Damage2p

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This command is used to construct a three-dimensional material object that has a Drucker-Prager plasticity model coupled with a two-parameter damage model.

nDMaterial Damage2p $matTag $fcc <-fct $fct> <-E $E> <-ni $ni> <-Gt $Gt> <-Gc $Gc> <-rho_bar $rho_bar> <-H $H> <-theta $theta> <-tangent $tangent>

$matTag	integer tag identifying material
$fcc	concrete compressive strength
$fct	optional concrete tensile strength
$E	optional Young modulus
$ni	optional Poisson coefficient
$Gt	optional tension fracture energy density
$Gc	optional compression fracture energy density
$rho_bar	ptional parameter of plastic volume change
$H	optional linear hardening parameter for plasticity
$theta	optional ratio between isotropic and kinematic hardening
$tangent	optional integer to choose the computational stiffness matrix

The material formulations for the Damage2p object are "ThreeDimensional" and "PlaneStrain"

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This code has been Developed by: Leopoldo Tesser - Dept. DICEA - Univeristy of Padua - Italy,

contact: leopoldo.tesser AT dicea.unipd.it

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NOTES

1. Admissible values: The input parameters vary as follows:

$fcc	negative real value (positive input is changed in sign automatically)
$fct	positive real value (for concrete like materials is less than $fcc)
$Gt	positive real value (integral of the stress-strain envelope in tension)
$Gc	positive real value (integral of the stress-strain envelope after the peak in compression)
$rhoBar	positive real value 0=rhoBar<sqrt(2/3)
$H	positive real value (usually less than $E)
$theta	positive real value 0=$theta=1 (with: 0 hardening kinematic only and 1 hardening isotropic only
$tangent	0: computational tangent; 1: damaged secant stiffness (hint: in case of strong nonlinearities use it with Krylov-Newton algorithm)

1. Default values: The Damage2p object hve the following defualt parameters:

$fct	= 0.1*abs(fcc)
$E	= 4750*sqrt(abs(fcc)) if abs(fcc)<2000 because fcc is assumed in MPa (see ACI 318) = 57000*sqrt(abs(fcc)) if abs(fcc)>2000 because fcc is assumed in psi (see ACI 318)
$ni'	= 0.15 (from comparison with tests by Kupfer Hilsdorf Rusch 1969)
'$Gt	= 1840*fct*fct/E (from comparison with tests by Gopalaratnam and Shah 1985)
$Gc	= 6250*fcc*fcc/E (from comparison with tests by Karsan and Jirsa 1969)
$rhoBar	= 0.2 (from comparison with tests by Kupfer Hilsdorf Rusch 1969)
$H	= 0.25*E (from comparison with tests by Karsan and Jirsa 1969 and Gopalaratnam and Shah 1985)
'$theta	= 0.5 (from comparison with tests by Karsan and Jirsa 1969 and Gopalaratnam and Shah 1985)	_	$tangent	= 0

References

Tesser L.,"Efficient 3-D plastic damage model for cyclic inelastic analysis of concrete structures", Report of the University of Padua, Italy, 2012. (soon available at paduareserach.cab.unipd.it)

Petek K.A., "Development and application of mixed beam-solid models for analysis of soil-pile interaction problems", Ph.D. dissertation, Univerisity of Washington, USA, 2006