Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The revisited phase-field approach to brittle fracture: Application to
  indentation and notch problems   In a recent contribution, Kumar, Bourdin, Francfort, and Lopez-Pamies (J.
Mech. Phys. Solids 142:104027, 2020) have introduced a comprehensive
macroscopic phase-field theory for the nucleation and propagation of fracture
in linear elastic brittle materials under arbitrary quasistatic loading
conditions. The theory can be viewed as a natural generalization of the
phase-field approximation of the variational theory of brittle fracture of
Francfort and Marigo (J. Mech. Phys. Solids 46:1319--1342, 1998) to account for
the material strength at large. This is accomplished by the addition of an
external driving force -- which physically represents the macroscopic
manifestation of the presence of inherent microscopic defects in the material
-- in the equation governing the evolution of the phase field. The main purpose
of this paper is to continue providing validation results for the theory by
confronting its predictions with direct measurements from three representative
types of experimentally common yet technically challenging problems: $i$) the
indentation of glass plates with flat-ended cylindrical indenters and the
three-point bending of $ii$) U-notched and $iii$) V-notched PMMA beams.

23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
2
The categories of this paper are: math
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex