Uncertain Elasto-Plasticity

Speaker: Dr. Boris Jeremic, Department of Civil and Environmental Engineering, University of California, Davis, jeremic@ucdavis.eduAbstract:
Behavior of realistic materials is inherently uncertain. Two main sources of
such behavior are (a) the constitutive level uncertainties and (b) the uncertain
spatial variability of material.Presented in this talk is the method for simulating uncertain elastic-plastic
behavior. On the constitutive level, an Euler-Lagrange form of
Fokker-Planck-Kolmogorov (FPK) equation is applied to the description of the
evolution of probability density function of stress response for (any) elastic
and/or elastic-plastic material model with random material properties. The FPK
approach does not suffer from the "closure problem" associated with perturbation
methods nor does it require repetitive use of deterministic elastic-plastic
simulations as associated with Monte Carlo technique. Furthermore, the FPK
approach transforms the nonlinear stochastic constitutive ordinary differential
equation into linear deterministic partial differential equation, which, even if
not amenable to analytical solution, greatly simplifies the numerical solution
process. On the finite element level, spatial variability of material properties
is modeled and simulated using Karhunen-Loeve expansions of input random fields
in eigen-modes of their covariance function and polynomial chaos expansion with
Galerkin method to represent the solution random field.Number of examples will be presented, illustrating methodology and main results,
some of which are quite surprising and can be seen, at first glance as
counter-intuitive.

Location: Kaprielian Hall (KAP) - 209

Audiences: Everyone Is Invited

Contact: Evangeline Reyes