the continuum based approaches don’t provide the correct physics in atomic scales. on the other hand, the molecular based approaches are limited by the length and simulated process time. as an attractive alternative, this paper proposes the fixed interfacial multiscale method (fimm) for computationally and mathematically efficient modeling of solid structures. the approach is applicable to mult...

At the beginning of 1941, Ludwig Föppl published an 8-page paper “Elastische Beanspruchung des Erdbodens unter Fundamenten”. The main result this was further developed by his doctoral student Gerhard Schubert in 1942. These publications and contain many results obtained researchers contact mechanics subsequent decades 20th century. Unfortunately, both papers have been forgotten, which is not pa...

In this paper, we continue the construction of variational integrators adapted to contact geometry started in \cite{VBS}, particular, introduce a discrete Herglotz Principle and corresponding Equations for Lagrangian setting. This allows us develop convenient numerical systems that are conformally by construction. The existence an exact function is also discussed.