MATX21

This law is based on the Drücker-Prager yield criteria and is used to model materials with internal friction such as rock-concrete. The plastic behavior of these materials is dependent on the pressure in the material. This law is only applicable to solid elements.

Format

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
MATX21	`MID`	`A0`	`A1`	`A2`	`AMAX`
	`TPID`	`KT`	`FSCAL`	`P`	`B`	`MUMAX`	`P`

Example

(1)	(2)	(3)	(5)	(6)
MAT1	102	3.1E10	0.33	1000.0
MATX21	102		3
	1	1E10

Definitions

Field	Contents	SI Unit Example
`MID`	Material ID of the associated MAT1. 1 No default (Integer > 0)
`A0`	Coefficient. (Real)
`A1`	Coefficient. (Real)
`A2`	Coefficient. (Real)
`AMAX`	von Mises limit. Default = 10³⁰ (Real > 0)
`TPID`	Identification number of a TABLES1 that defines the volumetric strain vs. pressure function. No default (Integer > 0)
`KT`	Tensile bulk modulus. Recommended to set equal to 1/100 of unloading bulk modulus. Must be positive. (Real > 0.0)
`FSCAL`	Scale factor for pressure function. Default = 1.0 (Real)
`P`	Minimum pressure. Default = -10³⁰ (Real)
`B`	Unloading bulk modulus. Recommended to set equal to the initial slope of function describing $P (μ)$ $P (μ)$ . Must be positive. (Real > 0.0)
`MUMAX`	Maximum compression volumetric strain. (Real)
`P`	External pressure. Required if relative pressure formulation is used. In this specific case, yield criteria and energy integration require the value of total pressure. Default = 0.0 (Real)

Comments

The material identification number must be that of an existing MAT1 Bulk Data Entry. Only one MATX21 material extension can be associated with a particular MAT1.
MATX21 is only applied in geometric nonlinear analysis subcases which are defined by ANALYSIS=EXPDYN. It is ignored for all other subcases.
Hydrodynamic behavior is given by a user-defined function $P = f (μ)$ $P = f (μ)$ .
Where,

$P$ $P$

Pressure in the material

$μ$ $μ$

Volumetric strain

Figure 1.
Drücker-Prager yield criteria uses a modified von Mises yield criteria to incorporate the effects of pressure for massive structures:(1)
$F = J_{2} - (A_{0} + A_{1} P + A_{2} P^{2})$ $F = J_{2} - (A_{0} + A_{1} P + A_{2} P^{2})$

Where,

$J_{2}$ $J_{2}$

Second invariant of deviatoric stress

$P$ $P$

Pressure

$A_{0}$ $A_{0}$ , $A_{1}$ $A_{1}$ , and $A_{2}$ $A_{2}$

Material coefficients

$A_{1} = A_{2} = 0$ $A_{1} = A_{2} = 0$ means that the yield criteria is von Mises ( $σ_{vm} = \sqrt{3 A_{0}}$ $σ_{vm} = \sqrt{3 A_{0}}$ ).

Figure 2.
This card is represented as an extension to a MAT1 material in HyperMesh.