Damage2p
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
