### 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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