@dealiiVideoLecture{19}
-In this tutorial program we will want to solve the
+In this tutorial program we will want to solve the
<a href="https://en.wikipedia.org/wiki/Linear_elasticity">elastic equations</a>.
They are an extension to Laplace's equation with a vector-valued solution that
describes the displacement in each space direction of a rigid body
which is subject to a force. Of course, the force is also
vector-valued, meaning that in each point it has a direction and an
-absolute value.
+absolute value.
One can write the elasticity equations in a number of ways. The one that shows
the symmetry with the Laplace equation in the most obvious way is to write it
where $\mathbf u$ is the vector-valued displacement at each point,
$\mathbf f$ the force, and ${\mathbf C}$ is a rank-4 tensor (i.e., it has four
indices) that encodes the stress-strain relationship -- in essence,
-it represents the
+it represents the
<a href="https://en.wikipedia.org/wiki/Hooke%27s_law">"spring constant"</a> in
Hookes law that relates the displacement to the forces. ${\mathbf C}$ will, in many
cases, depend on $\mathbf x$ if the body whose deformation we want to