diff --git a/modules/solid_mechanics/doc/content/modules/solid_mechanics/generalized_plane_strain.md b/modules/solid_mechanics/doc/content/modules/solid_mechanics/generalized_plane_strain.md index 15679ed8e84a..c190fb04ea5b 100644 --- a/modules/solid_mechanics/doc/content/modules/solid_mechanics/generalized_plane_strain.md +++ b/modules/solid_mechanics/doc/content/modules/solid_mechanics/generalized_plane_strain.md @@ -92,44 +92,18 @@ 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: - - - - - - - - - - - - - - - - - - - - - - - - - - \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\} @@ -137,7 +111,7 @@ the displacement vectors in the $x$ and $y$ directions, $\boldsymbol{f}_x$ and $ \left\{ \begin{array}{c} \boldsymbol{f}_x \\ -\boldsymbol{f}_y \\ +\boldsymbol{f}_y \\ \hline N_{z} \end{array} \right\} diff --git a/modules/solid_mechanics/doc/content/source/materials/ADRadialReturnStressUpdate.md b/modules/solid_mechanics/doc/content/source/materials/ADRadialReturnStressUpdate.md index 46986c70897c..7caf101f626b 100644 --- a/modules/solid_mechanics/doc/content/source/materials/ADRadialReturnStressUpdate.md +++ b/modules/solid_mechanics/doc/content/source/materials/ADRadialReturnStressUpdate.md @@ -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 !bibtex bibliography diff --git a/modules/solid_mechanics/doc/content/source/materials/RadialReturnStressUpdate.md b/modules/solid_mechanics/doc/content/source/materials/RadialReturnStressUpdate.md index 9043694bc431..8ffe8c605329 100644 --- a/modules/solid_mechanics/doc/content/source/materials/RadialReturnStressUpdate.md +++ b/modules/solid_mechanics/doc/content/source/materials/RadialReturnStressUpdate.md @@ -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 !bibtex bibliography diff --git a/modules/solid_mechanics/doc/content/source/utils/RankTwoScalarTools.md b/modules/solid_mechanics/doc/content/source/utils/RankTwoScalarTools.md index 6b6094e90a4c..852c9660e408 100644 --- a/modules/solid_mechanics/doc/content/source/utils/RankTwoScalarTools.md +++ b/modules/solid_mechanics/doc/content/source/utils/RankTwoScalarTools.md @@ -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 - +// -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 $Q-P$.