Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A new restriction for initially stressed elastic solids   We introduce a fundamental restriction on the strain energy function and
stress tensor for initially stressed elastic solids. The restriction applies to
strain energy functions $W$ that are explicit functions of the elastic
deformation gradient $\mathbf{F}$ and initial stress $\boldsymbol \tau$, i.e.
$W:= W(\mathbf F, \boldsymbol \tau)$. The restriction is a consequence of
energy conservation and ensures that the predicted stress and strain energy do
not depend upon an arbitrary choice of reference configuration. We call this
restriction: initial stress reference independence (ISRI). It transpires that
almost all strain energy functions found in the literature do not satisfy ISRI,
and may therefore lead to unphysical behaviour, which we illustrate via a
simple example. To remedy this shortcoming we derive three strain energy
functions that do satisfy the restriction. We also show that using initial
strain (often from a virtual configuration) to model initial stress leads to
strain energy functions that automatically satisfy ISRI. Finally, we reach the
following important result: ISRI reduces the number of unknowns of the linear
stress tensor of initially stressed solids. This new way of reducing the linear
stress may open new pathways for the non-destructive determination of initial
stresses via ultrasonic experiments, among others.

15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th