Common Material Properties

These material properties are common to all types of materials used in MPM simulations.

Fracture Toughness Properties

These properties set material properties that determine the fracture toughness of the material and control various aspects of crack propagation.

Property	Description	Units	Default
JIc	Critical energy release rate fracture toughness for mode I. It is only used for crack propagation by criteria 2, 3, or 7. For criterion 2, it is only used if initTime is not specified. It is also used to set toughness of traction law materials.	J/m2	none
JIIc	Critical energy release rate fracture toughness for mode II. It is currently only used to set toughness of traction law materials.	J/m2	none
KIc	Critical mode I stress intensity factor. It is only used for crack propagation by criteria 1, 4, or 5.	MPa m1/2	none
KIIc	Critical mode II stress intensity factor. It is only used for crack propagation by criteria 1, 4, or 5.	MPa m1/2	none
KIexp	Exponent p in the elliptical criteria for crack growth. It is only used for crack propagation by criterion 5.	none	2
KIIexp	Exponent q in the elliptical criteria for crack growth. It is only used for crack propagation by criterion 5.	none	2
delIc	Critical crack opening displacement for mode I. Only used for crack propagation by criterion 6. It is also used by traction-law materials.	mm	none
delIIc	Critical crack opening displacement for mode II. Only used for crack propagation by criterion 6. It is also used by traction-law materials.	mm	none
initTime	The time when crack propagation starts. It is only used for crack propagation by criterion 2. For criterion 2, when initTime is specified, takes precedence over the JIc property.	ms	none
speed	The crack speed in steady state crack propagation. This speed, however, is only active for crack propagation by criterion 2. (also used in criterion 3 as an initial crack speed, but that criterion is not meant for general use)	m/sec	1
nmix	An exponent used in mixed-modes failure of some traction laws.	none	1
gamma	Crack surface energy. It is only used for crack propagation by criterion 3, which is in development and not meant for general use.	J/m2	none
p	Irreversible energy term in energy balance crack growth and probably should be between 0 and 1. It is only used for crack propagation by criterion 3, which is in development and not meant for general use.	none	1
gain	Gain used in feedback loop to maintain energy balance during crack growth. It is only used for crack propagation by criterion 3, which is in development and not meant for general use.	1e5	1

Crack Propagation Properties

The setting of crack propagation properties are done differently for scripted and XML files. For scripted commands, you can set the following material properties:

Property	Description	Units	Default
criterion	To set a custom crack propagation criterion. You can use any propagation option, but must enter using the numeric setting. Setting this property in a material overrides the default propagation criterion setting.	none	none
direction	To set a custom crack propagation direction. You can use any direction option, but must enter using the numeric setting. Setting this property in a material overrides the default propagation direction setting.	none	none
traction	To set a custom traction law to create for crack propagation in this material. A traction law set in a material overrides the default traction law. The traction law must be set by number (1, 2, etc.) where the number corresponds to the material number, in order, as defined by Material commands. You cannot use a material ID. Numerical values are needed because you may be using this option before the traction law material has been created.	=	xGrow	This property along with yGrow (if on one given the other is set to 0) specify a unit vector for a constant crack growth direction. t is only used for crack propagation by criterion 2 and then only if that criterion is using its default propagation direction. The result is a constant crack growth direction regardless of stress state or crack tip orientation. Any input vector will be normalized to a unit vector. If a constant crack growth direction with a fixed crack is located precisely on grid lines, it is possible the crack algorithm will not recognize the crack plane. Is it better to move such a crack slightly off grid lines.	none	none
yGrow	Crack growth direction - see xGrow above.	none	none

Script Notes

The following material properties are common to all types of materials, although not used by all materials. These properties are only used in MPM analyses.

• rho for density in g/cm^3.
• Cp or Cv for heat capacity (in J/(kg-K)). Heat capacity is used when doing <a href="conduction.html">conduction calculations and/or coupled mechancial energy</a> adn by some material models. Both Cp and Cv set the same (and only) heat capacity used in the MPM calculations. MPM is a strain-drive method, which implies the heat capacity should be interpreted as the constant-volume heat capacity.
• <a name="csat"></a>csat The saturation concentration (in weight fraction) for diffusion calculations.
• maxLength for maximum crack length (in mm) for steady state crack propagation. The simulation will stop soon after crack reaches the input length. This limit, however, is only active when there is crack propagation with <a href="propagate.html">criterion 2</a>.
• altcriterion is identical to criterion, but applies instead to the alternate crack growth criterion in the <a href="altpropagate.html">AltPropagate Command</a>.
• altdirection is identical to direction, but applies instead to the alternate crack growth direction in the <a href="altpropagate.html">AltPropagate Command</a>.
• alttraction is identical to traction, but applies instead to the alternate crack growth traction law material in the <a href="altpropagate.html">AltPropagate Command</a>.
• xGrow and yGrow: These properties (one or both with default 0) specify a unit vector for a constant crack growth direction. They only apply for crack propagation with <a href="propagate.html">criterion 2</a> and then only when that criterion selects the default propagation direction. The result is a constant crack growth direction regardless of stress state or crack tip orientation. Any input vector will be normalized to a unit vector. If constant crack growth directions with a fixed crack are located precisely on grid lines, it is possible for the crack algorithm to not recognize the crack plane. Is it better to move such a crack slightly off grid lines.
• <a name="artificialvisc"></a>ArtificialVisc can be on or off to turn artificial viscosity on. When it is on, it adds a pressure, Q, related to velocity gradient on the particle, but only when it is compressing. The equation is

  Q = Δx*|D_kk|*(A1*C + A2*Δx*|D_kk|)

  where Δx is the cell size of the mesh, |D_kk| is the relative volume change rate, C is the bulk wave speed in the material, and A1 and A2 are adjustable constants, which are entered using the above avA1 and avA2 properties. The defaults are artificial viscosity off, A1=0.2, and A2=2.0. It is common, but not required, to choose A2 = 10*A1.
      The artificial viscosity property is supported in some materials (as documented under each material). If you use these commands in a material that does not support, an error will result.

