Common Material Properties

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

Basic Properties

These are basic material properties.

Property	Description	Units	Default
rho	The material's density	g/cm3	1
csat	The saturation concentration potential as a weight friction from 0 to 1. it is only used when doing diffusion calculations.	none	1
Cv	The constant-volume heat capacity. It is used when doing conduction calculations and/or coupled mechanical energy and by some material constitutitive laws. You do not need to enter a constant pressure heat capacity (which is need in conductivity equations) because material models calculates it from Cv and thermodynamic relations for the difference between Cp and Cv	J/(kg-K	1
color	Sets the color of the material. The color is used in material point method plots material type in NairnFEAMPM and in NairnFEAMPMViz. If no color is provided, a color will be picked from the current spectrum using the material number. In scripted files, this property takes four arguments being red, green, blue, and alpha values between 0.0 and 1.0. A single argument means to set gray level between 0.0 and 1.0 (with alpha=1.0). Three arguments means set red, green, and blue with alpha=1.0. In XML files, the color is set with "red", "green", "blue" and "alpha" attributes (and the element's content is ignored).	none	none

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
maxLength	The maximum crack length for steady state crack propagation. The simulation will stop soon after crack reaches the input length. This length, however, is only active for crack propagation by criterion 2.	mm	none
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. Setting this property in a material overrides the default propagation criterion setting. This command is for scripted files only; see below to set criterion in XML files.	none	none
direction	To set a custom crack propagation direction. You can use any direction option. Setting this property in a material overrides the default propagation direction setting. This command is for scripted files only; see below to set traction in XML files.	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 can be set by material ID (if the traction law has already been defined) or by number (if it is not defined yet). This command is for scripted files only; see below to set criterion in XML files.	none	none
altcriterion	Same as "criterion" property above except that it applies to the alternate propagation criterion for the material	none	none
altdirection	Same as "direction" property above except that it applies to the alternate propagation criterion for the material	none	none
alttraction	Same as "traction" property above except that it applies to the alternate propagation criterion for the material	none	none
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
constantTip	Set to 0 or 1. The default of 0 means the crack tip will track the material around the crack tip. Changing it to 1 means crack tips with this material will always use this material even if the crack propagates into another material. The default 0 allows modeling crack growth in composites with fracture properties changing as cracks move between materials. Using 1 allows modeling multiple cracks in the same material having different fracture propertie by using the following steps: Define multiple materials that are identical except for their fracture and/or propagation properties and all with constantTip=1. Create a model and uses one of the materials for all material points. For each crack tip, assign its material to be the material in step 1 with the appropriate fracture properties.	none	0

Propagation Properties in XML Files

In XML files, the criterion, direction, and traction properties (and the analogous alternate propagation properties) are set differently. To set crack propagation criteria, you use instead

<Propagate criterion='(critNum)' direction='(dirNum)' traction='(traction)'/>
<AltPropagate criterion='(critNum)' direction='(dirNum)' traction='(traction)'/>

where the settings are the same as defined in the default crack propagation commands (or the alternate propagation command), but the XML element is now used within a <Material> definition instead of within the <Cracks> element in the <MPMHeader>.

Contact Properties

These properties can set custom friction and interface properties between two specific materials. If these properties are not used, material-to-material contact and interface will use the global friction and interface propertties.

Property	Description	Units	Default
Friction	A Friction property within a material definition can define custom frictional properties for multimaterial mode MPM contact between the current material and another material. This property takes two parameters; the first is the same as for the standard Friction command and the second gives the other material.	none	none
Interface	An Interface property within a material definition can define custom imperfect interface parameters properties for multimaterial mode MPM contact between the current material and another material. This property takes four parameters; the first three are the same as for a standard ImperfectInterface command (which is actually a <Friction> element in XML files) and the fourth gives the other material.	none	none

In scripted files, the other material is specified by its material ID, which means the Friction and Interface properties must be used in the secondly-defined materials (such that material ID for the first material is available). In XML files, the second material is defined by number (or by name) using a mat or matname attribute. You all need a Friction or an Interface command in one materials for each pair of materials with custom contact properties.

Artificial Viscosity

Some materials support artificial viscosity to dampen pressure waves. 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

      [math]\displaystyle{ Q = \Delta x|D_{kk}\bigl|(A_1C + A_2\Delta X|D_{kk}|\bigr) }[/math]

where Δx is the cell size of the mesh, |D_kk| is the relative volume change rate (i.e. trace of the velocity gradient), C is the bulk wave speed in the material, and A₁ and A₂ are adjustable constants.

Property	Description	Units	Default
ArtificialVisc	Set to "on" or "off" to activate artificial viscosity	none	off
avA1	The 'A1 constant in the artificial viscosity law	none	0.2
avA2	The 'A2 constant in the artificial viscosity law	none	2.0

The artificial viscosity property is supported in some isotropic materials (because the theory assume isotropy). If you use these commands in a material that does not support, an error will result. The following materials currently support artificial viscosity:

• HEIsotropic and it subclasses
• MGEOSMaterial
• Mooney MaterialMooney