Isotropic Material Failure Surface - Revision history

Nairnj: /* Failure Surface */

2023-11-18T00:23:05Z

Failure Surface

← Older revision		Revision as of 00:23, 18 November 2023
Line 12:		Line 12:
	A challenge when detecting initiation, however, is that crack normal is not yet defined and therefore one cannot find tractions on the crack plane. In brief, damage initiation must determine when traction along any normal in 3D space reaches a failure surface. This calculation is done in principal stress space and finds critical stress by Mohr's circle calculations (more details are given in Ref. <ref name="dmGen"/>). The plot on the right shows the resulting initiation failure surfaces in a plot of minimum ''vs.'' maximum principle stresses. Stress states that reach these plots cause initiation of damage. The crack normal is given by the normal at the point where stress state reaches the surface. This normal is with respect to principal stress directions and that is rotated into global axes to get normal to the initiated crack surface. In this plot the 45 degree lists are when maximum shear stress (<math>\tau_{max}=(\sigma_1-\sigma_3)/2</math>) is equal to shear strength.		A challenge when detecting initiation, however, is that crack normal is not yet defined and therefore one cannot find tractions on the crack plane. In brief, damage initiation must determine when traction along any normal in 3D space reaches a failure surface. This calculation is done in principal stress space and finds critical stress by Mohr's circle calculations (more details are given in Ref. <ref name="dmGen"/>). The plot on the right shows the resulting initiation failure surfaces in a plot of minimum ''vs.'' maximum principle stresses. Stress states that reach these plots cause initiation of damage. The crack normal is given by the normal at the point where stress state reaches the surface. This normal is with respect to principal stress directions and that is rotated into global axes to get normal to the initiated crack surface. In this plot the 45 degree lists are when maximum shear stress (<math>\tau_{max}=(\sigma_1-\sigma_3)/2</math>) is equal to shear strength.

	[[Isotropic Softening Material\|IsoSoftening materials]] can choose ovoid, cuboid, or elliptical failure surfaces using its <tt>tractionFailureSurface</tt> property. The solid line in the plot is for ovoid surfaces. The dashed lines are for both cuboid and elliptical [[Isotropic Softening Material#Damage Evolution\|failure surfaces]]. For ovoid surfaces, the normal varies smoothly from 0 to 45 degrees as failure transitions from tensile to shear failure. For cuboid and elliptical surfaces, cracks are either at 0 degrees or 45 degrees. [[Isotropic Damage Mechanics\|IsoDamageMechanics materials]] use the cuboid surface, but only need that surface when using its mixed-mode metric.		[[Isotropic Softening Material\|IsoSoftening materials]] can choose ovoid, cuboid, or elliptical failure surfaces using its <tt>tractionFailureSurface</tt> property. The solid line in the plot is for ovoid surfaces. The dashed lines are for both cuboid and elliptical [[Isotropic Softening Material#Damage Evolution\|failure surfaces]]. For ovoid surfaces, the normal varies smoothly from 0 to 45 degrees as failure transitions from tensile to shear failure. For cuboid and elliptical surfaces, cracks are either at 0 degrees or 45 degrees. [[Isotropic Damage Mechanics\|IsoDamageMechanics materials]] use the cuboid surface, but only need that surface when using its mixed-mode metric. This material handles initiation internally rather than selecting an initiation law.

	== Pressure Dependent Shear Strength ==		== Pressure Dependent Shear Strength ==

Nairnj: /* Pressure Dependent Shear Strength */

2023-11-18T00:18:25Z

Pressure Dependent Shear Strength

← Older revision		Revision as of 00:18, 18 November 2023
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	== Pressure Dependent Shear Strength ==		== Pressure Dependent Shear Strength ==

	Although generalized damage mechanics<ref name="dmGen"/> provides a method to allow the failure surface to depend on any external variable, the only external dependence currently modeled is to allow shear strength to depend on pressure.		Although generalized damage mechanics<ref name="dmGen"/> provides a method to allow the failure surface to depend on any external variable, the only external dependence currently modeled is to allow shear strength to depend on pressure. This pressure dependence is only implement for [[Isotropic Softening Material\|IsoSoftening materials]] and [[Isotropic Plastic Softening Material\|IsoPlasticSoftening materials]].

