Michael Ortiz

TL;DR: It is shown that concentration-of-measure inequalities rigorously bound probabilities of failure and thus supply conservative certification criteria and supply unambiguous quantitative definitions of terms such as margins, epistemic and aleatoric uncertainties, verification and validation measures, confidence factors, and others, as well as providing clear procedures for computing these quantities.

TL;DR: A simple class of Lagrangians and variational integrators derived by time discretization of the action functional is established and the relation between Γ-convergence and the convergence of the Fourier transform of the discrete trajectories as measured in the flat norm is established.

TL;DR: In this paper, a method is presented for calculating stress intensity factors at the tip of a slightly wavy three-dimensional crack and the solution is used to calculate the direction of propagation of an initially planar semi-infinite crack, which is subjected to uniform remote loading.

TL;DR: In this paper, the authors present a streamlined limiting case of the theory of Oritz & Repetto for crystals with microstructure in which the crystals are assumed to exhibit infinitely strong latent hardening.

TL;DR: In this article, the authors investigated the stability of quasi-static boundary value problems for two semi-infinite solids bonded along a planar interface and showed that the instability plays a role in the transition from a uniform mode of separation to crack-like behavior.