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Remove usage of HTML comments in solid_mechanics
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cticenhour committed Dec 19, 2024
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Expand Up @@ -92,52 +92,26 @@ The formulation above for the generalized plane strain problem shares many simil
The out-of-plane strain is a scalar variable, and it can be added to the standard system of equations for a mechanics problem, where $\boldsymbol{u}_x$ and $\boldsymbol{u}_y$ represent
the displacement vectors in the $x$ and $y$ directions, $\boldsymbol{f}_x$ and $\boldsymbol{f}_y$ represent the corresponding reaction forces. The discussion here is for the case where the two-dimensional model lies in the $x$-$y$ plane, The partitioned linearized system of equations, in which the block entries in the stiffness matrix are represented by subscripted $\boldsymbol{K}$ terms, can be written including the scalar strain variable as follows:

<!--This is the intended equation, but \hline was not working when the equation was created-->
<!-- \begin{equation} -->
<!-- \left[ -->
<!-- \begin{array}{cc|c} -->
<!-- \boldsymbol{K}_{xx} & \boldsymbol{K}_{xy} & \boldsymbol{K}_{xz} \\ -->
<!-- \boldsymbol{K}_{yx} & \boldsymbol{K}_{yy} & \boldsymbol{K}_{yz} \\ \hline -->
<!-- \boldsymbol{K}_{zx} & \boldsymbol{K}_{zy} & K_{zz} -->
<!-- \end{array} -->
<!-- \right] -->
<!-- \left\{ -->
<!-- \begin{array}{c} -->
<!-- \boldsymbol{u}_x \\ -->
<!-- \boldsymbol{u}_y \\ \hline -->
<!-- \epsilon_{zz} -->
<!-- \end{array} -->
<!-- \right\} -->
<!-- = -->
<!-- \left\{ -->
<!-- \begin{array}{c} -->
<!-- \boldsymbol{f}_x \\ -->
<!-- \boldsymbol{f}_y \\ \hline -->
<!-- N_{z} -->
<!-- \end{array} -->
<!-- \right\} -->
<!-- \end{equation} -->

\begin{equation}
\left[
\begin{array}{ccc}
\begin{array}{cc|c}
\boldsymbol{K}_{xx} & \boldsymbol{K}_{xy} & \boldsymbol{K}_{xz} \\
\boldsymbol{K}_{yx} & \boldsymbol{K}_{yy} & \boldsymbol{K}_{yz} \\
\boldsymbol{K}_{yx} & \boldsymbol{K}_{yy} & \boldsymbol{K}_{yz} \\ \hline
\boldsymbol{K}_{zx} & \boldsymbol{K}_{zy} & K_{zz}
\end{array}
\right]
\left\{
\begin{array}{c}
\boldsymbol{u}_x \\
\boldsymbol{u}_y \\
\boldsymbol{u}_y \\ \hline
\epsilon_{zz}
\end{array}
\right\}
=
\left\{
\begin{array}{c}
\boldsymbol{f}_x \\
\boldsymbol{f}_y \\
\boldsymbol{f}_y \\ \hline
N_{z}
\end{array}
\right\}
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Expand Up @@ -110,6 +110,6 @@ We provide the substepping capability in `ADRadialReturnStressUpdate` for nonlin

!listing modules/solid_mechanics/test/tests/substepping/power_law_creep.i block=Materials/power_law_creep

<!-- !syntax children /Materials/RadialReturnStressUpdate -->
!! !syntax children /Materials/RadialReturnStressUpdate

!bibtex bibliography
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Expand Up @@ -140,6 +140,6 @@ the MOOSE `Material` class.
More details on how to write the equivalent yield surface equation for a creep
model are given in Dunne and Petrinic.

<!-- !syntax children /Materials/RadialReturnStressUpdate -->
!! !syntax children /Materials/RadialReturnStressUpdate

!bibtex bibliography
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Expand Up @@ -74,10 +74,12 @@ where $P^c$ is the current sampling position point, and $\hat{n}^r$ is the direc

## Hoop Stress in Spherical System

<!-- // Given normal vector N=(n1,n2,n3) and current point C(c1,c2,c3), the tangential plane is then
!!!
// Given normal vector N=(n1,n2,n3) and current point C(c1,c2,c3), the tangential plane is then
// defined as n1(x-c1 + n2(y-c2) + n3(z-c3)=0. Let us assume n1!=0, the arbitrary point P on this
// plane can be taken as P(x,c2+r,c3+r) where r is the radius. The x can be solved as x =
// -r(n2+n3)/n1 + c1. The tangential vector PC is given as P-C. -->
// -r(n2+n3)/n1 + c1. The tangential vector PC is given as P-C.
!!!

`HoopStress` calculates the value of a Rank -2 tensor along the
tangential direction of a sphere, shown in [eq:hoop_stress_scalar_type_spherical]. The spherical system is defined by the center point $C(c_1,c_2,c_3)$. The radial direction $R(r_1,r_2,r_3)$ at current point $P(p_1,p_2,p_3)$ is calculated as $(P-C)$. The tangential plane at the Point $P$ is given as $r_1(x-p_1) + r_2(y-p_2) + r_3(z-p_3)=0$. Any vector that passes through $P$ on this plane is tangential to the spherical surface. To find a point $Q(q_1,q_2,q_3)$ on the tangential plane, we can freely set the values of two coordinates and the solve for last one using the equation of the plane. For example, we set $q_1=p_1+r$ and $q_2=p_2+r$ where $r$ is the norm of the radial direction vector. Then the $q_3$ is calculated as $q_3 = -(r_1+r_2)r/r_3+p_3$. The tangential vector $\hat{t}$ is defined as $Q-P$.
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