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`	`F`	`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
`F`	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 F 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.