We describe a new class of
asynchronous variational integrators (AVI)
for nonlinear 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 form of a discrete
version of Hamilton's variational principle. As a consequence of this variational
structure, the algorithms conserve local momenta and a local discrete
multisymplectic structure exactly. To guide the development of the discretizations,
a spacetime multisymplectic formulation of elastodynamics is presented.
The variational principle used incorporates both configuration and spacetime
reference variations. This allows a unified treatment of all the conservation
properties of the system. A discrete version of reference configuration is also
considered, providing a natural definition of a discrete energy. The possibilities
for discrete energy conservation are evaluated.
Numerical tests reveal that, even when local energy balance is not enforced
exactly, the global and local energy behavior of the AVIs is quite remarkable, a
property which can probably be traced to the symplectic nature of the algorithm.