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Multiaxial Probabilistic Elastic-Plastic Constitutive Simulations of Soils

Sadrinezhad, Arezoo
http://rave.ohiolink.edu/etdc/view?acc_num=akron1406637815

Abstract Details

2014, Doctor of Philosophy, University of Akron, Civil Engineering.
Fokker-Planck-Kolmogorov (FPK) equation approach has recently been developed to simulate elastic-plastic constitutive behaviors of materials with uncertain material properties. The FPK equation approach transforms the stochastic constitutive rate equation, which is a stochastic, nonlinear, ordinary differential equation (ODE) in the stress-pseudo time space into a second-order accurate, deterministic, linear FPK partial differential equation (PDE) in the probability density of stress-pseudo time space. This approach does not suffer from the drawbacks of the traditional approaches such as the Monte Carlo approach and the perturbation approach for solving nonlinear ODEs with random coefficients. In this study, the existing one dimensional FPK framework for probabilistic constitutive modeling of soils is extended to multi--dimension. However, the multivariate FPK PDEs cannot be solved using the traditional mathematical techniques such as finite difference techniques due to their high computational cost. Therefore, computationally efficient algorithms based on the Fourier spectral approach are developed for solving a class of FPK PDEs that arises in probabilistic elasto-plasticity. This class includes linear FPK PDEs in (stress) space and (pseudo) time - having space-independent but time-dependent, and both space- and time-dependent coefficients - with impulse initial conditions and reflecting boundary conditions. The solution algorithms, rely on first mapping the stress space of the governing PDE between 0 and 2pi using the change of coordinates rule, followed by approximating the solution of the PDE in the 2pi-periodic domain by a finite Fourier series in the stress space and unknown time-dependent solution coefficients. Finally, the time-dependent solution coefficients are obtained from the initial condition. The accuracy and efficiency of the developed algorithms are tested. The developed algorithms are used to simulate uniaxial and multiaxial, monotonic and cyclic constitutive behaviors of uncertain elasto--plastic soils. In particular, the effects of uncertainties in soil properties on constitutive behaviors of soils subjected to an unconfined compression test and to an unconsolidated undrained triaxial test are evaluated. To this end, the governing FPK equation of probabilistic elasto-plasticity is specialized to uniaxial stress space and to two dimensional principal stress space. Then, the specialized FPK PDEs are solved using the developed algorithms. Simulation results show that by considering soil uncertainties in the constitutive simulation, more realistic constitutive behavior can be ontained which agrees well with the principles of micromechanics. It is also observed that by explicit treatment to soil uncertainties, some of the important aspects of soil behaviors-for example, hardening and Bauschinger effect- can be captured even with the simplest elastic-perfectly plastic von Mises (two-parameters) model.
S. I Hariharan, Dr. (Advisor)
Kallol Sett, Dr. (Advisor)
Robert Y Liang , Dr (Committee Member)
David Roke, Dr (Committee Member)
Wieslaw K Binienda , Dr. (Committee Member)
Ali Hajjafar, Dr. (Committee Member)
128 p.
Civil Engineering
Elasto-plasticity, uncertainty, soils, Fokker-Planck equation, Fourier spectral method, finite difference method

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Citations

  • Sadrinezhad, A. (2014). Multiaxial Probabilistic Elastic-Plastic Constitutive Simulations of Soils [Doctoral dissertation, University of Akron]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=akron1406637815

    APA Style (7th edition)

  • Sadrinezhad, Arezoo. Multiaxial Probabilistic Elastic-Plastic Constitutive Simulations of Soils. 2014. University of Akron, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=akron1406637815.

    MLA Style (8th edition)

  • Sadrinezhad, Arezoo. "Multiaxial Probabilistic Elastic-Plastic Constitutive Simulations of Soils." Doctoral dissertation, University of Akron, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=akron1406637815

    Chicago Manual of Style (17th edition)

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This open access ETD is published by University of Akron and OhioLINK.