TY - JOUR
T1 - Constitutive modeling of porous viscoelastic materials
AU - Xu, F.
AU - Sofronis, P.
AU - Aravas, N.
AU - Meyer, S.
N1 - Funding Information:
This work was supported by the Center for Simulation of Advanced Rockets, funded by the U.S. Department of Energy through the University of California under subcontract number DOE/LLNL/B523819. The finite element calculations were carried out at the National Center for Supercomputing Applications at the University of Illinois at Urbana-Champaign.
PY - 2007/11
Y1 - 2007/11
N2 - The effect of porosity on the constitutive response of an isotropic linearly viscoelastic solid that obeys a constitutive law of the standard differential form is investigated under small strain deformation conditions. The correspondence principle of linear viscoelasticity is used to solve the viscoelastic boundary value problem at a unit cell containing a spherical void and loaded axisymmetrically by macroscopic stresses. The results are used to devise a constitutive potential for the description of the porous material for any arbitrary combination of hydrostatic and deviatoric loadings, and the associated 3-D constitutive relationship is determined in the Laplace transform domain. Inversion to the time domain yields the constitutive law of the porous material as a function of porosity in the standard form of convolution integrals. The presence of porosity establishes relaxation time scales for the porous body that differ from the relaxation time of the pure matrix material and brings about a viscous character to the overall hydrostatic response. The numerical implementation of the model in a general purpose finite element code is outlined. The model is used to predict the response of a porous solid propellant material in uniaxial tension and cyclic loading at room temperature.
AB - The effect of porosity on the constitutive response of an isotropic linearly viscoelastic solid that obeys a constitutive law of the standard differential form is investigated under small strain deformation conditions. The correspondence principle of linear viscoelasticity is used to solve the viscoelastic boundary value problem at a unit cell containing a spherical void and loaded axisymmetrically by macroscopic stresses. The results are used to devise a constitutive potential for the description of the porous material for any arbitrary combination of hydrostatic and deviatoric loadings, and the associated 3-D constitutive relationship is determined in the Laplace transform domain. Inversion to the time domain yields the constitutive law of the porous material as a function of porosity in the standard form of convolution integrals. The presence of porosity establishes relaxation time scales for the porous body that differ from the relaxation time of the pure matrix material and brings about a viscous character to the overall hydrostatic response. The numerical implementation of the model in a general purpose finite element code is outlined. The model is used to predict the response of a porous solid propellant material in uniaxial tension and cyclic loading at room temperature.
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U2 - 10.1016/j.euromechsol.2007.05.008
DO - 10.1016/j.euromechsol.2007.05.008
M3 - Article
AN - SCOPUS:34548602404
SN - 0997-7538
VL - 26
SP - 936
EP - 955
JO - European Journal of Mechanics, A/Solids
JF - European Journal of Mechanics, A/Solids
IS - 6
ER -