Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Evaluation of mechanical and energy properties for the phase field
  modeling of failure   In recent years, various phase field models have been developed in
variational methods to simulate the failure of brittle solids. However, there
is a lack of objective evaluation of the existing results, and in particular,
there are few studies on model nonhomogeneous resolution, stress-strain linear
elastic properties, and failure stress estimation. To compensate for the above
gaps, the commonly used variational phase field model is systematically
analyzed to solve the problem of evaluating the mechanics and energy properties
of the model in this paper. The unified expression of the analytical solution
and the nonhomogeneous solution under specific boundary conditions is analyzed
and verified. Additionally, we theoretically analyze the energy properties of
the phase field model and study the influence of the critical strain energy on
the damage field, stress and strain of different models. Finally, the effect of
different effective material parameters on the material failure stress is
analyzed, the stress estimation formula for the failure of mode I of various
phase field models is given, and the accuracy of the theory is verified by some
examples.

31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int