Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fast and slow dynamics in a nonlinear elastic bar excited by
  longitudinal vibrations   Heterogeneous materials, such as rocks and concrete, have a complex dynamics
including hysteresis, nonlinear elasticity and viscoelasticity. It is very
sensitive to microstructural changes and damage. The goal of this paper is to
propose a physical model describing the longitudinal vibrations of this class
of material, and to develop a numerical strategy for solving the evolution
equations. The theory relies on the coupling between two processes with
radically-different time scales: a fast process at the frequency of the
excitation, governed by nonlinear elasticity and viscoelasticity; a slow
process, governed by the evolution of defects. The evolution equations are
written as a nonlinear hyperbolic system with relaxation. A time-domain
numerical scheme is developed, based on a splitting strategy. The numerical
simulations show qualitative agreement with the features observed
experimentally by Dynamic Acousto-Elastic Testing.

14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn