Variational Formulations and Functional Approximation Algorithms in Stochastic Plasticity of Materials

Iterative algorithms for families of variational inequalities fixed points and equilibrium problems

Symmetric Confidence Regions and Confidence Intervals for Normal Map Formulations of Stochastic Variational Inequalities

Stochastic variational inequalities (SVI) model a large class of equilibrium problems subject to data uncertainty, and are closely related to stochastic optimization problems. The SVI solution is usually estimated by a solution to a sample average approximation (SAA) problem. This paper considers the normal map formulation of an SVI, and proposes a method to build asymptotically exact confidenc...

Variational Characterization of Free Energy: Theory and Algorithms

The article surveys and extends variational formulations of the thermodynamic free energy and discusses their information-theoretic content from the perspective of mathematical statistics. We revisit the well-known Jarzynski equality for nonequilibrium free energy sampling within the framework of importance sampling and Girsanov change-of-measure transformations. The implications of the differe...

On the Formulation of Closest-Point Projection Algorithms in Elastoplasticity

We present in this paper the characterization of the variational structure behind the discrete equations defining the closest-point projection approximation in elastoplasticity. Rate-independent and viscoplastic formulations are considered in the infinitesimal and the finite deformation range, the later in the context of isotropic finite strain multiplicative plasticity. Primal variational prin...

Conjugate gradient neural network in prediction of clay behavior and parameters sensitivities

The use of artificial neural networks has increased in many areas of engineering. In particular, this method has been applied to many geotechnical engineering problems and demonstrated some degree of success. A review of the literature reveals that it has been used successfully in modeling soil behavior, site characterization, earth retaining structures, settlement of structures, slope stabilit...