	'''Model 0''': shear strength is independent of pressure		'''Model 0''': shear strength is independent of pressure

Nairnj: /* Failure Surface */

2023-11-18T00:15:26Z

Failure Surface

← Older revision		Revision as of 00:15, 18 November 2023
Line 12:		Line 12:
	A challenge when detecting initiation, however, is that crack normal is not yet defined and therefore one cannot find tractions on the crack plane. In brief, damage initiation must determine when traction along any normal in 3D space reaches a failure surface. This calculation is done in principal stress space and finds critical stress by Mohr's circle calculations (more details are given in Ref. <ref name="dmGen"/>). The plot on the right shows the resulting initiation failure surfaces in a plot of minimum ''vs.'' maximum principle stresses. Stress states that reach these plots cause initiation of damage. The crack normal is given by the normal at the point where stress state reaches the surface. This normal is with respect to principal stress directions and that is rotated into global axes to get normal to the initiated crack surface. In this plot the 45 degree lists are when maximum shear stress (<math>\tau_{max}=(\sigma_1-\sigma_3)/2</math>) is equal to shear strength.		A challenge when detecting initiation, however, is that crack normal is not yet defined and therefore one cannot find tractions on the crack plane. In brief, damage initiation must determine when traction along any normal in 3D space reaches a failure surface. This calculation is done in principal stress space and finds critical stress by Mohr's circle calculations (more details are given in Ref. <ref name="dmGen"/>). The plot on the right shows the resulting initiation failure surfaces in a plot of minimum ''vs.'' maximum principle stresses. Stress states that reach these plots cause initiation of damage. The crack normal is given by the normal at the point where stress state reaches the surface. This normal is with respect to principal stress directions and that is rotated into global axes to get normal to the initiated crack surface. In this plot the 45 degree lists are when maximum shear stress (<math>\tau_{max}=(\sigma_1-\sigma_3)/2</math>) is equal to shear strength.

	[[Isotropic Softening Material\|IsoSoftening materials]] can choose ovoid, cuboid, or elliptical failure surfaces using its <tt>tractionFailureSurface</tt> property. The solid line in the plot is for ovoid surfaces. The dashed lines are for both cuboid and elliptical [[Isotropic Softening Material#Damage Evolution\|failure surfaces]]. For ovoid surfaces, the normal varies smoothly from 0 to 45 degrees as failure transitions from tensile to shear failure. For cuboid and elliptical surfaces, cracks are either at 0 degrees or 45 degrees. [[Isotropic Damage Mechanics\|IsoDamageMechanics materials]] use the cuboid surface, but only need that surface when using is mixed mode ~~failure surface~~.		[[Isotropic Softening Material\|IsoSoftening materials]] can choose ovoid, cuboid, or elliptical failure surfaces using its <tt>tractionFailureSurface</tt> property. The solid line in the plot is for ovoid surfaces. The dashed lines are for both cuboid and elliptical [[Isotropic Softening Material#Damage Evolution\|failure surfaces]]. For ovoid surfaces, the normal varies smoothly from 0 to 45 degrees as failure transitions from tensile to shear failure. For cuboid and elliptical surfaces, cracks are either at 0 degrees or 45 degrees. [[Isotropic Damage Mechanics\|IsoDamageMechanics materials]] use the cuboid surface, but only need that surface when using its mixed-mode metric.

