# 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 initial density. density units 0.001
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 (Cp). Instead, when MPM thermodynamics are done correctly, the simulations will automatically account for all boundary condition effects (constant volume, constant pressure, or mixed) on effective heat capacity. heat capacity units 1
kCond Thermal conductivity for isotropic materials (anisotropic materials will have alternate properties for setting thermal conductivity tensor). conductivity units 0
csat The saturation concentration potential as a weight friction from 0 to 1. it is only used when doing diffusion calculations. none 1
beta Moisture expansion coefficient for isotropic materials (anisotropic materials will have alternate properties for setting moisture expansion tensor). strain/(wt fraction) 0
D Solvent diffusion constant for isotropic materials (anisotropic materials will have alternate properties for setting diffusion tensor). diffusion units 0
largeRotation To use (1) or not use (0) polar decomposition when calculating rotations in small-stain materials. This option applies only to linear elastic small strain materials and to elastic-plastic small strain materials. Option 1 finds incremental deformation gradient use the selected number of terms and evaluates the rotational part of that increment using polar decomposition. The stress update is then rotated according to the decomposed rotation. In contrast, option 0 finds incremental deformation gradient from a linear expansion (kmax=1) and evaluates the rotation component using second order (in 2D) or first order (in 3D) approximate polar decomposition. The stress update is rotated by standard hypoelastic methods. Both methods can handle large total rotations (provided they are incrementally small). Option 1 may be more accurate, but it is less efficient. none 0
matDamping Sets custom particle damping to apply only to particles of this material. Its value replaces global particle damping setting and must be a constant (function of time not allowed). In XML files, set matDamping using <PDamping>matDamping</PDamping> 1/time units none
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. energy release units none
JIIc Critical energy release rate fracture toughness for mode II. It is currently only used to set toughness of traction law materials. energy release units none
KIc Critical mode I stress intensity factor. It is only used for crack propagation by criteria 1, 4, or 5. stress intensity units none
KIIc Critical mode II stress intensity factor. It is only used for crack propagation by criteria 1, 4, or 5. stress intensity units 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. length units 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. length units 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. alt time units 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) alt velocity units 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. length units none
nmix An exponent used in mixed-modes failure of some traction laws. none 1
allowsCracks Set to 1 to allow the material to have cracks or 0 to not allow cracks. The default is 1 for non-rigid materials and 0 for rigid materials. Setting a non-rigid material to 0 lets that material enter a crack in another material such as to simulate cutting, to wedge open a crack, or model hydraulic fracturing. The non-cracking material can open the crack in the other material by contact on its crack surfaces. none varies

## 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 direction 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 traction 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:
1. Define multiple materials that are identical except for their fracture and/or propagation properties and all with constantTip=1.
2. Create a model and uses one of the materials for all material points.
3. 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>.

XML files set xGrow, yGrow, and constantTip as ordinary properties and they function as described above.

## Contact Properties

These properties can set custom the contact mechanics between two specific materials. If these properties are not used, material-to-material contact will be determined by the global setting made using a ContactMM command (for scripted files) or a <Friction> command within the <MultimaterialMode> element in the <MPMHeader> (for XML files). For more details see these commands under friction settings and interface setting.

Property Description Units Default
Contact
<Friction>
In scripted files, use the Contact property with two arguments — (lawID) and (matID). It sets a custom contact law (by its material ID in (lawID)) to use for contact between this material and the material defined by (matID). You only need to enter a Contact property for one of the two materials in each pair. Since you have to provide the other material's ID, you should use the Contact command in the second material after the first one has already been defined (and after the contact law has been defined as well).

In XML files use the command:
<Friction law='(lawnum)' lawname='(lawID)' mat='(matnum)' matname='(matID)'/>
to set the custom contact law by number or ID for both the law and the other material. If both number and ID are used, the ID will take precedence. || none || none

shareMatField The value selects another material to share the same velocity field such that the two materials move together and interact by perfect contact (see below for how to have more than two materials share one field). Although materials in the same velocity field interact by perfect contact, they can interact with materials in different velocity fields by multimaterial mode contact or interface laws. Finally, materials sharing velocity fields must use "compatible" fields (e.g., all rigid or all nonrigid); an error will occur (with an explanation) if you try to share velocity fields of incompatible materials. none none

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

To share velocity fields, you first create one "base material" that is not shared and then any number that share that field with a shareMatField property. The base material is specified in the shareMatField property by material ID in scripted files, but must be by number (as the value of the property command) in XML files. To specify custom friction or interfaces between shared materials and other materials, you use any material in the shared block; if you use custom commands for more then one material in a block, only the last one will be used.

### Deprecated Contact Properties

The following material properties for setting contact properties are deprecated. They should be replaced by the Contact property above. Note that in XML files, contact properties are still with with a <Friction> command but prior attributes are deprecated to be replaced by attributes to specify the desired contact law.

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

## 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

$\displaystyle{ {Q\over\rho} = \Delta x|D_{kk}\bigl|(A_1C + A_2\Delta x|D_{kk}|\bigr) }$

where Δx is the cell size of the mesh, |Dkk| 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. In XML files, an <Artificial/> command turns it on and its absence keeps the default setting of "off". 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 assumes isotropy). If you use these commands in a material that does not support it, an error will result. The following materials currently support artificial viscosity:

## Poroelasticity Properties

Some materials support poroelasticity calculations and the properties in this section control pore pressure flow between particles and coupling between stress and strain and pore pressure. The properties to use depend on symmetry of the parent material.

### Isotropic Poroelasticity Properties

Property Description Units Default
Ku Undrained bulk modulus. It must be greater than the material bulk modulus. pressure units none
alphaPE The poroelasticity Biot coefficient that translates fraction of volume change the results in pore pressure change. It must be between 0 and 1 none 0
Darcy Darcy law permittivity for the material length units2 0

### Transversely Isotropic Poroelasticity Properties

Property Description Units Default
Ku Undrained bulk modulus. It must be greater than the material bulk modulus. pressure units none
alphaAPE
alphaTPE
The axial and transverse poroelasticity Biot coefficients that translate how strains results in pore pressure change. They must be between 0 and 1 none 0
DarcyA
DarcyT
The axial and transverse Darcy law permittivities for the material length units2 0

### Orthotropic Poroelasticity Properties

Property Description Units Default
Ku Undrained bulk modulus. It must be greater than the material bulk modulus. pressure units none
alphaxPE
alphayPE
alphazPE
The poroelasticity Biot coefficients for the three orthotropic directions that translate how strains results in pore pressure change. They must be between 0 and 1 none 0
alphaRPE
alphaZPE
alphaTPE
For cylindrical, orthotropic materials, these are radial, axial, and hoop Biot coefficients. They are synonyms for orthotropic coefficients (with R=x, Z=y, and T=z). none 0
Darcyx
Darcyy
Darcyz
The Darcy law permittivities for the three orthotropic directions material length units2 0
DarcyR
DarcyZ
DarcyT
For cylindrical, orthotropic materials, these are radial, axial, and hoop Darcy law permittivities for the material. They are synonyms for orthotropic coefficients (with R=x, Z=y, and T=z). length units2 0