MPM Methods and Simulation Timing - Revision history

Nairnj: /* Theory: MPM Time Step */

2026-04-12T18:09:18Z

Theory: MPM Time Step

← Older revision		Revision as of 18:09, 12 April 2026
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	<math> C = { v\Delta t\over \Delta x} \qquad {\rm or} \qquad\Delta t =C { \Delta x\over v}</math>		<math> C = { v\Delta t\over \Delta x} \qquad {\rm or} \qquad\Delta t =C { \Delta x\over v}</math>

	The entered ''C'' must be less then 1.0. The default in [[NairnMPM]] is ''C'' = 0.5. Lower values may be needed depending on simulations features such as [[Setting Velocity and Transport Values\|fixed-velocity boundary conditions]] on the grid or created by [[Rigid Material\|rigid particles]] when modeling [[Multimaterial MPM\|contact]], when modeling brittle materials using [[Material Models#Softening Materials\|damage mechanics]] or when using high order FMPM(k). An alternative to very low ''C'' is to try [[#Restarting Time Steps\|restarting time steps]] that develop high accelerations on the grid.		The entered ''C'' must be less then 1.0. The default in [[NairnMPM]] is ''C'' = 0.5. Lower values may be needed depending on simulations features such as [[Setting Velocity and Transport Values\|fixed-velocity boundary conditions]] on the grid or created by [[Rigid Material\|rigid particles]] when modeling [[Multimaterial MPM\|contact]], when modeling brittle materials using [[Material Models#Softening Materials\|damage mechanics]], or when using [[PeriodicXPIC Custom Task\|high order FMPM(k)]]. An alternative to very low ''C'' is to try [[#Restarting Time Steps\|restarting time steps]] that develop high accelerations on the grid.

	When transport tasks are activated ([[Thermal Calculations\|conduction]], [[Diffusion Calculations\|diffusion]], or [[Poroelasticity Calculations\|poroelasticity]]), convergence of transport calculations requires the time step to satisfy		When transport tasks are activated ([[Thermal Calculations\|conduction]], [[Diffusion Calculations\|diffusion]], or [[Poroelasticity Calculations\|poroelasticity]]), convergence of transport calculations requires the time step to satisfy

Nairnj: /* Theory: MPM Time Step */

2026-04-12T18:07:30Z

Theory: MPM Time Step

← Older revision		Revision as of 18:07, 12 April 2026
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	<math> C = { v\Delta t\over \Delta x} \qquad {\rm or} \qquad\Delta t =C { \Delta x\over v}</math>		<math> C = { v\Delta t\over \Delta x} \qquad {\rm or} \qquad\Delta t =C { \Delta x\over v}</math>

	The entered ''C'' must be less then 1.0. The default in [[NairnMPM]] is ''C'' = 0.5. Lower values may be ~~are~~ needed ~~to resolve instabilities around~~ [[Setting Velocity and Transport Values\|fixed-velocity boundary conditions]] on the grid or created by [[Rigid Material\|rigid particles]] when modeling [[Multimaterial MPM\|contact]], ~~and~~ when modeling brittle materials using [[Material Models#Softening Materials\|damage mechanics]]. An alternative to very low ''C'' is to try [[#Restarting Time Steps\|restarting time steps]] that develop high accelerations on the grid.		The entered ''C'' must be less then 1.0. The default in [[NairnMPM]] is ''C'' = 0.5. Lower values may be needed depending on simulations features such as [[Setting Velocity and Transport Values\|fixed-velocity boundary conditions]] on the grid or created by [[Rigid Material\|rigid particles]] when modeling [[Multimaterial MPM\|contact]], when modeling brittle materials using [[Material Models#Softening Materials\|damage mechanics]] or when using high order FMPM(k). An alternative to very low ''C'' is to try [[#Restarting Time Steps\|restarting time steps]] that develop high accelerations on the grid.

	When transport tasks are activated ([[Thermal Calculations\|conduction]], [[Diffusion Calculations\|diffusion]], or [[Poroelasticity Calculations\|poroelasticity]]), convergence of transport calculations requires the time step to satisfy		When transport tasks are activated ([[Thermal Calculations\|conduction]], [[Diffusion Calculations\|diffusion]], or [[Poroelasticity Calculations\|poroelasticity]]), convergence of transport calculations requires the time step to satisfy

Nairnj: /* Restarting Time Steps */

2021-04-26T18:15:53Z

Restarting Time Steps

← Older revision		Revision as of 18:15, 26 April 2021
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	where Δ''t'' is the current time step. If any node's ''d'' relative to its cell size is greater than an entered rescaling factor, the time step is discarded and restarted using a smaller time step. This option is invoked using the [[#Input Commands\|<RestartScaling> command]]. To prevent the time step from permanently remaining small (and making a simulation too slow), this option should always be used in conjunction with an [[AdjustTimeStep Custom Task]]. This tasks will allow the time step to increase once nodal accelerations get under control, but should include its <tt>maxIncrease</tt> parameter to prevent returning immediately to the previous time step.		where Δ''t'' is the current time step. If any node's ''d'' relative to its cell size is greater than an entered rescaling factor, the time step is discarded and restarted using a smaller time step. This option is invoked using the [[#Input Commands\|<RestartScaling> command]]. To prevent the time step from permanently remaining small (and making a simulation too slow), this option should always be used in conjunction with an [[AdjustTimeStep Custom Task]]. This tasks will allow the time step to increase once nodal accelerations get under control, but should include its <tt>maxIncrease</tt> parameter to prevent returning immediately to the previous time step.

	Note that not all simulations can restart time steps. If your simulation is using a feature that cannot be restarted and you invoke restarting, an error message will be printed and the simulation not start. Most prominently, simulations with restarting are limited to [[#Theory: Stress and Strain Updates\|USL- and USL+ strain updates]].		Note that not all simulations can restart time steps. If your simulation is using a feature that cannot be restarted and you invoke restarting, an error message will be printed and the simulation will not start. Most prominently, simulations with restarting are limited to [[#Theory: Stress and Strain Updates\|USL- and USL+ strain updates]].

	== Input Commands ==		== Input Commands ==

Nairnj: /* Notes */

2021-01-04T19:41:16Z

Notes

← Older revision		Revision as of 19:41, 4 January 2021
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	<li>These methods are based on quadratic spline N<sub>i</sub>(x) grid shape functions.		<li>These methods are based on quadratic spline N<sub>i</sub>(x) grid shape functions.
	<li><tt>qCPDI</tt> is less efficient than <tt>lCPDI</tt> and in trial runs appears to have little or no benefit. It is available for comparison and potential future research into MPM shape function methods.		<li><tt>qCPDI</tt> is less efficient than <tt>lCPDI</tt> and in trial runs appears to have little or no benefit. It is available for comparison and potential future research into MPM shape function methods.
	<li>The number of points per element must be set before defining material points in your analysis. If desired, however you can use a different ~~numbers~~ of points per element in selected [[MPM Region and Hole Commands\|regions]] or when [[BMPRegion Command\|assigning particles using an image]]. Note that script files and <tt>XML</tt> files set this number differently. Script files set the number for each axis (which is squared for 2D or cubed for 3D) while <tt>XML</tt> files gives the total number per element.		<li>The number of points per element must be set before defining material points in your analysis. If desired, however you can use a different number of points per element in selected [[MPM Region and Hole Commands\|regions]] or when [[BMPRegion Command\|assigning particles using an image]]. Note that script files and <tt>XML</tt> files set this number differently. Script files set the number for each axis (which is squared for 2D or cubed for 3D) while <tt>XML</tt> files gives the total number per element.
	<li>The default number of terms for the incremental deformation gradient is 2 for 2D simulations and 1 for 3D simulations (the latter for efficieny). Because these settings work well for most calculations, there is currently no script command to change this setting. If necessary, you use an [[XMLData Command]]:		<li>The default number of terms for the incremental deformation gradient is 2 for 2D simulations and 1 for 3D simulations (the latter for efficieny). Because these settings work well for most calculations, there is currently no script command to change this setting. If necessary, you use an [[XMLData Command]]:
	<pre>XMLData "MPMHeader"		<pre>XMLData "MPMHeader"

Nairnj: /* Notes */

2021-01-04T19:40:45Z

Notes

← Older revision		Revision as of 19:40, 4 January 2021
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	<li>These methods are based on quadratic spline N<sub>i</sub>(x) grid shape functions.		<li>These methods are based on quadratic spline N<sub>i</sub>(x) grid shape functions.
	<li><tt>qCPDI</tt> is less efficient than <tt>lCPDI</tt> and in trial runs appears to have little or no benefit. It is available for comparison and potential future research into MPM shape function methods.		<li><tt>qCPDI</tt> is less efficient than <tt>lCPDI</tt> and in trial runs appears to have little or no benefit. It is available for comparison and potential future research into MPM shape function methods.
	<li>The number of points per element must be set before defining material points in your analysis. ~~Once~~ you ~~start defining material points, it cannot be changed. In other words elements with~~ different numbers of ~~material~~ points ~~cannot be used~~ in ~~a single analysis~~. Note that script files and <tt>XML</tt> files set this number differently. Script files set the number for each axis (which is squared for 2D or cubed for 3D) while <tt>XML</tt> files gives the total number ~~for the cells~~.		<li>The number of points per element must be set before defining material points in your analysis. If desired, however you can use a different numbers of points per element in selected [[MPM Region and Hole Commands\|regions]] or when [[BMPRegion Command\|assigning particles using an image]]. Note that script files and <tt>XML</tt> files set this number differently. Script files set the number for each axis (which is squared for 2D or cubed for 3D) while <tt>XML</tt> files gives the total number per element.
	<li>The default number of terms for the incremental deformation gradient is 2 for 2D simulations and 1 for 3D simulations (the latter for efficieny). Because these settings work well for most calculations, there is currently no script command to change this setting. If necessary, you use an [[XMLData Command]]:		<li>The default number of terms for the incremental deformation gradient is 2 for 2D simulations and 1 for 3D simulations (the latter for efficieny). Because these settings work well for most calculations, there is currently no script command to change this setting. If necessary, you use an [[XMLData Command]]:
	<pre>XMLData "MPMHeader"		<pre>XMLData "MPMHeader"

Nairnj: /* Restarting Time Steps */

2021-01-02T19:45:28Z

Restarting Time Steps

← Older revision		Revision as of 19:45, 2 January 2021
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	where Δ''t'' is the current time step. If any node's ''d'' relative to its cell size is greater than an entered rescaling factor, the time step is discarded and restarted using a smaller time step. This option is invoked using the [[#Input Commands\|<RestartScaling> command]]. To prevent the time step from permanently remaining small (and making a simulation too slow), this option should always be used in conjunction with an [[AdjustTimeStep Custom Task]]. This tasks will allow the time step to increase once nodal accelerations get under control, but should include its <tt>maxIncrease</tt> parameter to prevent returning immediately to the previous time step.		where Δ''t'' is the current time step. If any node's ''d'' relative to its cell size is greater than an entered rescaling factor, the time step is discarded and restarted using a smaller time step. This option is invoked using the [[#Input Commands\|<RestartScaling> command]]. To prevent the time step from permanently remaining small (and making a simulation too slow), this option should always be used in conjunction with an [[AdjustTimeStep Custom Task]]. This tasks will allow the time step to increase once nodal accelerations get under control, but should include its <tt>maxIncrease</tt> parameter to prevent returning immediately to the previous time step.

	Note that not all simulations can restart time steps. If your ~~simulations~~ is using a feature that cannot be ~~restarting~~ and invoke restarting, an error message will be printed and the ~~simulations will stop~~. Most ~~prominantly~~, simulations with restarting are limited to [[#Theory: Stress and Strain Updates\|USL- and USL+ strain updates]].		Note that not all simulations can restart time steps. If your simulation is using a feature that cannot be restarted and you invoke restarting, an error message will be printed and the simulation not start. Most prominently, simulations with restarting are limited to [[#Theory: Stress and Strain Updates\|USL- and USL+ strain updates]].

	== Input Commands ==		== Input Commands ==

Nairnj: /* Restarting Time Steps */

2021-01-02T19:44:09Z

Restarting Time Steps

← Older revision		Revision as of 19:44, 2 January 2021
Line 199:		Line 199:
	where Δ''t'' is the current time step. If any node's ''d'' relative to its cell size is greater than an entered rescaling factor, the time step is discarded and restarted using a smaller time step. This option is invoked using the [[#Input Commands\|<RestartScaling> command]]. To prevent the time step from permanently remaining small (and making a simulation too slow), this option should always be used in conjunction with an [[AdjustTimeStep Custom Task]]. This tasks will allow the time step to increase once nodal accelerations get under control, but should include its <tt>maxIncrease</tt> parameter to prevent returning immediately to the previous time step.		where Δ''t'' is the current time step. If any node's ''d'' relative to its cell size is greater than an entered rescaling factor, the time step is discarded and restarted using a smaller time step. This option is invoked using the [[#Input Commands\|<RestartScaling> command]]. To prevent the time step from permanently remaining small (and making a simulation too slow), this option should always be used in conjunction with an [[AdjustTimeStep Custom Task]]. This tasks will allow the time step to increase once nodal accelerations get under control, but should include its <tt>maxIncrease</tt> parameter to prevent returning immediately to the previous time step.

