/FAIL/HC_DSSE
Block Format Keyword Strainbased Ductile Failure Model: HosfordCoulomb with Domain of ShelltoSolid Equivalence. A nonlinear strain based failure criteria for shells with linear damage accumulation.
The failure strain is described by the HosfordCoulomb function (refer to /FAIL/EMC for solids). Works only with elastoplastic material laws > 28. This failure criteria was developed by Keunhwan Pack (Massachusetts Institute of Technology MIT) and Dirk Mohr (Swiss Federal Institute of Technology ETH Zurich). ^{1}
Format
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

/FAIL/HC_DSSE/mat_ID/unit_ID  
I_{fail_sh}  P_thick_{fail}  IFlag 
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

a  b  c  d  ${n}_{f}$ 
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

c2  c3  c4  Inst_str  ${n}_{f}$ 
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

fail_ID 
Definitions
Field  Contents  SI Unit Example 

mat_ID  Material identifier (Integer, maximum 10 digits) 

unit_ID  Unit Identifier (Integer, maximum 10 digits) 

I_{fail_sh}  Shell failure flag.
(Integer) 

P_thick_{fail}  Ratio of through thickness integration
points that must fail before the element is deleted. (shells only). Default = 1.0 (Real) 

IFlag  Input type flag.
(Integer) 

a  Failure model parameter
a. (Real) 

b  Failure model parameter
b. (Real) 

c  Failure model parameter
c. (Real) 

d  Failure model parameter
d. (Real) 

c2  Failure strain in pure shear
(triaxiality
$\eta =0$
). (Real) 

c3  Failure strain in uniaxial tension
(triaxiality
$\eta =\frac{1}{3}$
). (Real) 

c4  Failure strain in plane strain tension
(triaxiality =
$\eta =\frac{1}{\sqrt{3}}$
). (Real) 

Inst_str  Instability strain in plane strain
tension for localized necking. (Real) 

${n}_{f}$  Parameter
${n}_{f}$
. Default = 0.1 (Real) 