	== Pressure Dependent Shear Strength ==		== Pressure Dependent Shear Strength ==

Nairnj: /* Failure Surface */

2023-11-18T00:14:25Z

Failure Surface

← Older revision		Revision as of 00:14, 18 November 2023
Line 12:		Line 12:
	A challenge when detecting initiation, however, is that crack normal is not yet defined and therefore one cannot find tractions on the crack plane. In brief, damage initiation must determine when traction along any normal in 3D space reaches a failure surface. This calculation is done in principal stress space and finds critical stress by Mohr's circle calculations (more details are given in Ref. <ref name="dmGen"/>). The plot on the right shows the resulting initiation failure surfaces in a plot of minimum ''vs.'' maximum principle stresses. Stress states that reach these plots cause initiation of damage. The crack normal is given by the normal at the point where stress state reaches the surface. This normal is with respect to principal stress directions and that is rotated into global axes to get normal to the initiated crack surface. In this plot the 45 degree lists are when maximum shear stress (<math>\tau_{max}=(\sigma_1-\sigma_3)/2</math>) is equal to shear strength.		A challenge when detecting initiation, however, is that crack normal is not yet defined and therefore one cannot find tractions on the crack plane. In brief, damage initiation must determine when traction along any normal in 3D space reaches a failure surface. This calculation is done in principal stress space and finds critical stress by Mohr's circle calculations (more details are given in Ref. <ref name="dmGen"/>). The plot on the right shows the resulting initiation failure surfaces in a plot of minimum ''vs.'' maximum principle stresses. Stress states that reach these plots cause initiation of damage. The crack normal is given by the normal at the point where stress state reaches the surface. This normal is with respect to principal stress directions and that is rotated into global axes to get normal to the initiated crack surface. In this plot the 45 degree lists are when maximum shear stress (<math>\tau_{max}=(\sigma_1-\sigma_3)/2</math>) is equal to shear strength.

	[[Isotropic Softening Material\|IsoSoftening materials]] can choose ovoid, cuboid, or elliptical failure surfaces using its <tt>tractionFailureSurface</tt> property. The solid line in the plot is for ovoid surfaces. The dashed lines are for both cuboid and elliptical [[Isotropic Softening Material#Damage Evolution\|failure surfaces]]. For ovoid surfaces, the normal varies smoothly from 0 to 45 degrees as failure transitions ~~for~~ tensile to shear failure. For cuboid and elliptical surfaces, cracks are either at 0 degrees or 45 degrees. [[Isotropic Damage Mechanics\|IsoDamageMechanics materials]] use the cuboid surface, but only need that surface when using is mixed mode failure surface.		[[Isotropic Softening Material\|IsoSoftening materials]] can choose ovoid, cuboid, or elliptical failure surfaces using its <tt>tractionFailureSurface</tt> property. The solid line in the plot is for ovoid surfaces. The dashed lines are for both cuboid and elliptical [[Isotropic Softening Material#Damage Evolution\|failure surfaces]]. For ovoid surfaces, the normal varies smoothly from 0 to 45 degrees as failure transitions from tensile to shear failure. For cuboid and elliptical surfaces, cracks are either at 0 degrees or 45 degrees. [[Isotropic Damage Mechanics\|IsoDamageMechanics materials]] use the cuboid surface, but only need that surface when using is mixed mode failure surface.

	== Pressure Dependent Shear Strength ==		== Pressure Dependent Shear Strength ==

Nairnj: /* Failure Surface */

2023-11-18T00:14:00Z

Failure Surface

← Older revision		Revision as of 00:14, 18 November 2023
Line 12:		Line 12:
	A challenge when detecting initiation, however, is that crack normal is not yet defined and therefore one cannot find tractions on the crack plane. In brief, damage initiation must determine when traction along any normal in 3D space reaches a failure surface. This calculation is done in principal stress space and finds critical stress by Mohr's circle calculations (more details are given in Ref. <ref name="dmGen"/>). The plot on the right shows the resulting initiation failure surfaces in a plot of minimum ''vs.'' maximum principle stresses. Stress states that reach these plots cause initiation of damage. The crack normal is given by the normal at the point where stress state reaches the surface. This normal is with respect to principal stress directions and that is rotated into global axes to get normal to the initiated crack surface. In this plot the 45 degree lists are when maximum shear stress (<math>\tau_{max}=(\sigma_1-\sigma_3)/2</math>) is equal to shear strength.		A challenge when detecting initiation, however, is that crack normal is not yet defined and therefore one cannot find tractions on the crack plane. In brief, damage initiation must determine when traction along any normal in 3D space reaches a failure surface. This calculation is done in principal stress space and finds critical stress by Mohr's circle calculations (more details are given in Ref. <ref name="dmGen"/>). The plot on the right shows the resulting initiation failure surfaces in a plot of minimum ''vs.'' maximum principle stresses. Stress states that reach these plots cause initiation of damage. The crack normal is given by the normal at the point where stress state reaches the surface. This normal is with respect to principal stress directions and that is rotated into global axes to get normal to the initiated crack surface. In this plot the 45 degree lists are when maximum shear stress (<math>\tau_{max}=(\sigma_1-\sigma_3)/2</math>) is equal to shear strength.

	[[Isotropic Softening Material\|IsoSoftening materials]] can choose ovoid, cuboid, or elliptical failure surfaces using its <tt>tractionFailureSurface</tt> property. The solid line in the plot is for ~~cuboid~~ surfaces. The dashed lines are for both cuboid and elliptical [[Isotropic Softening Material#Damage Evolution\|failure surfaces]]. For ovoid surfaces, the normal varies smoothly from 0 to 45 degrees as failure transitions for tensile to shear failure. For cuboid and elliptical surfaces, cracks are either at 0 degrees or 45 degrees. [[Isotropic Damage Mechanics\|IsoDamageMechanics materials]] use the cuboid surface, but only need that surface when using is mixed mode failure surface.		[[Isotropic Softening Material\|IsoSoftening materials]] can choose ovoid, cuboid, or elliptical failure surfaces using its <tt>tractionFailureSurface</tt> property. The solid line in the plot is for ovoid surfaces. The dashed lines are for both cuboid and elliptical [[Isotropic Softening Material#Damage Evolution\|failure surfaces]]. For ovoid surfaces, the normal varies smoothly from 0 to 45 degrees as failure transitions for tensile to shear failure. For cuboid and elliptical surfaces, cracks are either at 0 degrees or 45 degrees. [[Isotropic Damage Mechanics\|IsoDamageMechanics materials]] use the cuboid surface, but only need that surface when using is mixed mode failure surface.

	== Pressure Dependent Shear Strength ==		== Pressure Dependent Shear Strength ==

Nairnj: /* Failure Surface */

2023-11-18T00:13:32Z

Failure Surface

← Older revision		Revision as of 00:13, 18 November 2023
Line 10:		Line 10:
	Although some damage mechanics papers allow various initiation criteria to be be paired with various damage evolution methods, that suggestion is wrong. Instead, the initiation law must be identical to the postulated traction failure surface with the initiation stress equal to the undamaged strength in the damage mechanics softening laws. This initiation law thus uses the [[Isotropic Softening Material#Damage Evolution\|chosen failure surface]] with the initiation normal stress, <math>\sigma_c</math> equal to the undamage tensile strength and the initiation shear stress, <math>\tau_c</math>, equal to undamaged shear strength (both of which are entered as parameters in this law).		Although some damage mechanics papers allow various initiation criteria to be be paired with various damage evolution methods, that suggestion is wrong. Instead, the initiation law must be identical to the postulated traction failure surface with the initiation stress equal to the undamaged strength in the damage mechanics softening laws. This initiation law thus uses the [[Isotropic Softening Material#Damage Evolution\|chosen failure surface]] with the initiation normal stress, <math>\sigma_c</math> equal to the undamage tensile strength and the initiation shear stress, <math>\tau_c</math>, equal to undamaged shear strength (both of which are entered as parameters in this law).

	A challenge when detecting initiation, however, is that crack normal is not yet defined and therefore one cannot find tractions on the crack plane. In brief, damage initiation must determine when traction along any normal in 3D space reaches a failure surface. This calculation is done in principal stress space and finds critical stress by Mohr's circle calculations (more details are given in Ref. <ref name="dmGen"/>). The plot on the right shows the resulting initiation failure surfaces in a plot of minimum ''vs.'' maximum principle stresses. Stress states that reach these plots cause initiation of damage. The crack normal is given by the normal at the point where stress state reaches the surface. This normal is with respect to principal stress directions and that is rotated into global axes to get normal to the initiated crack surface. In this plot ~~''r'' is~~ the maximum shear stress ~~given by~~ <math>(\sigma_1-\sigma_3)/2</math>.		A challenge when detecting initiation, however, is that crack normal is not yet defined and therefore one cannot find tractions on the crack plane. In brief, damage initiation must determine when traction along any normal in 3D space reaches a failure surface. This calculation is done in principal stress space and finds critical stress by Mohr's circle calculations (more details are given in Ref. <ref name="dmGen"/>). The plot on the right shows the resulting initiation failure surfaces in a plot of minimum ''vs.'' maximum principle stresses. Stress states that reach these plots cause initiation of damage. The crack normal is given by the normal at the point where stress state reaches the surface. This normal is with respect to principal stress directions and that is rotated into global axes to get normal to the initiated crack surface. In this plot the 45 degree lists are when maximum shear stress (<math>\tau_{max}=(\sigma_1-\sigma_3)/2</math>) is equal to shear strength.

