/MAT/LAW44 (COWPER)

Block Format Keyword

/MAT/LAW44 - Cowper-Symonds Material

Description

The Cowper-Symonds law models an elasto-plastic material. The basic principle is the same as the standard Johnson-Cook model; the only difference between the two laws lies in the expression for strain rate effect on flow stress.

Format

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
/MAT/LAW44/mat_ID/unit_ID or /MAT/COWPER/mat_ID/unit_ID
mat_title

E
a		b		n		Chard
c		p		ICC	Fsmooth	Fcut

Field	Contents	SI Unit Example
mat_ID	Material identifier (Integer, maximum 10 digits)
unit_ID	Optional unit identifier (Integer, maximum 10 digits)
mat_title	Material title (Character, maximum 100 characters)
	Initial density (Real)
E	Young’s modulus (Real)
	Poisson’s ratio (Real)
a	Plasticity yield stress (Real)
b	Plasticity hardening parameter (Real)
n	Plasticity hardening exponent Default = 1.0 (Real)
Chard	Plasticity Iso-kinematic hardening factor Default = 0.0 (Real) = 0: hardening is full isotropic model = 1: hardening uses the kinematic Prager-Ziegler model = between 0 and 1: hardening is interpolated between the two models
	Plasticity maximum stress Default = 1030 (Real)
c	Strain rate coefficient = 0: no strain rate effect (default) (Real)
p	Strain rate exponent Default = 1.0 (Real)
ICC	Strain rate computation flag (Comment 6) (Integer) = 0: default set to 1 = 1: strain rate effect on = 2: no strain rate effect on
Fsmooth	Smooth strain rate option flag (Integer) = 0: no strain rate smoothing (default value) = 1: strain rate smoothing active
Fcut	Cutoff frequency for strain rate filtering Default = 1030 (Real)
	Failure plastic strain Default = 1030 (Real)
	Tensile failure strain 1 Default = 1030 (Real)
	Tensile failure strain 2 Default = 2.1030 (Real)

#RADIOSS STARTER

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/UNIT/1

unit for mat

g mm ms

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#- 2. MATERIALS:

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/MAT/COWPER/1/1

metal

# RHO_I

.0078

# E NU

20500 .3

# a b n C_hard SIGMA_max0

50 100 .5 1 90

# c p ICC F_smooth F_cut

100 5 1 0 0

# EPS_max EPS_t1 EPS_t2

0 0 0

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#ENDDATA

/END

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1.	The difference between the Cowper-Symonds law and the standard Johnson-Cook model lies only in the strain rate dependent formulation:

Where, is the plastic strain and is the strain rate.

2.	The law is only defined for solids and shells. The global plasticity option for shells is not available in the actual version.

3.	Yield stress should be strictly positive.

4.	The hardening exponent n must be less than 1.

clip0050

5.	The strain rate filtering is used to smooth strain rates.

6.	ICC is a flag of the strain rate effect on material maximum stress :

law_plaszeril

7.	Strain rate filtering input (Fcut) is only available for shell and solid elements.

8.	When reaches in one integration point, then based on the element type:

•	Shell elements: The corresponding shell element is deleted.

•	Solid elements: The deviatoric stress of the corresponding integral point is permanently set to 0, however, the solid element is not deleted

9.	If ( is the largest principal strain), the stress is reduced as follows:

10.	If , the stress is reduced to 0 (but the element is not deleted).