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 |
| matPIC | Sets custom PIC damping (0 to 1) to apply only to particles of this material. Its value replaces the global PIC damping setting. In XML files, set matPIC using <PDamping PIC="matPIC"/>. To set both matDamping and matPIC in XML files, use one command <PDamping PIC="matPIC">matDamping</PDamping>. Note that to use custom XPIC damping in materials and FLIP in others requires careful settings (as explained below this table). | none | 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 |
Note that when customizing the PIC damping properties for material points of one material types, the options have some limitations, depending on the simulation's global PIC damping setting. The following table summarizes the options.
| Global Setting | Material Options |
|---|---|
| FLIP/PIC (f≥0) | A material can change f to switch to pure FLIP (f=0) or to any new amount of PIC (f>0). XPIC cannot be selected by a material. |
| FLIP/XPIC(m) (f>0) | A material can change to pure FLIP (f=0) or to any new amount of XPIC(m) (f>0). The XPIC order cannot be selected by a material. |
The only limitations are when using XPIC damping. Such simulations must select XPIC order and set f>0 as the global options. Individual materials can change the amount of XPIC (i.e., change f), but cannot change the XPIC order.
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 |
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:
|
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 | Set to another material to share material velocity field with that material. Two (or more) materials sharing the same velocity field will move with perfect contact (i.e., in a single velocity field) among themselves, but can interact with other materials in different velocity fields by multimaterial mode contact or interface laws. Materials sharing velocity fields must be compatible and the shared material must not be sharing it's field. The meaning of "compatible" fields (e.g., all rigid or all nonrigid) may evolve; 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
[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, |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:
- HEIsotropic and its subclasses
- Mooney
- Neohookean
- Viscoelastic - but only supports it in OSParticulas
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. | 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 |
Transversely Isotropic Poroelasticity Properties
| Property | Description | Units | Default |
|---|---|---|---|
| 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 |
Orthotropic Poroelasticity Properties
| Property | Description | Units | Default |
|---|---|---|---|
| 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. The are synonyms for orthotropic coefficients (with R=x, Z=y, and T=z). | none | 0 |