Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Localization Study of a Regularized Variational Damage Model   The paper presents a detailed analysis and extended formulation of a
rate-independent regularized damage model proposed by Mielke and Roub\'i\v{c}ek
(2006). Localization properties are studied in the context of a simple
one-dimensional problem, but the results reveal the fundamental features of the
basic model and of its modified versions. The initial bifurcation from a
uniform solution is described analytically while the complete failure process
is studied numerically. Modifications of the regularizing term and of the
dissipation distance are introduced and their effect on the global response is
investigated. It is shown that, with a proper combination of model parameters,
a realistic shape of the load-displacement diagram can be achieved and
pathological effects such as extremely brittle response or expansion of the
damage zone accompanied by stress locking can be eliminated.

10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs