Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Analysis of staggered evolutions for nonlinear energies in phase field
  fracture   We consider a class of separately convex phase field energies employed in
fracture mechanics, featuring non-interpenetration and a general softening
behavior. We analyze the time-discrete evolutions generated by a staggered
minimization scheme, where fracture irreversibility is modeled by a
monotonicity constraint on the phase field variable. After recasting the
staggered scheme by means of gradient flows, we characterize the
time-continuous limits of the discrete solutions in terms of balanced viscosity
evolutions, parametrized by their arc-length with respect to the L2-norm (for
the phase field) and the H1-norm (for the displacement field). By a careful
study of the energy balance we deduce that time-continuous evolutions may still
exhibit an alternate behavior in discontinuity times.

30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
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The categories of this paper are: supr-con
18
The categories of this paper are: econ
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess