extension to orthotropic materials is described in a paper on generalized damage mechanics methods.<ref name="dmGen">		The MPM implementation of softening isotropic materials is described in Nairn, Hammerquist, and Aimene.<ref name="dmref"/> The extension to orthotropic materials is described in a paper on generalized damage mechanics methods.<ref name="dmGen"/>

	== Damage Process ==		== Damage Process ==

Nairnj at 17:39, 29 March 2026

2026-03-29T17:39:08Z

← Older revision		Revision as of 17:39, 29 March 2026
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	where '''C''' is stiffness tensor for the underlying orthotopic material and '''D''' is an anisotropic 4<sup>th</sup> rank damage tensor appropriate for damage in orthotropic materials, and <math>\mathbf{\varepsilon}_{res}</math> is any residual strain (such as thermal or solvent induced strains).		where '''C''' is stiffness tensor for the underlying orthotopic material and '''D''' is an anisotropic 4<sup>th</sup> rank damage tensor appropriate for damage in orthotropic materials, and <math>\mathbf{\varepsilon}_{res}</math> is any residual strain (such as thermal or solvent induced strains).

	The MPM implementation of softening isotropic materials is described in Nairn, Hammerquist, and Aimene.<ref name="dmref">J. A. Nairn, C. C. Hammerquist, and Y. E. Aimene, "Numerical Implementation of Anisotropic Damage Mechanics," Int. J. for Numerical Methods in Engineering, 112(12), 1846-1868 (2017). [http://www.cof.orst.edu/cof/wse/faculty/Nairn/papers/MPMSoftening.pdf PDF]</~~ref~~> The extension to orthotropic materials is described in a paper on generalized damage mechanics methods.<ref name="~~genref~~">J. A. Nairn, "Generalization of Anisotropic Damage Mechanics Modeling in the Material Point Method," Int. J. for Numerical Methods in Engineering, 123, 5072-5097 (2022). [https://www.cof.orst.edu/cof/wse/faculty/Nairn/papers/GenDamage.pdf PDF]</ref>		The MPM implementation of softening isotropic materials is described in Nairn, Hammerquist, and Aimene.<ref name="dmref"/> The extension to orthotropic materials is described in a paper on generalized damage mechanics methods.<ref name="dmGen">

	== Damage Process ==		== Damage Process ==

Nairnj: /* References */

2026-03-29T17:38:30Z

References

← Older revision		Revision as of 17:38, 29 March 2026
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	== References ==		== References ==

	<references/>		<references>

			<ref name="dmref">J. A. Nairn, C. C. Hammerquist, and Y. E. Aimene, "Numerical Implementation of Anisotropic Damage Mechanics," Int. J. for Numerical Methods in Engineering, 112(12), 1846-1868 (2017). ([http://www.cof.orst.edu/cof/wse/faculty/Nairn/papers/MPMSoftening.pdf See PDF])</ref>

			<ref name="dmGen">J. A. Nairn, "Generalization of Anisotropic Damage Mechanics Modeling in the Material Point Method," ''Int. J. for Numerical Methods in Engineering'', '''123''', 5072-5097 (2022). ([https://www.cof.orst.edu/cof/wse/faculty/Nairn/papers/GenDamage.pdf See PDF])</ref>

			</references>

Nairnj: /* Constitutive Law */

2024-04-18T02:33:45Z

Constitutive Law

← Older revision		Revision as of 02:33, 18 April 2024
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	where '''C''' is stiffness tensor for the underlying orthotopic material and '''D''' is an anisotropic 4<sup>th</sup> rank damage tensor appropriate for damage in orthotropic materials, and <math>\mathbf{\varepsilon}_{res}</math> is any residual strain (such as thermal or solvent induced strains).		where '''C''' is stiffness tensor for the underlying orthotopic material and '''D''' is an anisotropic 4<sup>th</sup> rank damage tensor appropriate for damage in orthotropic materials, and <math>\mathbf{\varepsilon}_{res}</math> is any residual strain (such as thermal or solvent induced strains).

	The MPM implementation of softening isotropic materials is described in Nairn, Hammerquist, and Aimene<ref name="dmref">J. A. Nairn, C. C. Hammerquist, and Y. E. Aimene, "Numerical Implementation of Anisotropic Damage Mechanics," Int. J. for Numerical Methods in Engineering, 112(12), 1846-1868 (2017). [http://www.cof.orst.edu/cof/wse/faculty/Nairn/papers/MPMSoftening.pdf PDF]</ref> The extension to orthotropic materials is described in a paper on generalized damage mechanics methods<ref name="~~dmref~~">J. A. Nairn, "Generalization of Anisotropic Damage Mechanics Modeling in the Material Point Method," Int. J. for Numerical Methods in Engineering, 123, 5072-5097 (2022). [https://www.cof.orst.edu/cof/wse/faculty/Nairn/papers/GenDamage.pdf PDF]</ref>		The MPM implementation of softening isotropic materials is described in Nairn, Hammerquist, and Aimene.<ref name="dmref">J. A. Nairn, C. C. Hammerquist, and Y. E. Aimene, "Numerical Implementation of Anisotropic Damage Mechanics," Int. J. for Numerical Methods in Engineering, 112(12), 1846-1868 (2017). [http://www.cof.orst.edu/cof/wse/faculty/Nairn/papers/MPMSoftening.pdf PDF]</ref> The extension to orthotropic materials is described in a paper on generalized damage mechanics methods.<ref name="genref">J. A. Nairn, "Generalization of Anisotropic Damage Mechanics Modeling in the Material Point Method," Int. J. for Numerical Methods in Engineering, 123, 5072-5097 (2022). [https://www.cof.orst.edu/cof/wse/faculty/Nairn/papers/GenDamage.pdf PDF]</ref>

	== Damage Process ==		== Damage Process ==

Nairnj at 02:33, 18 April 2024

2024-04-18T02:33:13Z

← Older revision		Revision as of 02:33, 18 April 2024
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	where '''C''' is stiffness tensor for the underlying orthotopic material and '''D''' is an anisotropic 4<sup>th</sup> rank damage tensor appropriate for damage in orthotropic materials, and <math>\mathbf{\varepsilon}_{res}</math> is any residual strain (such as thermal or solvent induced strains).		where '''C''' is stiffness tensor for the underlying orthotopic material and '''D''' is an anisotropic 4<sup>th</sup> rank damage tensor appropriate for damage in orthotropic materials, and <math>\mathbf{\varepsilon}_{res}</math> is any residual strain (such as thermal or solvent induced strains).

	The MPM implementation of softening isotropic materials is described in Nairn, Hammerquist, and Aimene<ref name="dmref">J. A. Nairn, C. C. Hammerquist, and Y. E. Aimene, "Numerical Implementation of Anisotropic Damage Mechanics," Int. J. for Numerical Methods in Engineering, 112(12), 1846-1868 (2017). [http://www.cof.orst.edu/cof/wse/faculty/Nairn/papers/MPMSoftening.pdf PDF]</ref> ~~This~~ extension to orthotropic materials ~~will be~~ in a ~~future publication~~.		The MPM implementation of softening isotropic materials is described in Nairn, Hammerquist, and Aimene<ref name="dmref">J. A. Nairn, C. C. Hammerquist, and Y. E. Aimene, "Numerical Implementation of Anisotropic Damage Mechanics," Int. J. for Numerical Methods in Engineering, 112(12), 1846-1868 (2017). [http://www.cof.orst.edu/cof/wse/faculty/Nairn/papers/MPMSoftening.pdf PDF]</ref> The extension to orthotropic materials is described in a paper on generalized damage mechanics methods<ref name="dmref">J. A. Nairn, "Generalization of Anisotropic Damage Mechanics Modeling in the Material Point Method," Int. J. for Numerical Methods in Engineering, 123, 5072-5097 (2022). [https://www.cof.orst.edu/cof/wse/faculty/Nairn/papers/GenDamage.pdf PDF]</ref>

	== Damage Process ==		== Damage Process ==

Nairnj: /* Material Properties */

2024-04-18T02:29:43Z

Material Properties

← Older revision		Revision as of 02:29, 18 April 2024
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	\| coefVariation<br>wShape<br>wV0<br>statDistributionMode \|\| See the corresponding properties defined for an [[Isotropic Softening Material#Material Properties\|Isotropic softening material]]. \|\| \|\|		\| coefVariation<br>wShape<br>wV0<br>statDistributionMode \|\| See the corresponding properties defined for an [[Isotropic Softening Material#Material Properties\|Isotropic softening material]]. \|\| \|\|
	\|-		\|-
	\| coeff \|\| coefficient of friction for post-decohesion contact (default is 0 or frictionless~~) (experimental implementation in development in [[OSParticulas]] only~~) \|\| none \|\| 0		\| coeff \|\| coefficient of friction for post-decohesion contact (default is 0 or frictionless) \|\| none \|\| 0
	\|-		\|-
	\| ([[Common Material Properties\|other]]) \|\| Properties common to all materials \|\| varies \|\| varies		\| ([[Common Material Properties\|other]]) \|\| Properties common to all materials \|\| varies \|\| varies

Nairnj at 02:29, 18 April 2024

2024-04-18T02:29:18Z

← Older revision		Revision as of 02:29, 18 April 2024
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	== Constitutive Law ==		== Constitutive Law ==

	~~(This material is available only in [[OSParticulas]] because it is still in development)~~

	This [[Material Models#Softening Materials\|MPM softening material]] is an orthotropic, elastic material, but once it fails, it develops anisotropic damage. It will remain orthotropic, but properties in some dirrections will change. The constitutive law for this material is		This [[Material Models#Softening Materials\|MPM softening material]] is an orthotropic, elastic material, but once it fails, it develops anisotropic damage. It will remain orthotropic, but properties in some dirrections will change. The constitutive law for this material is

Nairnj: /* Constitutive Law */

2023-11-18T17:48:59Z

Constitutive Law

← Older revision		Revision as of 17:48, 18 November 2023
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	(This material is available only in [[OSParticulas]] because it is still in development)		(This material is available only in [[OSParticulas]] because it is still in development)

	This [[Material Models\|MPM ~~Material~~]] is an orthotropic, elastic material, but once it fails, it develops anisotropic damage. It will remain orthotropic, but properties in some dirrections will change. The constitutive law for this material is		This [[Material Models#Softening Materials\|MPM softening material]] is an orthotropic, elastic material, but once it fails, it develops anisotropic damage. It will remain orthotropic, but properties in some dirrections will change. The constitutive law for this material is

Nairnj: /* History Variables */

2023-09-21T21:17:54Z

History Variables

← Older revision		Revision as of 21:17, 21 September 2023
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	# For 2D it is cos(θ), but for 3D it is Euler angle α.		# For 2D it is cos(θ), but for 3D it is Euler angle α.
	# For 2D it is sin(θ), but for 3D it is Euler angle β.		# For 2D it is sin(θ), but for 3D it is Euler angle β.
	# For ~~2D it is not used, but for~~ 3D it is Euler angle γ.		# For 3D it is Euler angle γ. In 2D has total dissipated energy by damage mechanics (in [[ConsistentUnits Command#Legacy and Consistent Units\|energy units]])
	# ''A<sub>c</sub>''/''V<sub>p</sub>'' where ''A<sub>c</sub>'' is crack area within the particle and ''V<sub>p</sub>'' is particle volume.		# ''A<sub>c</sub>''/''V<sub>p</sub>'' where ''A<sub>c</sub>'' is crack area within the particle and ''V<sub>p</sub>'' is particle volume.
	# Relative strength derived at the start by <tt>coefVariation</tt> and <tt>coefVariationMode</tt> properties.		# Relative strength derived at the start by <tt>coefVariation</tt> and <tt>coefVariationMode</tt> properties.

Nairnj: /* History Variables */

2023-09-14T17:13:22Z

History Variables

← Older revision		Revision as of 17:13, 14 September 2023
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	# δ<sub>n</sub> or the maximum normal cracking strain.		# δ<sub>n</sub> or the maximum normal cracking strain.
	# δ<sub>xy</sub> or the maximum x-y shear cracking strain.		# δ<sub>xy</sub> or the maximum x-y shear cracking strain.
	# δ<sub>xz</sub> or the maximum x-z cracking strain ~~(zero for 2D)~~.		# This variable has two options:
			#* For 3D when using decoupled cuboid surface: δ<sub>xz</sub> or the maximum x-z cracking strain.
			#* For all other cases: G<sub>I</sub> or cumulative mode I dissipated energy.
	# d<sub>n</sub> or damage variable for normal loading. It varies from 0 to 1 where 1 is complete damage or failure.		# d<sub>n</sub> or damage variable for normal loading. It varies from 0 to 1 where 1 is complete damage or failure.
	# d<sub>xy</sub> or damage variable for x-y shear loading. It varies from 0 to 1 where 1 is complete damage or failure.		# d<sub>xy</sub> or damage variable for x-y shear loading. It varies from 0 to 1 where 1 is complete damage or failure.
	# d<sub>xz</sub> or damage variable for x-z shear loading. It varies from 0 to 1 where 1 is complete damage or failure ~~(zero for 2D)~~.		# This variable has two options:
			#* For 3D when using decoupled cuboid surface: d<sub>xz</sub> or damage variable for x-z shear loading. It varies from 0 to 1 where 1 is complete damage or failure.
			#* For all other cases: G<sub>II</sub> or cumulative mode II dissipated energy.
	# For 2D it is cos(θ), but for 3D it is Euler angle α.		# For 2D it is cos(θ), but for 3D it is Euler angle α.
	# For 2D it is sin(θ), but for 3D it is Euler angle β.		# For 2D it is sin(θ), but for 3D it is Euler angle β.