	Note that not all simulations can restart time steps. If your simulations is using a feature that cannot be restarting and invoke restarting, an error message will be printed and the simulations will stop.		Note that not all simulations can restart time steps. If your simulations is using a feature that cannot be restarting and invoke restarting, an error message will be printed and the simulations will stop. Most prominantly, simulations with restarting are limited to [[#Theory: Stress and Strain Updates\|USL- and USL+ strain updates]].

	== Input Commands ==		== Input Commands ==

Nairnj: /* Theory: MPM Time Step */

2021-01-02T19:43:06Z

Theory: MPM Time Step

← Older revision		Revision as of 19:43, 2 January 2021
Line 163:		Line 163:
	<math> C = { v\Delta t\over \Delta x} \qquad {\rm or} \qquad\Delta t =C { \Delta x\over v}</math>		<math> C = { v\Delta t\over \Delta x} \qquad {\rm or} \qquad\Delta t =C { \Delta x\over v}</math>

	The entered ''C'' must be less then 1.0. The default in [[NairnMPM]] is ''C'' = 0.5. Lower values may be are needed to resolve instabilities around [[Setting Velocity and Transport Values\|fixed-velocity boundary conditions]] on the grid or created by [[Rigid Material\|rigid particles]] when modeling [[Multimaterial MPM\|contact]], and when modeling brittle materials using [[Material Models#Softening Materials\|damage mechanics]]. An alternative to very low ''C'' is to try [[Restarting Time Steps\|restarting time steps]] that develop high accelerations on the grid.		The entered ''C'' must be less then 1.0. The default in [[NairnMPM]] is ''C'' = 0.5. Lower values may be are needed to resolve instabilities around [[Setting Velocity and Transport Values\|fixed-velocity boundary conditions]] on the grid or created by [[Rigid Material\|rigid particles]] when modeling [[Multimaterial MPM\|contact]], and when modeling brittle materials using [[Material Models#Softening Materials\|damage mechanics]]. An alternative to very low ''C'' is to try [[#Restarting Time Steps\|restarting time steps]] that develop high accelerations on the grid.

	When transport tasks are activated ([[Thermal Calculations\|conduction]], [[Diffusion Calculations\|diffusion]], or [[Poroelasticity Calculations\|poroelasticity]]), convergence of transport calculations requires the time step to satisfy		When transport tasks are activated ([[Thermal Calculations\|conduction]], [[Diffusion Calculations\|diffusion]], or [[Poroelasticity Calculations\|poroelasticity]]), convergence of transport calculations requires the time step to satisfy

Nairnj: /* Restarting Time Steps */

2021-01-02T19:41:35Z

Restarting Time Steps

← Older revision		Revision as of 19:41, 2 January 2021
Line 198:		Line 198:

	where Δ''t'' is the current time step. If any node's ''d'' relative to its cell size is greater than an entered rescaling factor, the time step is discarded and restarted using a smaller time step. This option is invoked using the [[#Input Commands\|<RestartScaling> command]]. To prevent the time step from permanently remaining small (and making a simulation too slow), this option should always be used in conjunction with an [[AdjustTimeStep Custom Task]]. This tasks will allow the time step to increase once nodal accelerations get under control, but should include its <tt>maxIncrease</tt> parameter to prevent returning immediately to the previous time step.		where Δ''t'' is the current time step. If any node's ''d'' relative to its cell size is greater than an entered rescaling factor, the time step is discarded and restarted using a smaller time step. This option is invoked using the [[#Input Commands\|<RestartScaling> command]]. To prevent the time step from permanently remaining small (and making a simulation too slow), this option should always be used in conjunction with an [[AdjustTimeStep Custom Task]]. This tasks will allow the time step to increase once nodal accelerations get under control, but should include its <tt>maxIncrease</tt> parameter to prevent returning immediately to the previous time step.

