OpenSees Commands to Create Material Models using Template Elasto–Plastic Framework

Yield Surface Command

set ys "-YieldSurfaceType <parameter list>"

This command sets the yield surface variable ys to be the specified type. A list of paramaters can be passed to define the yield surface and the number of parameters depend on the type of yield surface. Valid strings for YieldSurfaceType are DP, VM, CC, and RMC01, which are described in the following subsections.

Drucker-Prager Yield Surface

set ys "-DP"

DP stands for Drucker-Prager type, i.e. cone shaped yield surface. In this case, no parameter needs to be supplied since the slope \(\alpha\) is treated as an internal variable.

von Mises Yield Surface

set ys "-VM"

VM stands for von Mises type, i.e. cylinder shaped yield surface. In this case, no parameter needs to be supplied since the size of the cylinder is treated as an internal variable.

Cam-Clay Yield Surface

set ys "-CC M?"

CC stands for Cam-Clay type, i.e. ellipsoid shaped yield surface. For CC type yield surface, the slope of the critical state line in p–q space, i.e. M, need to be supplied.

Rounded Mohr-Coulomb (Willam-Warnke) Yield Surface

set ys "-RMC01"

RMC01 stands for rounded Mohr-Coulomb (Willam-Warnke) type, i.e. cone shaped yield surface. In this case, no parameter needs to be supplied, this is similar to the Drucker-Prager yield surface.

Potential Surface Command

set ps "-PotentialSurfaceType <parameter list>"

This command sets the potential surface variable ps to be the specified type. A list of paramaters can be passed to define the potential surface and the number of parameters depend on the type of potential surface. Valid strings for PotentialSurfaceType are DP, VM, and CC, which are described in the following subsections.

Drucker-Prager Potential Surface

set ps "-DP"

DP stands for Drucker-Prager type, i.e. cone shaped potential surface. In this case, no parameter needs to be supplied since the slope \(\alpha\) is treated as an internal variable.

von Mises Potential Surface

set ps "-VM"

VM stands for von Mises type, i.e. cylinder shaped potential surface. In this case, no parameter needs to be supplied since the size of the cylinder is treated as an internal variable.

Cam-Clay Potential Surface

set ps "-CC M?"

CC stands for Cam-Clay type, i.e. ellipsoid shaped potential surface. For CC type potential surface, the slope of the critical state line in p–q space, i.e. M, need to be supplied.

Rounded Mohr-Coulomb (Willam-Warnke) Potential Surface

set ps "-RMC01"

RMC01 stands for rounded Mohr-Coulomb (Willam-Warnke) type, i.e. cone shaped Potential surface. In this case, no parameter needs to be supplied, this is similar to the Drucker-Prager Potential surface.

Evolution Law Command

set el "-EvolutionLawType <parameter list>"

This command sets the evolution law variable el to be the specified type. A list of paramaters can be passed to define the potential surface and the number of parameters depend on the type of potential surface. Valid strings for EvolutionLawType are Leq, NLp, and ``, which are described in the following subsections.

Linear Scalar Evolution Law

set el "-Leq a?"

Leq stands for Linear Scalar Evolution Law. This hardening rule is based on the equivalent deviatoric plastic strain \(\epsilon_q^{pl}\). In this case, linear hardening coefficient a needs to be supplied. This hardening rule can be applied to any scalar internal variable, such as the slope of Drucker–Prager yield surface, the diameter of von Mises yield surface, and so on.

Nonlinear Scalar Evolution Law

set el "-NLp e0? lambda? kappa? "

NLp stands for Nonlinear Scalar Evolution Law. This hardening rule is based on the volumetic plastic strain \(\epsilon_p^{pl}\). In this case, parameters including void ration e0, lambda and kappa need to be supplied. This hardening rule is primarily for the evolution of the tip stress \(p^{'}_{o}\) in Cam-Clay model.

Linear Tensorial Evolution Law

set et "-LEij a?"

LEij stands for Linear Tensorial Evolution Law. This hardening rule is based on the plastic strain \(\epsilon_{ij}^{pl}\). In this case, linear hardening coefficient a needs to be supplied. This hardening rule can be applied to any tensorial internal variable, such as the the center \(\alpha_{ij}\) of Drucker–Prager yield surface or von Mises yield surface, and so on.

Nonlinear Tensorial Evolution Law (Armstrong-Frederick model )

set et "-NLEij ha? Cr?" 

NLEij stands for Nonlinear Tensorial Evolution Law from Armstrong–Frederick nonlinear model. This kinematic hardening law is based on the plastic strain \(\epsilon_{ij}^{pl}\). In this case, nonlinear hardening coefficients ha and Cr need to be supplied. This hardening rule can be applied to any tensorial internal variable, such as the the center \(\alpha_{ij}\) of Drucker–Prager yield surface or von Mises yield surface, and so on.

EPState Command

<set sts "Sxx? Sxy? Sxz? Syx? Syy? Syz? Szx? Szy? Szz?"> 

set eps "<-NOD nt?> -NOS ns? sc1? sc2? ... <-stressp sts>"

First statement sets the initial stress tensor to variable sts (if it is not stated here, no initial stress by default). Second statement assigns to the Elasto-Plastic state variable eps the specified state parameters, including number of tensorial internal variables nt (if it is not stated here, \(nt=0\) by default), number of scalar internal variables ns and corresponding initial values sc1, sc2, ..., and initial stresses defined in $sts (if it has been previously defined).

Template Elasto-Plastic Material Command

nDMaterial Template3Dep mTag? -YS $ys? -PS $ps? -EPS $eps? <-ELS1 $el?> 
<$-ELT1 et?>

A template elasto-plastic material is constructed using nDMaterial command. The argument mTag is used to uniquely identify this nDMaterial object among nDMaterial objects in the BasicBuilder object. The other parameters include previously defined yield surface object ys, potential surface object ps, elasto-plastic state object eps, scalar evolution law object el, and tensorial evolution law object et.

Examples

von Mises Model

 

# Yield surface 
set ys "-VM"

# Potential surface
set ps "-VM"

# Scalar evolution law: linear hardening coef = 1.0
set ES1  "-Leq  1.10"

# EPState
#______________k=f(Cu)
set EPS "-NOD 0 -NOS 1 20"#

# Creating nDMaterial using Template Elastic-Plastic Model
nDMaterial Template3Dep 1 -YS $ys -PS $ps -EPS $EPS -ELS1 $ES1

Drucker–Prager Model

 

# Yield surface 
set ys "-DP"

# Potential surface
set ps "-DP 0.1"

# Scalar evolution law: linear hardening coef = 1.0
set ES1  "-Leq  1.10"

# Initial stress
set sts "0.10 0 0  0 0.10 0  0 0 0.10"

# EPState
#______________alpha___k
set EPS "-NOD 0 -NOS 2 0.2 0.0 -stressp $sts"
#
# where
#alpha = 2 sin(phi) / (3^0.5) / (3-sin(phi) ), phi is the friction angle
# and k is the cohesion

# Creating nDMaterial using Template Elastic-Plastic Model
nDMaterial Template3Dep 1 -YS $ys -PS $ps -EPS $EPS -ELS1 $ES1

Cam-clay Model

 

# Yield surface M = 1.2
set ys "-CC 1.2"

# Potential surface M = 1.2
set ps "-CC 1.2"

# Scalar evolution law___void ratio___Lamda___Kappa 
set ES1  "-NLp           0.85        0.19   0.06"

# Initial stress
set sts "0.10 0 0  0 0.10 0  0 0 0.10"

#________________po
set EPS "-NOS 1 200.1 -stressp $sts"

#
nDMaterial Template3Dep 1 -YS $ys -PS $ps -EPS $EPS -ELS1 $ES1