Rigid Material - Revision history

Nairnj: /* Deprecated Rigid Material */

2023-11-28T16:37:11Z

Deprecated Rigid Material

← Older revision		Revision as of 16:37, 28 November 2023
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	== Deprecated Rigid Material ==		== Deprecated Rigid Material ==

	Prior to introduction of separate rigid boundary condition particles and rigid contact particles, simulations had only one type of rigid material. This type had two functions by choosing <tt>SetDirection</tt> from 0 to 7 to get rigid boundary condition particles or <tt>SetDirection</tt> equal to 8 for rigid contact particles. Old simulations that define rigid materials by this method still work, but that approach is deprecated. New simulations should specify rigid materials ~~and~~ "RigidBC" or "RigidContact" materials.		Prior to introduction of separate rigid boundary condition particles and rigid contact particles, simulations had only one type of rigid material. This type had two functions by choosing <tt>SetDirection</tt> from 0 to 7 to get rigid boundary condition particles or <tt>SetDirection</tt> equal to 8 for rigid contact particles. Old simulations that define rigid materials by this method still work, but that approach is deprecated. New simulations should specify rigid materials as "RigidBC" or "RigidContact" materials.

	== Notes ==		== Notes ==

Nairnj: /* Constitutive Law */

2023-11-28T16:36:13Z

Constitutive Law

← Older revision		Revision as of 16:36, 28 November 2023
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	== Constitutive Law ==		== Constitutive Law ==

	These page documents two ~~type~~ of rigid [[Material Models\|MPM materials]] depending if you create a [[#RigidBC Material: Moving Boundary Condition\|RigidBC material]] or a [[#RigidContact Material\|RigidContact material]]. A <tt>RigidBC</tt> material implements moving boundary conditions while a <tt>RigidContact</tt> material is a moving rigid object that interacts with non-rigid materials by contact.		These page documents two types of rigid [[Material Models\|MPM materials]] depending if you create a [[#RigidBC Material: Moving Boundary Condition\|RigidBC material]] or a [[#RigidContact Material\|RigidContact material]]. A <tt>RigidBC</tt> material implements moving boundary conditions while a <tt>RigidContact</tt> material is a moving rigid object that interacts with non-rigid materials by contact.

	== RigidBC Material: Moving Boundary Condition ==		== RigidBC Material: Moving Boundary Condition ==

Nairnj: /* RigidContact Material Proiperties */

2022-09-02T16:04:52Z

RigidContact Material Proiperties

← Older revision		Revision as of 16:04, 2 September 2022
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	Rigid contact materials ignores [[Defining Cracks\|cracks]], but that actually makes it possible to use them for new crack problems. For example, these rigid particles can provide wedge opening of a crack. If the rigid particles run along an [[Defining Cracks\|explicit crack plane]], those particles may contact particles on both sides of the crack, which can move the top and bottom surfaces of the crack apart. It may be only way to wedge open a crack (<i>i.e.</i>, the only material that can act like it is within a crack rather than on either side of the crack). All crack calculations (<i>e.g.</i>, crack contact, traction laws, imperfect interfaces, updating of crack position, and J integral) will ignore the rigid particles. The interactions with the rigid particles arise only by contact laws between the rigid particles and the various crack velocity fields.		Rigid contact materials ignores [[Defining Cracks\|cracks]], but that actually makes it possible to use them for new crack problems. For example, these rigid particles can provide wedge opening of a crack. If the rigid particles run along an [[Defining Cracks\|explicit crack plane]], those particles may contact particles on both sides of the crack, which can move the top and bottom surfaces of the crack apart. It may be only way to wedge open a crack (<i>i.e.</i>, the only material that can act like it is within a crack rather than on either side of the crack). All crack calculations (<i>e.g.</i>, crack contact, traction laws, imperfect interfaces, updating of crack position, and J integral) will ignore the rigid particles. The interactions with the rigid particles arise only by contact laws between the rigid particles and the various crack velocity fields.

	=== RigidContact Material ~~Proiperties~~ ===		=== RigidContact Material Properties ===

	The rigid contact material properties are set with the following commands:		The rigid contact material properties are set with the following commands:

Nairnj: /* Rotation of Rigid Object */

2021-03-04T23:37:05Z

Rotation of Rigid Object

← Older revision		Revision as of 23:37, 4 March 2021
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	<math> (v_x,v_y) = \omega r\bigl(-\sin\theta,\cos\theta\bigr) = 2\pi f r\bigl(-(y-y_0),x-x_0\bigr)</math>		<math> (v_x,v_y) = \omega r\bigl(-\sin\theta,\cos\theta\bigr) = 2\pi f \bigl(-(y-y_0),x-x_0\bigr)</math>

	[[File:RigidRotation.jpg\|right]]		[[File:RigidRotation.jpg\|right]]
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	<math> v_x = {1\over \Delta t}\bigl((x-~~x_0~~)(\~~cos~~(2\pi f\Delta t)-1)-(~~y-y_0)~~\~~sin~~(2\pi f\Delta t)\bigr)</math>		<math> v_x = {1\over \Delta t}\bigl(-(y-y_0)\sin(2\pi f\Delta t)+(x-x_0)(\cos(2\pi f\Delta t)-1)\bigr)</math>

Nairnj: /* Rotation of Rigid Object */

2021-03-04T23:21:26Z

Rotation of Rigid Object

← Older revision		Revision as of 23:21, 4 March 2021
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	<math> (v_x,v_y) = \omega r\bigl(-\sin\theta,\cos\theta\bigr) = 2\pi f\bigl(-(y-y_0),x-x_0\bigr)</math>		<math> (v_x,v_y) = \omega r\bigl(-\sin\theta,\cos\theta\bigr) = 2\pi f r\bigl(-(y-y_0),x-x_0\bigr)</math>

	[[File:RigidRotation.jpg\|right]]		[[File:RigidRotation.jpg\|right]]

Nairnj: /* Rotation of Rigid Object */

2021-03-04T21:16:44Z

Rotation of Rigid Object

← Older revision		Revision as of 21:16, 4 March 2021
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	<math> v_y = {1\over \Delta t}\bigl((x-x_0)\sin(2\pi f\Delta t) + (y-y_0)(\cos(2\pi f\Delta t)-1)\bigr)</math>		<math> v_y = {1\over \Delta t}\bigl((x-x_0)\sin(2\pi f\Delta t) + (y-y_0)(\cos(2\pi f\Delta t)-1)\bigr)</math>

	where ''f'' is set to 1/''t<sub>rev</sub>'' where ''t<sub>rev</sub>'' is the amount of simulation time you want to complete one complete revolution. This function is an example of the need to allow time step as a variable in [[User Defined Functions\|user defined functions]]. It generalizes the tangential velocity field to allow for discrete rotation in each time step. A rotating and translating object can be modeled by adding the translational velocity and by accounting for any time dependence of <tt>x<sub>0</sub></tt> and <tt>y<sub>0</sub></tt>.		where ''f'' is set to 1/''t<sub>rev</sub>'' where ''t<sub>rev</sub>'' is the amount of simulation time you want to complete one complete revolution. For clockwise rotation, change the sign of each velocity. This function is an example of the need to allow time step as a variable in [[User Defined Functions\|user defined functions]]. It generalizes the tangential velocity field to allow for discrete rotation in each time step. A rotating and translating object can be modeled by adding the translational velocity and by accounting for any time dependence of <tt>x<sub>0</sub></tt> and <tt>y<sub>0</sub></tt>.