			Note that not all simulations can restart time steps. If your simulations is using a feature that cannot be restarting and invoke restarting, an error message will be printed and the simulations will stop.

	== Input Commands ==		== Input Commands ==

Nairnj: /* Input Commands */

2021-01-02T19:34:40Z

Input Commands

← Older revision		Revision as of 19:34, 2 January 2021
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	* <tt>(maxTime)</tt> - the time that the calculations will stop in [[ConsistentUnits Command#Legacy and Consistent Units\|alt time units]] (in <tt>XML</tt> files, the time is in [[ConsistentUnits Command#Legacy and Consistent Units\|time units]] or determined by a [[Units Attribute\|units attribute]]). In scripted files, this value can be entered as second argument to the <tt>TimeStep</tt> command or in a separate <tt>MaximumTime</tt> command (whichever is last will be the one that is used) (it can be an [[Entity Command\|entity]]).		* <tt>(maxTime)</tt> - the time that the calculations will stop in [[ConsistentUnits Command#Legacy and Consistent Units\|alt time units]] (in <tt>XML</tt> files, the time is in [[ConsistentUnits Command#Legacy and Consistent Units\|time units]] or determined by a [[Units Attribute\|units attribute]]). In scripted files, this value can be entered as second argument to the <tt>TimeStep</tt> command or in a separate <tt>MaximumTime</tt> command (whichever is last will be the one that is used) (it can be an [[Entity Command\|entity]]).
	* <tt>(timeFactor)</tt> and <tt>(transTimeFactor)</tt> - the [[#Theory: MPM Time Step\|Courant factors]] to use when determining the MPM time step. The time step used in the analysis will be the minimum of the one determined using these factors and the one entered in <tt>(timeStep)</tt>. The default [[#Theory: MPM Time Step\|Courant factors]] are 0.5. In scripted files, The <tt>(timeFactor)</tt> can be entered as third argument to the <tt>TimeStep</tt> command or first argument in a <tt>CFLFactor</tt> command		* <tt>(timeFactor)</tt> and <tt>(transTimeFactor)</tt> - the [[#Theory: MPM Time Step\|Courant factors]] to use when determining the MPM time step. The time step used in the analysis will be the minimum of the one determined using these factors and the one entered in <tt>(timeStep)</tt>. The default [[#Theory: MPM Time Step\|Courant factors]] are 0.5. In scripted files, The <tt>(timeFactor)</tt> can be entered as third argument to the <tt>TimeStep</tt> command or first argument in a <tt>CFLFactor</tt> command
	* <tt>(kmax)</tt> - the number of terms to use when evaluating the [[#Incremental Deformation Gradient\|incremental deformation gradient]].[[#Notes\|<sup>7</sup>]] The default is 2.		* <tt>(kmax)</tt> - the number of terms to use when evaluating the [[#Incremental Deformation Gradient\|incremental deformation gradient]].[[#Notes\|<sup>7</sup>]] The default is 2 for 2D and 1 for 3D.
	* <tt>(restartFactor)</tt> and <tt>(restartScaling)</tt> - these parameters invoke the [[#Restarting Time Steps\|time-step restarting option]]. If the implied displacement of any node is greater than <tt>(restartFactor)(cell size)</tt>, the time step is changed to <tt>\|(restartScaling)\|</tt>*Δ''t'' where Δ''t'' is the current time step. The entered <tt>(restartFactor)</tt> should be between -1 and 1. The scaling uses absolute value of the entered value. Negative values are a "verbose" mode that prints a warning eah time the time step is restarted; postive values restart time steps without notice. Values out side the range -1 to 1 are change to 0.5 (preserving the sign). A report at the end of a simulations summarizes the number of times steps that had to be restarted.[[#Notes\|<sup>8</sup>]]		* <tt>(restartFactor)</tt> and <tt>(restartScaling)</tt> - these parameters invoke the [[#Restarting Time Steps\|time-step restarting option]]. If the implied displacement of any node is greater than <tt>(restartFactor)(cell size)</tt>, the time step is changed to <tt>\|(restartScaling)\|</tt>*Δ''t'' where Δ''t'' is the current time step. The entered <tt>(restartFactor)</tt> should be between -1 and 1. The scaling uses absolute value of the entered value. Negative values are a "verbose" mode that prints a warning eah time the time step is restarted; postive values restart time steps without notice. Values out side the range -1 to 1 are change to 0.5 (preserving the sign). A report at the end of a simulations summarizes the number of times steps that had to be restarted.[[#Notes\|<sup>8</sup>]]