	[[Isotropic Softening Material\|IsoSoftening materials]] can choose ovoid, cuboid, or elliptical failure surfaces using its <tt>tractionFailureSurface</tt> property. The solid line in the plot is for cuboid surfaces. The dashed lines are for both cuboid and elliptical [[Isotropic Softening Material#Damage Evolution\|failure surfaces]]. For ovoid surfaces, the normal varies smoothly from 0 to 45 degrees as failure transitions for tensile to shear failure. For cuboid and elliptical surfaces, cracks are either at 0 degrees or 45 degrees. [[Isotropic Damage Mechanics\|IsoDamageMechanics materials]] use the cuboid surface, but only need that surface when using is mixed mode failure surface.		[[Isotropic Softening Material\|IsoSoftening materials]] can choose ovoid, cuboid, or elliptical failure surfaces using its <tt>tractionFailureSurface</tt> property. The solid line in the plot is for cuboid surfaces. The dashed lines are for both cuboid and elliptical [[Isotropic Softening Material#Damage Evolution\|failure surfaces]]. For ovoid surfaces, the normal varies smoothly from 0 to 45 degrees as failure transitions for tensile to shear failure. For cuboid and elliptical surfaces, cracks are either at 0 degrees or 45 degrees. [[Isotropic Damage Mechanics\|IsoDamageMechanics materials]] use the cuboid surface, but only need that surface when using is mixed mode failure surface.

Nairnj: /* Failure Surface */

2023-11-18T00:12:12Z

Failure Surface

← Older revision		Revision as of 00:12, 18 November 2023
Line 10:		Line 10:
	Although some damage mechanics papers allow various initiation criteria to be be paired with various damage evolution methods, that suggestion is wrong. Instead, the initiation law must be identical to the postulated traction failure surface with the initiation stress equal to the undamaged strength in the damage mechanics softening laws. This initiation law thus uses the [[Isotropic Softening Material#Damage Evolution\|chosen failure surface]] with the initiation normal stress, <math>\sigma_c</math> equal to the undamage tensile strength and the initiation shear stress, <math>\tau_c</math>, equal to undamaged shear strength (both of which are entered as parameters in this law).		Although some damage mechanics papers allow various initiation criteria to be be paired with various damage evolution methods, that suggestion is wrong. Instead, the initiation law must be identical to the postulated traction failure surface with the initiation stress equal to the undamaged strength in the damage mechanics softening laws. This initiation law thus uses the [[Isotropic Softening Material#Damage Evolution\|chosen failure surface]] with the initiation normal stress, <math>\sigma_c</math> equal to the undamage tensile strength and the initiation shear stress, <math>\tau_c</math>, equal to undamaged shear strength (both of which are entered as parameters in this law).

	A challenge when detecting initiation, however, is that crack normal is not yet defined and therefore one cannot find tractions on the crack plane. In brief, damage initiation must determine when traction along any normal in 3D space reaches a failure surface. This calculation is done in principal stress space and finds critical stress by Mohr's circle calculations (more details are given in Ref. <ref name="dmGen"/>). The plot on the right shows the resulting initiation failure surfaces in a plot of minimum ''vs.'' maximum principle stresses. Stress states that reach these plots cause initiation of damage. The crack normal given by the normal at the point where stress state reaches the surface. This normal is with respect to principal stress directions and that is rotated into global axes to get normal to the initiated crack surface. In this plot ''r'' is the maximum shear stress given by <math>(\sigma_1-\sigma_3)/2</math>.		A challenge when detecting initiation, however, is that crack normal is not yet defined and therefore one cannot find tractions on the crack plane. In brief, damage initiation must determine when traction along any normal in 3D space reaches a failure surface. This calculation is done in principal stress space and finds critical stress by Mohr's circle calculations (more details are given in Ref. <ref name="dmGen"/>). The plot on the right shows the resulting initiation failure surfaces in a plot of minimum ''vs.'' maximum principle stresses. Stress states that reach these plots cause initiation of damage. The crack normal is given by the normal at the point where stress state reaches the surface. This normal is with respect to principal stress directions and that is rotated into global axes to get normal to the initiated crack surface. In this plot ''r'' is the maximum shear stress given by <math>(\sigma_1-\sigma_3)/2</math>.

