  Soft materials, such as liquids, polymers, foams, gels, colloids, granular
materials, and most soft biological materials, play an important role in our
daily lives. From a mechanical viewpoint, soft materials can easily achieve
large deformations due to their low elastic moduli; meanwhile, surface
instabilities, including wrinkles, creases, folds, and ridges, among others,
are often observed. In particular, soft dielectrics subject to electrical
stimuli can achieve significantly large deformations that are often accompanied
by instabilities. While instabilities are often thought to cause failures in
the engineering context and carry a negative connotation, they can also be
harnessed for various applications such as surface patterning, giant actuation
strain, and energy harvesting. In the biological world, instability and
bifurcation phenomena often precede important events such as endocytosis, cell
fusion, among others. Stability and bifurcation analysis (especially for soft
materials) is challenging and often presents a formidable barrier to entry in
this important field. A multidisciplinary audience may lack the background in
one or more areas that are needed to carry out the requisite modeling or even
understand papers in the literature. Furthermore, combining electrostatics
together with large deformations brings its own challenges. In this article, we
provide a tutorial on the basics of stability and bifurcation analysis in the
context of soft electromechanical materials. The aim of the article is to use
simple examples and ``gently" lead a reader, unfamiliar with either stability
analysis or electrostatics of deformable media, to develop the ability to
understand the pertinent literature that already exists and position them to
embark on state-of-the-art research on this topic.

Soft Condensed Matter