Commit c24c4d65 authored by Paolo Tricerri's avatar Paolo Tricerri
Browse files

changed two things as Tiziano suggested

parent 230f73e1
......@@ -52,7 +52,7 @@ defined as:
\end{equation}
where the symbol $\delOp$ indicates that the
derivatives are computed with respect to the coordinates in the
reference configuration. In addition, the tensor \F allows defining
reference configuration. In addition, the tensor \F{} allows defining
other classical tensorial quantities, like the right Cauchy-Green and
Green-Lagrange tensors, to quantify the stretches and strains during
the deformation.\\
......@@ -71,7 +71,8 @@ surface of the body,
\end{equation}
where $\rho$ is the density of the material in the
current configuration (and it is related to its counterpart in \RefCon
thanks to $\rho=J\rho_0$) and $\velE$ is the Eulerian velocity. The
thanks to $\rho=J\rho_0$, where $J$ is the determinant of the deformation
gradient \F) and $\velE$ is the Eulerian velocity. The
vector $\underline{b}$ is the body force per unit of mass,
$\underline{t}=\underline{t}(\nposE,t, \underline{n})$ is the surface
force acting on the body in the current configuration per unit area of
......@@ -114,14 +115,12 @@ is:
\begin{equation}
\rho_0\frac{\partial^2\displL}{\partial
t^2}=\rho_0\underline{b}+\text{Div}(\Piola) \qquad \forall \posE
\subseteq \RefConE, \quad t>0.
\subseteq \RefConE, \quad t>0,
\label{eq::ConLinMom-Diff}
\end{equation}
When initial and boundary conditions are added to
Eq. \eqref{eq::ConLinMom-Diff} the mathematical problem associated to
\eqref{eq::ConLinMom-Diff} of structural mechanics is
defined. Subsequentely, this problem is characterized by specifying a
particular constitutive law for the Cauchy stress tensor.
which is then augmented with proper initial and boundary conditions.
Subsequentely, the mechanical behaviour of the material is characterized
by specifying a particular constitutive law for the Cauchy stress tensor.
\subsection{Constitutive laws}
\label{sct-Constitutive} Equation \eqref{eq::ConLinMom-Diff} must be
......@@ -193,7 +192,8 @@ simulations:
\begin{itemize}
\item by using high Poisson ratios for the first two
models\footnote{The choice of high Poisson ratios may be critical in
terms of a well-known problem: locking.}
terms of a well-known problem: locking [T. Hughes, \textit{The finite element method:
Linear Static and Dynamic Finite Element Analysis} - Englewood Cliffs - NJ : Prentice-Hall, 1987 ]}
\item by recovering the common multiplicative decomposition of the
deformation gradient \F into an isochoric and volumetric part for the
second two (see \cite{BonetWood}).
......
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