	[[Isotropic Softening Material\|IsoSoftening materials]] can choose ovoid, cuboid, or elliptical failure surfaces using its <tt>tractionFailureSurface</tt> property. The solid line in the plot is for cuboid surfaces. The dashed lines are for both cuboid and elliptical [[Isotropic Softening Material#Damage Evolution\|failure surfaces]]. For ovoid surfaces, the normal varies smoothly from 0 to 45 degrees as failure transitions for tensile to shear failure. For cuboid and elliptical surfaces, cracks are either at 0 degrees or 45 degrees. [[Isotropic Damage Mechanics\|IsoDamageMechanics materials]] use the cuboid surface, but only need that surface when using is mixed mode failure surface.		[[Isotropic Softening Material\|IsoSoftening materials]] can choose ovoid, cuboid, or elliptical failure surfaces using its <tt>tractionFailureSurface</tt> property. The solid line in the plot is for cuboid surfaces. The dashed lines are for both cuboid and elliptical [[Isotropic Softening Material#Damage Evolution\|failure surfaces]]. For ovoid surfaces, the normal varies smoothly from 0 to 45 degrees as failure transitions for tensile to shear failure. For cuboid and elliptical surfaces, cracks are either at 0 degrees or 45 degrees. [[Isotropic Damage Mechanics\|IsoDamageMechanics materials]] use the cuboid surface, but only need that surface when using is mixed mode failure surface.

Nairnj: /* Failure Surface */

2023-11-18T00:11:56Z

Failure Surface

← Older revision		Revision as of 00:11, 18 November 2023
Line 10:		Line 10:
	Although some damage mechanics papers allow various initiation criteria to be be paired with various damage evolution methods, that suggestion is wrong. Instead, the initiation law must be identical to the postulated traction failure surface with the initiation stress equal to the undamaged strength in the damage mechanics softening laws. This initiation law thus uses the [[Isotropic Softening Material#Damage Evolution\|chosen failure surface]] with the initiation normal stress, <math>\sigma_c</math> equal to the undamage tensile strength and the initiation shear stress, <math>\tau_c</math>, equal to undamaged shear strength (both of which are entered as parameters in this law).		Although some damage mechanics papers allow various initiation criteria to be be paired with various damage evolution methods, that suggestion is wrong. Instead, the initiation law must be identical to the postulated traction failure surface with the initiation stress equal to the undamaged strength in the damage mechanics softening laws. This initiation law thus uses the [[Isotropic Softening Material#Damage Evolution\|chosen failure surface]] with the initiation normal stress, <math>\sigma_c</math> equal to the undamage tensile strength and the initiation shear stress, <math>\tau_c</math>, equal to undamaged shear strength (both of which are entered as parameters in this law).

	A challenge when detecting initiation, however, is that crack normal is not yet defined and therefore one cannot find tractions on the crack plane. In brief, damage initiation must determine when traction along any normal in 3D space reaches a failure surface. This calculation is done in principal stress space and finds critical stress by Mohr's circle calculations (more details are given in Ref. <ref name="dmGen"/>). The plot on the right shows the resulting initiation failure surfaces in a plot of minimum ''vs.'' maximum principle stresses. Stress states ~~the~~ reach these plots cause initiation of damage. The crack normal given by the normal at the point where stress state reaches the surface. This normal is with respect to principal stress directions and that is rotated into global axes to get normal to the initiated crack surface. In this plot ''r'' is the maximum shear stress given by <math>(\sigma_1-\sigma_3)/2</math>.		A challenge when detecting initiation, however, is that crack normal is not yet defined and therefore one cannot find tractions on the crack plane. In brief, damage initiation must determine when traction along any normal in 3D space reaches a failure surface. This calculation is done in principal stress space and finds critical stress by Mohr's circle calculations (more details are given in Ref. <ref name="dmGen"/>). The plot on the right shows the resulting initiation failure surfaces in a plot of minimum ''vs.'' maximum principle stresses. Stress states that reach these plots cause initiation of damage. The crack normal given by the normal at the point where stress state reaches the surface. This normal is with respect to principal stress directions and that is rotated into global axes to get normal to the initiated crack surface. In this plot ''r'' is the maximum shear stress given by <math>(\sigma_1-\sigma_3)/2</math>.