• avA1 and avA2 to set the coefficients when artficial viscosity is on.
• color 0.1,0.5,0.2,1.0: Sets the color of the material with the four arguments being red, green, blue, and alpha values between 0.0 and 1.0. A single argument can be used instead to set gray level between 0.0 and 1.0 (with alpha=1.0). Three arguments set red, green, and blue with alpha=1.0. The color is used in <a href="../movieplots.html">material point method plots</a> of <a href="../quantities.html">material type</a>. If no color is provided, a color will be picked from the current spectrum using the material number.
• Friction: A <a href="friction.html">Friction command</a> within a material definition can define custom frictional properties for <a href="multimaterialmode.html">multimaterial mode MPM</a> contact between the current material and another material.
• Interface: An <a href="imperfectinterface.html">Interface command</a> within a material definition can define custom imperfect interface parameters properties for <a href="multimaterialmode.html">multimaterial mode MPM</a> contact between the current material and another material.

XML Notes

There are some material properties that are common to all material types. These properties are only used in NairnMPM and are not allowed in NairnFEA. Some of these properties only work for selected materials (refer to each material for possible details). The common properties are

<rho>1.5</rho>

The material density (in g/cm³) (can be used in NairnFEA files, but it is ignored).

<Cp>1.5</Cp> or <Cv>1.5</Cv>

The material's heat capacity (in J/(kg-K)). It is used when doing <a href="thermal.html">conduction calculations and/or coupled mechanical energy</a> and by some material constitutitive laws. Both Cp and Cv set the same (and only) heat capacity used in the MPM calculations. MPM is a strain-drive method, which implies the heat capacity should be interpreted as the constant-volume heat capacity.

<a name="csat"></a><csat>0.5</csat>

The material's saturation concentration entered as a weight fraction. Only used when doing diffusion calculations.

<Propagate criterion='1' direction='0' traction='1'/>
<AltPropagate criterion='7' direction='4' traction='1'/>

These properties let each material have a different primary and secondary propagation criterion and/or directions than the ones defined in the <a href="mpmheader.html">MPM Header</a>. Set these criterion as described for the <a href="mpmheader.html#propagate">Propagate</a> and <a href="mpmheader.html#altpropagate">AltPropagate</a> commands in the <a href="mpmheader.html">MPM Header</a>. To activate propagation:

1. The <a href="mpmheader.html">MPM Header</a> must have a <a href="mpmheader.html#propagate">Propagate</a> command.
2. The <a href="mpmheader.html">MPM Header</a> can optionally have an <a href="mpmheader.html#altpropagate">AltPropagate</a> command.
3. Any material can override the default primary and/or secondary criteria by using a Propagate and/or AltPropagate command within its material defintion. Even if the <a href="mpmheader.html">MPM Header</a> does not have an <a href="mpmheader.html#altpropagate">AltPropagate</a> command, a material can add a secondary criterion with its own AltPropagate command.

<maxLength>20</maxLength>

Define the maximum length of the crack (in mm). The crack growth will stop when this length is reached. This limit, however, is only active when there is crack propagation with <a href="mpmheader.html#cracks">criterion</a> 2.

<xGrow>20</xGrow> and <yGrow>0</yGrow>

These properties (one or both with default 0) specify a unit vector for a constant crack growth direction. They only apply for crack propagation with <a href="mpmheader.html#cracks">criterion</a> 2 and then only when that criterion selects the default propagation direction. The result is constant crack growth direction regardless of stress state or crack tip orientation. Any input vector will be normalized to a unit vector. If constant crack growth directions with a <a href="cracks.html">fixed crack</a> are located precisely on grid lines, it is possible for the crack algorithm to not recognize the crack plane. It is better to move such a crack sligthly off grid lines.

<a name="artificialvisc"></a><ArtificialVisc/>, <avA1>.2</avA1>, and <avA2>2.0</avA2>

This first empty tag turns artificial visocsity on, which adds a pressure, Q, related to velocity gradient on the particle, but only when it is compressing. The equation is

Q = Δx*|D_kk|*(A1*C + A2*Δx*|D_kk|)

where Δx is the cell size of the mesh, |D_kk| is the relative volume change rate, C is the bulk wave speed in the material, and A1 and A2 are adjustable constants, which are entered using the above <avA1> and <avA2> commands. The defaults are off, A1=0.2, and A2=2.0. It is common, but not required, to choose A2 = 10*A1.
    The artificial viscosity property is supported in some materials (as documented under each material). If you use these commands in a material that does not support, an error will result.

<a name="friction"></a><Friction mat='2'>0.3</Friction>

This command within a material definition allows multimaterial mode to have different contact laws between different pairs of materials. Set the contact law as explained for <a href="mpmheader.html#friction">Friction command</a> in the <a href="mpmheader.html#cracks">Cracks section of the MPM header</a> except that a setting less than -10 means to assume materials are always in contact and revert to single material mode. The mat attribute defines contact mechanics between this material and the one listed (self contact is ignored). Alternatively, the other material can be specified by name using a matname attribute as explained <a href="definematl.html#usemats">here</a>. If a node has more than two materials, the contact law used will be one between each material and the other material with the most volume.
    You only need to set friction on one of the materials in a pair. If you set both, the setting for the second material will override the one from the first material.

<color red='0.1' green='0.5' blue='0.3' alpha='1.0/>

Sets the color of the material with red, green, blue, and alpha values between 0.0 and 1.0. The color may be used by post-analysis software, but it has no affect on the calculations.