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We describe a new class of asynchronous variational integrators (AVI) for non-linear elastodynamics. The AVIs are distinguished by the following attributes: (i) 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; (ii) the algorithms derive from a spacetime(More)
To Tom Hughes on the occasion of his 60th birthday. Tom Hughes has been a friend, collaborator, and colleague to some of us for several decades and has been a major inspiration on many fronts. One aspect of his personality that is held most dear is his clarity of thought and his insistence on understanding things a little more deeply and at a more(More)
Iron shows a pressure-induced martensitic phase transformation from the ground state ferromagnetic bcc phase to a nonmagnetic hcp phase at approximately 13 GPa. The exact transformation pressure (TP) and pathway are not known. Here we present a multiscale model containing a quantum-mechanics-based multiwell energy function accounting for the bcc and hcp(More)
Acknowledgments This work would never have been possible without the support of many people, to whom I am sincerely grateful. I have been lucky to have at Caltech not one, but two incredible advisors and mentors, Jerrold E. Marsden and Mathieu Desbrun, who have always been generous with their time, knowledge, and advice. It has been a true honor to learn(More)
The ground state crystal structure of Fe, ferromagnetic body-centered cubic (bcc), undergoes a stress-induced martensitic phase transformation to a hexagonally close-packed (hcp) structure. Both bcc and hcp have been observed to coexist over a large range deformations, such that the nonlinearities in the constitutive behavior of each phase need to be(More)
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