	[[Isotropic Softening Material\|IsoSoftening materials]] can choose ovoid, cuboid, or elliptical failure surfaces using its <tt>tractionFailureSurface</tt> property. The solid line in the plot is for cuboid surfaces. The dashed lines are for both cuboid and elliptical [[Isotropic Softening Material#Damage Evolution\|failure surfaces]]. For ovoid surfaces, the normal varies smoothly from 0 to 45 degrees as failure transitions for tensile to shear failure. For cuboid and elliptical surfaces, cracks are either at 0 degrees or 45 degrees. [[Isotropic Damage Mechanics\|IsoDamageMechanics materials]] use the cuboid surface, but only need that surface when using is mixed mode failure surface.		[[Isotropic Softening Material\|IsoSoftening materials]] can choose ovoid, cuboid, or elliptical failure surfaces using its <tt>tractionFailureSurface</tt> property. The solid line in the plot is for cuboid surfaces. The dashed lines are for both cuboid and elliptical [[Isotropic Softening Material#Damage Evolution\|failure surfaces]]. For ovoid surfaces, the normal varies smoothly from 0 to 45 degrees as failure transitions for tensile to shear failure. For cuboid and elliptical surfaces, cracks are either at 0 degrees or 45 degrees. [[Isotropic Damage Mechanics\|IsoDamageMechanics materials]] use the cuboid surface, but only need that surface when using is mixed mode failure surface.

Nairnj: /* Failure Surface */

2023-11-18T00:11:32Z

Failure Surface

← Older revision		Revision as of 00:11, 18 November 2023
Line 10:		Line 10:
	Although some damage mechanics papers allow various initiation criteria to be be paired with various damage evolution methods, that suggestion is wrong. Instead, the initiation law must be identical to the postulated traction failure surface with the initiation stress equal to the undamaged strength in the damage mechanics softening laws. This initiation law thus uses the [[Isotropic Softening Material#Damage Evolution\|chosen failure surface]] with the initiation normal stress, <math>\sigma_c</math> equal to the undamage tensile strength and the initiation shear stress, <math>\tau_c</math>, equal to undamaged shear strength (both of which are entered as parameters in this law).		Although some damage mechanics papers allow various initiation criteria to be be paired with various damage evolution methods, that suggestion is wrong. Instead, the initiation law must be identical to the postulated traction failure surface with the initiation stress equal to the undamaged strength in the damage mechanics softening laws. This initiation law thus uses the [[Isotropic Softening Material#Damage Evolution\|chosen failure surface]] with the initiation normal stress, <math>\sigma_c</math> equal to the undamage tensile strength and the initiation shear stress, <math>\tau_c</math>, equal to undamaged shear strength (both of which are entered as parameters in this law).

	A challenge when detecting initiation, however, is that crack normal is not yet defined and therefore one cannot find tractions on the crack plane. In brief, damage initiation must determine when traction along any normal in 3D space reaches a failure surface. This calculation is done in ~~principle~~ stress space and finds critical stress by Mohr's circle calculations (more details are given in Ref. <ref name="dmGen"/>). The plot on the right shows the resulting initiation failure surfaces in a plot of minimum ''vs.'' maximum principle stresses. Stress states the reach these plots cause initiation of damage. The crack normal given by the normal at the point where stress state reaches the surface. This normal is with respect to principal stress directions and that is rotated into global axes to get normal to the initiated crack surface. In this plot ''r'' is the maximum shear stress given by <math>(\sigma_1-\sigma_3)/2</math>.		A challenge when detecting initiation, however, is that crack normal is not yet defined and therefore one cannot find tractions on the crack plane. In brief, damage initiation must determine when traction along any normal in 3D space reaches a failure surface. This calculation is done in principal stress space and finds critical stress by Mohr's circle calculations (more details are given in Ref. <ref name="dmGen"/>). The plot on the right shows the resulting initiation failure surfaces in a plot of minimum ''vs.'' maximum principle stresses. Stress states the reach these plots cause initiation of damage. The crack normal given by the normal at the point where stress state reaches the surface. This normal is with respect to principal stress directions and that is rotated into global axes to get normal to the initiated crack surface. In this plot ''r'' is the maximum shear stress given by <math>(\sigma_1-\sigma_3)/2</math>.

	[[Isotropic Softening Material\|IsoSoftening materials]] can choose ovoid, cuboid, or elliptical failure surfaces using its <tt>tractionFailureSurface</tt> property. The solid line in the plot is for cuboid surfaces. The dashed lines are for both cuboid and elliptical [[Isotropic Softening Material#Damage Evolution\|failure surfaces]]. For ovoid surfaces, the normal varies smoothly from 0 to 45 degrees as failure transitions for tensile to shear failure. For cuboid and elliptical surfaces, cracks are either at 0 degrees or 45 degrees. [[Isotropic Damage Mechanics\|IsoDamageMechanics materials]] use the cuboid surface, but only need that surface when using is mixed mode failure surface.		[[Isotropic Softening Material\|IsoSoftening materials]] can choose ovoid, cuboid, or elliptical failure surfaces using its <tt>tractionFailureSurface</tt> property. The solid line in the plot is for cuboid surfaces. The dashed lines are for both cuboid and elliptical [[Isotropic Softening Material#Damage Evolution\|failure surfaces]]. For ovoid surfaces, the normal varies smoothly from 0 to 45 degrees as failure transitions for tensile to shear failure. For cuboid and elliptical surfaces, cracks are either at 0 degrees or 45 degrees. [[Isotropic Damage Mechanics\|IsoDamageMechanics materials]] use the cuboid surface, but only need that surface when using is mixed mode failure surface.

Nairnj: /* Failure Surface */

2023-11-18T00:10:37Z

Failure Surface

← Older revision		Revision as of 00:10, 18 November 2023
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	[[File:MaxPrinciple.png\|400px\|right]]		[[File:MaxPrinciple.png\|400px\|right]]

	Although some damage mechanics papers allow various initiation criteria to be be paired with various damage evolution methods, that suggestion is wrong. Instead, the initiation law must be identical to the postulated traction failure surface with the initiation stress equal to the undamaged strength in the damage mechanics softening laws. This initiation law thus uses the [[Isotropic Softening Material#Damage Evolution\|chosen failure surface]] with the initiation normal stress, <math>\sigma_c</math> equal to the undamage tensile strength and the initiation shear stress, <math>\tau_c</math>, equal to undamaged shear strength (both of which are entered as parameters in ~~the~~ law.		Although some damage mechanics papers allow various initiation criteria to be be paired with various damage evolution methods, that suggestion is wrong. Instead, the initiation law must be identical to the postulated traction failure surface with the initiation stress equal to the undamaged strength in the damage mechanics softening laws. This initiation law thus uses the [[Isotropic Softening Material#Damage Evolution\|chosen failure surface]] with the initiation normal stress, <math>\sigma_c</math> equal to the undamage tensile strength and the initiation shear stress, <math>\tau_c</math>, equal to undamaged shear strength (both of which are entered as parameters in this law).

	A challenge when detecting initiation, however, is that crack normal is not yet defined and therefore one cannot find tractions on the crack plane. In brief, damage initiation must determine when traction along any normal in 3D space reaches a failure surface. This calculation is done in principle stress space and finds critical stress by Mohr's circle calculations (more details are given in Ref. <ref name="dmGen"/>). The plot on the right shows the resulting initiation failure surfaces in a plot of minimum ''vs.'' maximum principle stresses. Stress states the reach these plots cause initiation of damage. The crack normal given by the normal at the point where stress state reaches the surface. This normal is with respect to principal stress directions and that is rotated into global axes to get normal to the initiated crack surface. In this plot ''r'' is the maximum shear stress given by <math>(\sigma_1-\sigma_3)/2</math>.		A challenge when detecting initiation, however, is that crack normal is not yet defined and therefore one cannot find tractions on the crack plane. In brief, damage initiation must determine when traction along any normal in 3D space reaches a failure surface. This calculation is done in principle stress space and finds critical stress by Mohr's circle calculations (more details are given in Ref. <ref name="dmGen"/>). The plot on the right shows the resulting initiation failure surfaces in a plot of minimum ''vs.'' maximum principle stresses. Stress states the reach these plots cause initiation of damage. The crack normal given by the normal at the point where stress state reaches the surface. This normal is with respect to principal stress directions and that is rotated into global axes to get normal to the initiated crack surface. In this plot ''r'' is the maximum shear stress given by <math>(\sigma_1-\sigma_3)/2</math>.