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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"


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)


2. 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


Development Team

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

contact: leopoldo.tesser AT dicea.unipd.it

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

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