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 \(E)</p></td> </tr> <tr class="odd"> <td><code class="parameter-table-variable">theta</code></td> <td><p>positive real value 0=\)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)

      \(Gt</strong></p></td> <td><p>= 1840*fct*fct/E (from comparison with tests by Gopalaratnam and Shah 1985)</p></td> </tr> <tr class="odd"> <td><code class="parameter-table-variable">Gc</code></td> <td><p>= 6250*fcc*fcc/E (from comparison with tests by Karsan and Jirsa 1969)</p></td> </tr> <tr class="even"> <td><code class="parameter-table-variable">rhoBar</code></td> <td><p>= 0.2 (from comparison with tests by Kupfer Hilsdorf Rusch 1969)</p></td> </tr> <tr class="odd"> <td><code class="parameter-table-variable">H</code></td> <td><p>= 0.25*E (from comparison with tests by Karsan and Jirsa 1969 and Gopalaratnam and Shah 1985)</p></td> </tr> <tr class="even"> <td><p><strong>'\)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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