Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Transient stability analysis of composite hydrogel structures based on a
  minimization-type variational formulation   We employ a canonical variational framework for the predictive
characterization of structural instabilities that develop during the
diffusion-driven transient swelling of hydrogels under geometrical constraints.
The variational formulation of finite elasticity coupled with Fickian diffusion
has a two-field minimization structure, wherein the deformation map and the
fluid-volume flux are obtained as minimizers of a time-discrete potential
involving internal and external energetic contributions. Following spatial
discretization, the minimization principle is implemented using a conforming
Q$_1$RT$_0$ finite-element design, making use of the lowest-order
Raviart-Thomas-type interpolations for the fluid-volume flux. To analyze the
structural stability of a certain equilibrium state of the gel satisfying the
minimization principle, we apply the local stability criterion on the
incremental potential, which is based on the idea that a stable equilibrium
state has the lowest potential energy among all possible states within an
infinitesimal neighborhood. Using this criterion, it is understood that
bifurcation-type structural instabilities are activated when the coupled global
finite-element stiffness matrix loses its positive definiteness. This concept
is then applied to determine the onset and nature of wrinkling instabilities
occurring in a pair of representative film-substrate hydrogel systems. In
particular, we analyze the dependencies of the critical buckling load and mode
shape on the system geometry and material parameters.

11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph