MATX44

Bulk Data Entry Defines additional material properties for Cowper-Symonds elastic-plastic material for geometric nonlinear analysis.

Format

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
MATX44	`MID`	`A`	`B`	`N`	`ICH`	`SIGMAX`	`C`	`P`
	`ICC`	`FSMOOTH`	`FCUT`	`EPSMAX`	`EPST1`	`EPST2`

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
MAT1	144	0.11		0.11	9.92E-07
MATX44	144

Field	Contents	SI Unit Example
`MID`	Material ID of the associated MAT1. No default (Integer > 0)
`A`	Plasticity yield stress. (Real > 0)
`B`	Plasticity hardening parameter. (Real ≥ 0)
`N`	Plasticity hardening exponent. Default = 1.0 (Real)
`ICH`	Hardening coefficient. 0.0 The hardening is a full isotropic model. 1.0 (Default) Hardening uses the kinematic Prager-Ziegler model. Between 0.0 and 1.0 Hardening is interpolated between the two models. (Real ≥ 0)
`SIGMAX`	Maximum plastic stress $σ_{\max 0}$ . Default = 10³⁰ (Real > 0)
`C`	Strain rate coefficient. Default = 0.0 (Real)
`P`	Strain rate exponent. Default = 1.0 (Real)
`ICC`	Strain rate dependency of $σ_{\max}$ flag. 5 ON (Default) OFF
`FSMOOTH`	Strain rate smoothing flag. OFF (Default) ON
`FCUT`	Cutoff frequency for strain rate filtering. Default = 10³⁰ (Real ≥ 0)
`EPSMAX`	Failure plastic strain. Default = 10³⁰ (Real > 0)
`EPST1`	Tensile rupture strain 1. Default = 10³⁰ (Real > 0)
`EPST2`	Tensile rupture strain 2. Default = 2.0 * 10³⁰ (Real > 0)

The material identification number must be that of an existing MAT1 Bulk Data Entry. Only one MATXi material extension can be associated with a particular MAT1.
MATX44 is only applied in geometric nonlinear analysis subcases which are defined by ANALYSIS = EXPDYN. It is ignored for all other subcases.
The Cowper-Symonds models an elastic-plastic material, only for solids and shells. The basic principle is the same as the standard Johnson-Cook model; the only difference between the two lies in the expression for strain rate effect on flow stress.
(1)
$σ = (a + b ε_{p}^{n}) (1 + {(\frac{\dot{ε}}{c})}^{\frac{1}{p}})$

with $ε_{p}$ being plastic strain, and $\dot{ε}$ being the strain rate.
Hardening is defined by ICH.

Figure 1.

ICC controls the strain rate effect.

Figure 2.

$\begin{array}{l} σ = σ_{y} (1 + cIn (\frac{\dot{ε}}{{\dot{ε}}_{0}})) \\ σ_{\max} = σ_{\max 0} (1 + cIn \frac{\dot{ε}}{{\dot{ε}}_{0}}) \end{array}$	$\begin{array}{l} σ = σ_{y} (1 + cIn (\frac{\dot{ε}}{{\dot{ε}}_{0}})) \\ σ_{\max} = σ_{\max 0} \end{array}$

No strain rate effects are considered in rod elements.
Strain rate filtering is used to smooth strain rates. The input FCUT is available only for shell and solid elements.
When the plastic strain reaches EPSMAX, the element is deleted.
$ε$ if the first principal strain $ε$ ₁ reaches _t1 = EPST1, the stress $σ$ is reduced by:
(2)
$σ = σ (\frac{ε_{t 2} - ε_{1}}{ε_{t 2} - ε_{t 1}})$

with $ε$ _t2 = EPST2.
If the first principal strain $ε$ ₁ reaches $ε$ _t2 = EPST2, the stress is reduced to 0 (but the element is not deleted).
If the first principal strain $ε$ ₁ reaches $ε$ _f = EPSF, the element is deleted.
This card is represented as an extension to a MAT1 material in HyperMesh.