Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Primal and mixed finite element formulations for the relaxed
  micromorphic model   The classical Cauchy continuum theory is suitable to model highly homogeneous
materials. However, many materials, such as porous media or metamaterials,
exhibit a pronounced microstructure. As a result, the classical continuum
theory cannot capture their mechanical behaviour without fully resolving the
underlying microstructure. In terms of finite element computations, this can be
done by modelling the entire body, including every interior cell. The relaxed
micromorphic continuum offers an alternative method by instead enriching the
kinematics of the mathematical model. The theory introduces a microdistortion
field, encompassing nine extra degrees of freedom for each material point. The
corresponding elastic energy functional contains the gradient of the
displacement field, the microdistortion field and its Curl (the
micro-dislocation). Therefore, the natural spaces of the fields are
$[\mathit{H}^1]^3$ for the displacement and $[\mathit{H}(\mathrm{curl})]^3$ for
the microdistortion, leading to unusual finite element formulations. In this
work we describe the construction of appropriate finite elements using
N\'ed\'elec and Raviart-Thomas subspaces, encompassing solutions to the
orientation problem and the discrete consistent coupling condition. Further, we
explore the numerical behaviour of the relaxed micromorphic model for both a
primal and a mixed formulation. The focus of our benchmarks lies in the
influence of the characteristic length $L_\mathrm{c}$ and the correlation to
the classical Cauchy continuum theory.

6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat