A Total BETI (TBETI) based domain decomposition algorithm with the preconditioning by a natural coarse grid of the rigid body motions is adapted for the solution of multibody frictionless contact problems of linear elastostatics and proved to be scalable, i.e., the cost of the solution is asymptotically proportional to the number of variables. The analysis admits floating bodies. The proofs com...

We introduce a variational principle for field theories, referred to as the HamiltonPontryagin principle, and we show that the resulting field equations are the Euler-Lagrange equations in implicit form. Secondly, we introduce multi-Dirac structures as a graded analog of standard Dirac structures, and we show that the graph of a multisymplectic form determines a multi-Dirac structure. We then d...

In this paper, we first recall the general assumptions and results arising in mortar methods applied to elastostatics [Woh01]. By extension to the curved interfaces case of the ideas from Gopalakrishnan and Brenner [Gop99, Bre03, Bre04], and from the introduction a generalized Scott and Zhang interpolation operator [SZ90], we prove the independence of the coercivity constant of the broken elast...

An action functional is developed for nonlinear dislocation dynamics. This serves as a first step towards the application of effective field theory in physics to evaluate its potential obtaining macroscopic description dynamics describing plasticity crystalline solids. Connections arise between continuum mechanics and material science defects solids, techniques physics, fracton tensor gauge the...