← Older revision		Revision as of 19:34, 2 January 2021
Line 251:		Line 251:
	* <tt>(maxTime)</tt> - the time that the calculations will stop in [[ConsistentUnits Command#Legacy and Consistent Units\|alt time units]] (in <tt>XML</tt> files, the time is in [[ConsistentUnits Command#Legacy and Consistent Units\|time units]] or determined by a [[Units Attribute\|units attribute]]). In scripted files, this value can be entered as second argument to the <tt>TimeStep</tt> command or in a separate <tt>MaximumTime</tt> command (whichever is last will be the one that is used) (it can be an [[Entity Command\|entity]]).		* <tt>(maxTime)</tt> - the time that the calculations will stop in [[ConsistentUnits Command#Legacy and Consistent Units\|alt time units]] (in <tt>XML</tt> files, the time is in [[ConsistentUnits Command#Legacy and Consistent Units\|time units]] or determined by a [[Units Attribute\|units attribute]]). In scripted files, this value can be entered as second argument to the <tt>TimeStep</tt> command or in a separate <tt>MaximumTime</tt> command (whichever is last will be the one that is used) (it can be an [[Entity Command\|entity]]).
	* <tt>(timeFactor)</tt> and <tt>(transTimeFactor)</tt> - the [[#Theory: MPM Time Step\|Courant factors]] to use when determining the MPM time step. The time step used in the analysis will be the minimum of the one determined using these factors and the one entered in <tt>(timeStep)</tt>. The default [[#Theory: MPM Time Step\|Courant factors]] are 0.5. In scripted files, The <tt>(timeFactor)</tt> can be entered as third argument to the <tt>TimeStep</tt> command or first argument in a <tt>CFLFactor</tt> command		* <tt>(timeFactor)</tt> and <tt>(transTimeFactor)</tt> - the [[#Theory: MPM Time Step\|Courant factors]] to use when determining the MPM time step. The time step used in the analysis will be the minimum of the one determined using these factors and the one entered in <tt>(timeStep)</tt>. The default [[#Theory: MPM Time Step\|Courant factors]] are 0.5. In scripted files, The <tt>(timeFactor)</tt> can be entered as third argument to the <tt>TimeStep</tt> command or first argument in a <tt>CFLFactor</tt> command
	* <tt>(kmax)</tt> - the number of terms to use when evaluating the [[#Incremental Deformation Gradient\|incremental deformation gradient]].[[#Notes\|<sup>7</sup>]] The default is 2.		* <tt>(kmax)</tt> - the number of terms to use when evaluating the [[#Incremental Deformation Gradient\|incremental deformation gradient]].[[#Notes\|<sup>7</sup>]] The default is 2 for 2D and 1 for 3D.
	* <tt>(restartFactor)</tt> and <tt>(restartScaling)</tt> - these parameters invoke the [[#Restarting Time Steps\|time-step restarting option]]. If the implied displacement of any node is greater than <tt>(restartFactor)(cell size)</tt>, the time step is changed to <tt>\|(restartScaling)\|</tt>*Δ''t'' where Δ''t'' is the current time step. The entered <tt>(restartFactor)</tt> should be between -1 and 1. The scaling uses absolute value of the entered value. Negative values are a "verbose" mode that prints a warning eah time the time step is restarted; postive values restart time steps without notice. Values out side the range -1 to 1 are change to 0.5 (preserving the sign). A report at the end of a simulations summarizes the number of times steps that had to be restarted.[[#Notes\|<sup>8</sup>]]		* <tt>(restartFactor)</tt> and <tt>(restartScaling)</tt> - these parameters invoke the [[#Restarting Time Steps\|time-step restarting option]]. If the implied displacement of any node is greater than <tt>(restartFactor)(cell size)</tt>, the time step is changed to <tt>\|(restartScaling)\|</tt>*Δ''t'' where Δ''t'' is the current time step. The entered <tt>(restartFactor)</tt> should be between -1 and 1. The scaling uses absolute value of the entered value. Negative values are a "verbose" mode that prints a warning eah time the time step is restarted; postive values restart time steps without notice. Values out side the range -1 to 1 are change to 0.5 (preserving the sign). A report at the end of a simulations summarizes the number of times steps that had to be restarted.[[#Notes\|<sup>8</sup>]]