	=== Mirrored Velocity Property ===		=== Mirrored Velocity Property ===

Nairnj: /* Rotation of Rigid Object */

2021-03-04T21:08:47Z

Rotation of Rigid Object

← Older revision		Revision as of 21:08, 4 March 2021
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	<math> v_y = {1\over \Delta t}\bigl((x-x_0)\sin(2\pi f\Delta t) + (y-y_0)(\cos(2\pi f\Delta t)-1)\bigr)</math>		<math> v_y = {1\over \Delta t}\bigl((x-x_0)\sin(2\pi f\Delta t) + (y-y_0)(\cos(2\pi f\Delta t)-1)\bigr)</math>

	where ''f'' is set to 1/~~(2π~~''t<sub>rev</sub>''~~) when~~ ''t<sub>rev</sub>'' is the amount of simulation time you want to complete one complete revolution. This function is an example of the need to allow time step as a variable in [[User Defined Functions\|user defined functions]]. It generalizes the tangential velocity field to allow for discrete rotation in each time step. A rotating and translating object can be modeled by adding the translational velocity and by accounting for any time dependence of <tt>x<sub>0</sub></tt> and <tt>y<sub>0</sub></tt>.		where ''f'' is set to 1/''t<sub>rev</sub>'' where ''t<sub>rev</sub>'' is the amount of simulation time you want to complete one complete revolution. This function is an example of the need to allow time step as a variable in [[User Defined Functions\|user defined functions]]. It generalizes the tangential velocity field to allow for discrete rotation in each time step. A rotating and translating object can be modeled by adding the translational velocity and by accounting for any time dependence of <tt>x<sub>0</sub></tt> and <tt>y<sub>0</sub></tt>.

	=== Mirrored Velocity Property ===		=== Mirrored Velocity Property ===

Nairnj: /* Rotation of Rigid Object */

2021-03-04T21:07:57Z

Rotation of Rigid Object

← Older revision		Revision as of 21:07, 4 March 2021
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	<math> v_y = {1\over \Delta t}\bigl((x-x_0)\sin(2\pi f\Delta t) + (y-y_0)(\cos(2\pi f\Delta t)-1)\bigr)</math>		<math> v_y = {1\over \Delta t}\bigl((x-x_0)\sin(2\pi f\Delta t) + (y-y_0)(\cos(2\pi f\Delta t)-1)\bigr)</math>

	This function is an example of the need to allow time step as a variable in [[User Defined Functions\|user defined functions]]. It generalizes the tangential velocity field to allow for discrete rotation in each time step. A rotating and translating object can be modeled by adding the translational velocity and by accounting for any time dependence of <tt>x<sub>0</sub></tt> and <tt>y<sub>0</sub></tt>.		where ''f'' is set to 1/(2π''t<sub>rev</sub>'') when ''t<sub>rev</sub>'' is the amount of simulation time you want to complete one complete revolution. This function is an example of the need to allow time step as a variable in [[User Defined Functions\|user defined functions]]. It generalizes the tangential velocity field to allow for discrete rotation in each time step. A rotating and translating object can be modeled by adding the translational velocity and by accounting for any time dependence of <tt>x<sub>0</sub></tt> and <tt>y<sub>0</sub></tt>.

	=== Mirrored Velocity Property ===		=== Mirrored Velocity Property ===

Nairnj: /* Rotation of Rigid Object */

2021-03-04T21:05:38Z

Rotation of Rigid Object

← Older revision		Revision as of 21:05, 4 March 2021
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	<math> v_{eff} = {r\over \Delta t}\bigl( \cos(\theta+d\theta) - \cos\theta, \sin(\theta+d\theta) - \sin\theta\bigr)</math>		<math> v_{eff} = {r\over \Delta t}\bigl( \cos(\theta+d\theta) - \cos\theta, \sin(\theta+d\theta) - \sin\theta\bigr)</math>

	In terms of variables available to [[User Defined Functions\|user defined functions]], the effective velocity field (in [[ConsistentUnits Command#Legacy and Consistent Units\|velocity units]]) for a rotating rigid object is:		In terms of variables available to [[User Defined Functions\|user defined functions]], the effective velocity field (in [[ConsistentUnits Command#Legacy and Consistent Units\|velocity units]] when using consistent units) for a rotating rigid object is:


	<math> v_x = {~~1000~~\over \Delta t}\bigl((x-x_0)(\cos(2\pi f\Delta t)-1)-(y-y_0)\sin(2\pi f\Delta t)\bigr)</math>		<math> v_x = {1\over \Delta t}\bigl((x-x_0)(\cos(2\pi f\Delta t)-1)-(y-y_0)\sin(2\pi f\Delta t)\bigr)</math>


	<math> v_y = {~~1000~~\over \Delta t}\bigl((x-x_0)\sin(2\pi f\Delta t) + (y-y_0)(\cos(2\pi f\Delta t)-1)\bigr)</math>		<math> v_y = {1\over \Delta t}\bigl((x-x_0)\sin(2\pi f\Delta t) + (y-y_0)(\cos(2\pi f\Delta t)-1)\bigr)</math>

	This function is an example of the need to allow time step as a variable in [[User Defined Functions\|user defined functions]]. It generalizes the tangential velocity field to allow for discrete rotation in each time step. A rotating and translating object can be modeled by adding the translational velocity and by accounting for any time dependence of <tt>x<sub>0</sub></tt> and <tt>y<sub>0</sub></tt>.		This function is an example of the need to allow time step as a variable in [[User Defined Functions\|user defined functions]]. It generalizes the tangential velocity field to allow for discrete rotation in each time step. A rotating and translating object can be modeled by adding the translational velocity and by accounting for any time dependence of <tt>x<sub>0</sub></tt> and <tt>y<sub>0</sub></tt>.

Nairnj: /* Rotation of Rigid Object */

2021-03-04T21:03:53Z

Rotation of Rigid Object

← Older revision		Revision as of 21:03, 4 March 2021
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	[[File:RigidRotation.jpg\|right]]		[[File:RigidRotation.jpg\|right]]

	where <tt>r</tt> and <tt>θ</tt> are polar coordinates based on the center of the object, ω is the angular velocity and ''f'' is frequency in cycles per second. If you model rotation of these particles by setting these <tt>x</tt> and <tt>y</tt> velocities, the shape might distort with time and could distort rapidly at high rotation speeds. The problem is this tangential velocity field does not account for the discrete rotation that occurs during each time step. As illustrated on the right, a tangential velocity (''v<sub>tang</sub>'') moves the particle in the tangential direction, but after a finite time step, the motion should be to a rotated positioned. If this rotation affect is not accounted for, the rigid object will slowly expand as the simulation proceeds. The solution is to replace ''v<sub>tang</sub>'' with an effective velocity, ''v<sub>eff</sub>''. A particle that starts at <tt>(x-x<sub>0</sub>,y-y<sub>0</sub>)</tt> = <tt>(r</tt> <tt>cosθ,r</tt> <tt>sinθ)</tt>, ~~will~~ end at <tt>(r</tt> <tt>cos(θ+dθ),r</tt> <tt>sin(θ+dθ))</tt> where the incremental rotation angle is:		where <tt>r</tt> and <tt>θ</tt> are polar coordinates based on the center of the object, ω is the angular velocity and ''f'' is frequency in cycles per second. If you model rotation of these particles by setting these <tt>x</tt> and <tt>y</tt> velocities, the shape might distort with time and could distort rapidly at high rotation speeds. The problem is this tangential velocity field does not account for the discrete rotation that occurs during each time step. As illustrated on the right, a tangential velocity (''v<sub>tang</sub>'') moves the particle in the tangential direction, but after a finite time step, the motion should be to a rotated positioned. If this rotation affect is not accounted for, the rigid object will slowly expand as the simulation proceeds. The solution is to replace ''v<sub>tang</sub>'' with an effective velocity, ''v<sub>eff</sub>''. A particle that starts at <tt>(x-x<sub>0</sub>,y-y<sub>0</sub>)</tt> = <tt>(r</tt> <tt>cosθ,r</tt> <tt>sinθ)</tt>, should end at <tt>(r</tt> <tt>cos(θ+dθ),r</tt> <tt>sin(θ+dθ))</tt> where the incremental rotation angle is: