Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A stabilized finite element formulation of non-smooth contact   The computational modeling of many engineering problems using the Finite
Element method involves the modeling of two or more bodies that meet through an
interface. The interface can be physical, as in multi-physics and contact
problems, or purely numerical, as in the coupling of non-conforming meshes. The
most critical part of the modeling process is to ensure geometric compatibility
and a complete transfer of surface tractions between the different components
at the connecting interfaces. Popular contact modeling techniques rely on
geometric projections to detect and resolve overlapping or mass
interpenetration between two or more contacting bodies. Such approaches have
been shown to have two major drawbacks: they are not suitable for contact at
highly nonlinear surfaces and sharp corners where smooth normal projections are
not feasible, and they fail to guarantee a complete and accurate transfer of
pressure across the interface. This dissertation presents a novel formulation
for the modeling of contact problems that possesses the ability to resolve
complicated contact scenarios effectively, while being simpler to implement and
more widely applicable than currently available methods. We show that the
formulation boils down to a node-to-surface gap function that works effectively
for non-smooth contact. The numerical implementation using the midpoint rule
shows the need to guarantee the conservation of the total energy during impact,
for which a Lagrange multiplier method is used. We propose a local enrichment
of the interface and a simple stabilization procedure based on the
discontinuous Galerkin method to guarantee an accurate transfer of the pressure
field. The result is a robust interface formulation for contact problems and
the coupling of non-conforming meshes.

11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an