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We develop a new paradigm for thin-shell finite-element analysis based on the use of subdivision surfaces for: i) describing the geometry of the shell in its undeformed configuration, and ii)â€¦ (More)

- Razvan C. Fetecau, Jerrold E. Marsden, Michael Ortiz, Matthew West
- SIAM J. Applied Dynamical Systems
- 2003

Variational techniques are used to analyze the problem of rigid-body dynamics with impacts. The theory of smooth Lagrangian mechanics is extended to a nonsmooth context appropriate for collisions,â€¦ (More)

The physical basis of computationally tractable models of crystalline plasticity is reviewed. A statistical mechanical model of dislocation motion through forest dislocations is formulated. Followingâ€¦ (More)

- Bernd Schmidt, Fernando Fraternali, Michael Ortiz
- Multiscale Modeling & Simulation
- 2008

We propose an approximation scheme for a variational theory of brittle fracture. In this scheme, the energy functional is approximated by a family of functionals depending on a small parameter and onâ€¦ (More)

This work is concerned with the reformulation of evolutionary problems in a weak form enabling consideration of solutions that may exhibit evolving microstructures. This reformulation is accomplishedâ€¦ (More)

- Houman Owhadi, Clint Scovel, Timothy John Sullivan, Mike McKerns, Michael Ortiz
- SIAM Review
- 2013

We propose a rigorous framework for uncertainty quantification (UQ) in which the UQ objectives and its assumptions/information set are brought to the forefront. This framework, which we call optimalâ€¦ (More)

We present a real-space, non-periodic, finite-element formulation for Kohnâ€“Sham density functional theory (KS-DFT). We transform the original variational problem into a local saddle-point problem,â€¦ (More)

We consider single-crystal plasticity in the limiting case of infinite latent hardening, which signifies that the crystal must deform in single slip at all material points. This requirementâ€¦ (More)

Discontinuous Galerkin (DG) finite-element methods for secondand fourth-order elliptic problems were introduced about three decades ago. These methods stem from the hybrid methods developed by Pianâ€¦ (More)

- Anna Pandolfi, Michael Ortiz
- Engineering with Computers
- 2002

We present a simple set of data structures, and a collection of methods for constructing and updating the structures, designed to support the use of cohesive elements in simulations of fracture andâ€¦ (More)