Michael Ortiz

TL;DR: In this article, a quasicontinuum method is proposed for the simultaneous treatment of multiple scales, which is based upon a continuum formulation of the problem of interest as a boundary value problem within the confines of the finite element method.

TL;DR: In this article, a class of asynchronous variational integrators (AVI) for nonlinear elastodynamics is described, which is characterized by the following distinguishing attributes: the algorithms permit the selection of independent time steps in each element, and the local time steps need not bear an integral relation to each other; the algorithms derive from a spacetime form of a discrete version of Hamilton's principle.

TL;DR: In this paper, an implicit finite element formulation of the rate tangent modulus method is derived for which the consistent tangents, resulting in quadratic convergence of the equilibrium iterations, can be written out in closed form for arbitrary material models.

TL;DR: In this paper, a mixed atomistic and continuum method is reformulated to allow for the examination of the interactions between grain boundaries, dislocations, and cracks, which elucidate plausible microscopic mechanisms for these defect interactions and allow for quantitative evaluation of critical parameters such as the force needed to induce GB migration.

TL;DR: In this paper, a design and method for the fabrication of microfluidic valves using multilayer soft lithography is presented, which can be used to fabricate active functions, such as pumps and mixers in integrated microfluidity chips.