An unstructured immersed finite element method for nonlinear solid mechanics.

We present an immersed finite element technique for boundary-value and interface problems from nonlinear solid mechanics. Its key features are the implicit representation of domain boundaries and interfaces, the use of Nitsche's method for the incorporation of boundary conditions, accurate numerical integration based on marching tetrahedrons and cut-element stabilisation by means of extrapolation. For discretisation structured and unstructured background meshes with Lagrange basis functions are considered. We show numerically and analytically that the introduced cut-element stabilisation technique provides an effective bound on the size of the Nitsche parameters and, in turn, leads to well-conditioned system matrices. In addition, we introduce a novel approach for representing and analysing geometries with sharp features (edges and corners) using an implicit geometry representation. This allows the computation of typical engineering parts composed of solid primitives without the need of boundary-fitted meshes.

Oscillatory thermomechanical instability of an ultrathin catalyst.

Because of the small thermal capacity of ultrathin ( approximately 200 nanometers) metal single crystals, it is possible to explore the coupling of catalytic and thermal action at low pressures. We analyzed a chemothermomechanical instability in this regime, in which catalytic reaction kinetics interact with heat transfer and mechanical buckling to create oscillations. These interacting components are separated and explored through experimentation, mathematical modeling, and scientific computation, and an explanation of the phenomenon emerges from their synthesis.