fail_ID  Failure criteria
identifier. (Integer, maximum 10 digits) 
Example
This example uses the HCDSSE parameter input (a, b, c, d parameters with IFlag = 0).
$\begin{array}{l}IFlag=0\\ a=1.742\\ b=0.7\\ c=0.029\\ d=1.6\end{array}$ ⇔ $\begin{array}{l}IFlag=1\\ c2=0.8\begin{array}{c}\end{array}(PureShear)\\ c3=0.7\begin{array}{c}\end{array}(UniaxialTension)\\ c4=0.58\begin{array}{c}\end{array}(PlaneStrainTension)\\ \end{array}$
and one use physical input (failure strain input with IFlag=1). HCDSSE parameters a, b, c, d will be calculated using a curve fit by the Radioss Starter.
Example (HCDSSE Parameter Input)
#RADIOSS STARTER
#12345678910
/UNIT/1
unit for mat
# MUNIT LUNIT TUNIT
kg mm ms
#12345678910
#12345678910
# 1. MATERIALS:
/MAT/PLAS_TAB/2/1
DP600 from SSAB Homepage
# RHO_I
7.8E6 0
# E Nu Eps_p_max Eps_t Eps_m
210 .3 0 0 0
# N_funct F_smooth C_hard F_cut Eps_f
1 0 0 0 0
# fct_IDp Fscale Fct_IDE EInf CE
0 0 0 0 0
# func_ID1 func_ID2 func_ID3 func_ID4 func_ID5
14
# Fscale_1 Fscale_2 Fscale_3 Fscale_4 Fscale_5
1
# Eps_dot_1 Eps_dot_2 Eps_dot_3 Eps_dot_4 Eps_dot_5
0
#12345678910
/FAIL/HC_DSSE/2/1
# Ishell P_thickfail I_Flag
1 .5 0
# a b c d n_f
1.742 0.7 0.029 1.6 0.1
#12345678910
/FUNCT/14
Mat_Curev Quasistatic DOCOL DP 600 (Material from SSAB Homepage 2010)
# X Y
0 .306
.00112 .415
.00218 .445
.003 .461
.00404 .474
.00517 .489
.00613 .498
.0071 .505
.00806 .512
.00901 .522
.0102 .53
.0121 .543
.013 .55
.014 .555
.015 .561
.0159 .567
.0171 .572
.0181 .577
.0204 .592
.0303 .632
.0405 .663
.0502 .687
.06 .706
.0702 .722
.0807 .737
.09 .749
.0997 .758
.101 .759
.11 .768
.15000001 .805
.2 .84
.30000001 .9
.5 1
1 1.21
#12345678910
#enddata
/END
#12345678910
Example (Physical Input)
#RADIOSS STARTER
#12345678910
/UNIT/1
unit for mat
# MUNIT LUNIT TUNIT
kg mm ms
#12345678910
#12345678910
# 1. MATERIALS:
/MAT/PLAS_TAB/2/1
DP600 from SSAB Homepage
# RHO_I
7.8E6 0
# E Nu Eps_p_max Eps_t Eps_m
210 .3 0 0 0
# N_funct F_smooth C_hard F_cut Eps_f
1 0 0 0 0
# fct_IDp Fscale Fct_IDE EInf CE
0 0 0 0 0
# func_ID1 func_ID2 func_ID3 func_ID4 func_ID5
14
# Fscale_1 Fscale_2 Fscale_3 Fscale_4 Fscale_5
1
# Eps_dot_1 Eps_dot_2 Eps_dot_3 Eps_dot_4 Eps_dot_5
0
#12345678910
/FAIL/HC_DSSE/2/1
# Ishell P_thickfail I_Flag
1 .5 1
# c2 c3 c4 Inst_str n_f
0.8 0.7 0.58 0.1 0.1
#12345678910
/FUNCT/14
Mat_Curev Quasistatic DOCOL DP 600 (Material from SSAB Homepage 2010)
# X Y
0 .306
.00112 .415
.00218 .445
.003 .461
.00404 .474
.00517 .489
.00613 .498
.0071 .505
.00806 .512
.00901 .522
.0102 .53
.0121 .543
.013 .55
.014 .555
.015 .561
.0159 .567
.0171 .572
.0181 .577
.0204 .592
.0303 .632
.0405 .663
.0502 .687
.06 .706
.0702 .722
.0807 .737
.09 .749
.0997 .758
.101 .759
.11 .768
.15000001 .805
.2 .84
.30000001 .9
.5 1
1 1.21
#12345678910
#enddata
/END
#12345678910
Comments
 This failure criterion is defined in
the space of equivalent plastic strain at failure versus stress triaxiality (state of
stress) for plane stress condition. This allows for definition of failure strain that
varies with different loading conditions. It consists of two curves. One is the fracture
locus (that is, below the red curve) and the other is the localized necking locus (blue
curve).
The former takes the following form:
(1) $${\overline{\epsilon}}_{HC}^{pr}\left(\eta ,\theta \right)=b{(1+c)}^{\frac{1}{{n}_{f}}}{\left\{{\left[\frac{1}{2}\left({\left({\mathrm{f}}_{1}{\mathrm{f}}_{2}\right)}^{a}+{\left({\mathrm{f}}_{2}{\mathrm{f}}_{3}\right)}^{a}+{\left({\mathrm{f}}_{1}{\mathrm{f}}_{3}\right)}^{a}\right)\right]}^{\frac{1}{a}}+c\left(2\eta +{\mathrm{f}}_{1}+{\mathrm{f}}_{3}\right)\right\}}^{\frac{1}{{n}_{f}}}$$${\mathrm{f}}_{1}$ , ${\mathrm{f}}_{2}$ and ${\mathrm{f}}_{3}$ are functions of the Lode angle $\theta $ :
$with\{\begin{array}{c}{\mathrm{f}}_{1}\left(\theta \right)=\frac{2}{3}\mathrm{cos}\left(\frac{\pi}{6}\left(1\theta \right)\right)\\ {\mathrm{f}}_{2}\left(\theta \right)=\frac{2}{3}\mathrm{cos}\left(\frac{\pi}{6}\left(3+\theta \right)\right)\\ {\mathrm{f}}_{3}\left(\theta \right)=\frac{2}{3}\mathrm{cos}\left(\frac{\pi}{6}\left(1+\theta \right)\right)\end{array}$
$\theta =1\frac{2}{\pi}arc\mathrm{cos}\left(\frac{27}{2}\eta \left({\eta}^{2}\frac{1}{3}\right)\right)$
$d{D}_{HC}=\frac{d{\overline{\epsilon}}_{p}}{{\overline{\epsilon}}_{HC}^{pr}\left(\eta \right)}$
The latter is defined only between uniaxial and eqibiaxial tension conditions for ( $\frac{1}{3}<\eta <\frac{2}{3}$ ) in which localized necking can occur.(2) $${\overline{\epsilon}}_{DSSE}^{pr}\left(\eta \right)=b\{{{\left[\frac{1}{2}\left({\left({\mathrm{g}}_{1}{\mathrm{g}}_{2}\right)}^{d}+{\mathrm{g}}_{1}^{d}+{\mathrm{g}}_{2}^{d}\right)\right]}^{\frac{1}{d}}\}}^{\frac{1}{p}}$$$with\{\begin{array}{c}{\mathrm{g}}_{1}\left(\eta \right)=\frac{2}{3}\eta +\sqrt{\frac{1}{3}\frac{3}{4}{\eta}^{2}}\\ {\mathrm{g}}_{2}\left(\eta \right)=\frac{2}{3}\eta \sqrt{\frac{1}{3}\frac{3}{4}{\eta}^{2}}\end{array}$(3) $$d{D}_{DSSE}=\frac{d{\overline{\epsilon}}_{p}}{{\overline{\epsilon}}_{DSSE}^{pr}\left(\eta \right)}$$ The universal exponent of $p$ =0.01 is used.
 Localized necking is predicted in a nonlocal manner when all integration points or layers have $d{D}_{DSSE}>1$ > 1.
 The failure curve parameters a, b,
c, and d, must be calibrated based on test
results.
$\eta $ is the triaxiality.
 Alternatively, switching the IFlag to 1, allows Radioss to do the parameter fit internally.
 No shell fracture in compression area ( $\eta <\frac{1}{3}$ ).
 Damage is calculated as:
(4) $$D={\displaystyle \sum \frac{\text{\Delta}{\overline{\epsilon}}_{p}}{{\overline{\epsilon}}_{HC}^{pr}\left(\eta \right)}}$$