Cavity Pressure Action

Description

The CavityPressure Action system is used to calculate the pressure from an ideal gas trapped within an internal volume.

The pressure in the cavity is computed based on the ideal gas law, $(1)var element = document.getElementById("moose-equation-a2da2e1c-9777-4f94-88e1-0042e6b80f07");katex.render(" P=\\frac{nRT}{V}", element, {displayMode:true,throwOnError:false,macros:{"\\bs":"\\boldsymbol{#1}","\\normal":"\\bs{n}","\\grad":"\\bs{\\nabla}","\\divergence":"\\grad \\cdot","\\norm":"\\left\\lVert#1\\right\\rVert","\\abs":"\\left\\lvert#1\\right\\rvert","\\tr":"\\text{tr}","\\dev":"\\text{dev}","\\sym":"\\text{sym}","\\diff":"\\text{ d}#1","\\activepart":"{\\left< A \\right>}","\\inactivepart":"{\\left}","\\Gc":"{\\mathcal{G}_c}","\\strain":"\\bs{\\varepsilon}","\\stress":"\\bs{\\sigma}","\\macaulay":"\\left<#1\\right>","\\body":"\\Omega","\\bodyboundary":"{\\partial\\body}","\\ep":"{\\varepsilon^p}","\\ep0":"{\\varepsilon_0^p}","\\epdot":"{\\dot{\\varepsilon}}^p","\\epdot0":"{\\dot{\\varepsilon}}_0^p","\\bfa":"\\boldsymbol{a}","\\bfb":"\\boldsymbol{b}","\\bfc":"\\boldsymbol{c}","\\bfd":"\\boldsymbol{d}","\\bfe":"\\boldsymbol{e}","\\bff":"\\boldsymbol{f}","\\bfg":"\\boldsymbol{g}","\\bfh":"\\boldsymbol{h}","\\bfi":"\\boldsymbol{i}","\\bfj":"\\boldsymbol{j}","\\bfk":"\\boldsymbol{k}","\\bfl":"\\boldsymbol{l}","\\bfm":"\\boldsymbol{m}","\\bfn":"\\boldsymbol{n}","\\bfo":"\\boldsymbol{o}","\\bfp":"\\boldsymbol{p}","\\bfq":"\\boldsymbol{q}","\\bfr":"\\boldsymbol{r}","\\bfs":"\\boldsymbol{s}","\\bft":"\\boldsymbol{t}","\\bfu":"\\boldsymbol{u}","\\bfv":"\\boldsymbol{v}","\\bfw":"\\boldsymbol{w}","\\bfx":"\\boldsymbol{x}","\\bfy":"\\boldsymbol{y}","\\bfz":"\\boldsymbol{z}","\\bfA":"\\boldsymbol{A}","\\bfB":"\\boldsymbol{B}","\\bfC":"\\boldsymbol{C}","\\bfD":"\\boldsymbol{D}","\\bfE":"\\boldsymbol{E}","\\bfF":"\\boldsymbol{F}","\\bfG":"\\boldsymbol{G}","\\bfH":"\\boldsymbol{H}","\\bfI":"\\boldsymbol{I}","\\bfJ":"\\boldsymbol{J}","\\bfK":"\\boldsymbol{K}","\\bfL":"\\boldsymbol{L}","\\bfM":"\\boldsymbol{M}","\\bfN":"\\boldsymbol{N}","\\bfO":"\\boldsymbol{O}","\\bfP":"\\boldsymbol{P}","\\bfQ":"\\boldsymbol{Q}","\\bfR":"\\boldsymbol{R}","\\bfS":"\\boldsymbol{S}","\\bfT":"\\boldsymbol{T}","\\bfU":"\\boldsymbol{U}","\\bfV":"\\boldsymbol{V}","\\bfW":"\\boldsymbol{W}","\\bfX":"\\boldsymbol{X}","\\bfY":"\\boldsymbol{Y}","\\bfZ":"\\boldsymbol{Z}"}});$ where $var element = document.getElementById("moose-equation-fd26f7a4-8caf-4b87-bccd-de349dcd8dff");katex.render("P", element, {displayMode:false,throwOnError:false,macros:{"\\bs":"\\boldsymbol{#1}","\\normal":"\\bs{n}","\\grad":"\\bs{\\nabla}","\\divergence":"\\grad \\cdot","\\norm":"\\left\\lVert#1\\right\\rVert","\\abs":"\\left\\lvert#1\\right\\rvert","\\tr":"\\text{tr}","\\dev":"\\text{dev}","\\sym":"\\text{sym}","\\diff":"\\text{ d}#1","\\activepart":"{\\left< A \\right>}","\\inactivepart":"{\\left}","\\Gc":"{\\mathcal{G}_c}","\\strain":"\\bs{\\varepsilon}","\\stress":"\\bs{\\sigma}","\\macaulay":"\\left<#1\\right>","\\body":"\\Omega","\\bodyboundary":"{\\partial\\body}","\\ep":"{\\varepsilon^p}","\\ep0":"{\\varepsilon_0^p}","\\epdot":"{\\dot{\\varepsilon}}^p","\\epdot0":"{\\dot{\\varepsilon}}_0^p","\\bfa":"\\boldsymbol{a}","\\bfb":"\\boldsymbol{b}","\\bfc":"\\boldsymbol{c}","\\bfd":"\\boldsymbol{d}","\\bfe":"\\boldsymbol{e}","\\bff":"\\boldsymbol{f}","\\bfg":"\\boldsymbol{g}","\\bfh":"\\boldsymbol{h}","\\bfi":"\\boldsymbol{i}","\\bfj":"\\boldsymbol{j}","\\bfk":"\\boldsymbol{k}","\\bfl":"\\boldsymbol{l}","\\bfm":"\\boldsymbol{m}","\\bfn":"\\boldsymbol{n}","\\bfo":"\\boldsymbol{o}","\\bfp":"\\boldsymbol{p}","\\bfq":"\\boldsymbol{q}","\\bfr":"\\boldsymbol{r}","\\bfs":"\\boldsymbol{s}","\\bft":"\\boldsymbol{t}","\\bfu":"\\boldsymbol{u}","\\bfv":"\\boldsymbol{v}","\\bfw":"\\boldsymbol{w}","\\bfx":"\\boldsymbol{x}","\\bfy":"\\boldsymbol{y}","\\bfz":"\\boldsymbol{z}","\\bfA":"\\boldsymbol{A}","\\bfB":"\\boldsymbol{B}","\\bfC":"\\boldsymbol{C}","\\bfD":"\\boldsymbol{D}","\\bfE":"\\boldsymbol{E}","\\bfF":"\\boldsymbol{F}","\\bfG":"\\boldsymbol{G}","\\bfH":"\\boldsymbol{H}","\\bfI":"\\boldsymbol{I}","\\bfJ":"\\boldsymbol{J}","\\bfK":"\\boldsymbol{K}","\\bfL":"\\boldsymbol{L}","\\bfM":"\\boldsymbol{M}","\\bfN":"\\boldsymbol{N}","\\bfO":"\\boldsymbol{O}","\\bfP":"\\boldsymbol{P}","\\bfQ":"\\boldsymbol{Q}","\\bfR":"\\boldsymbol{R}","\\bfS":"\\boldsymbol{S}","\\bfT":"\\boldsymbol{T}","\\bfU":"\\boldsymbol{U}","\\bfV":"\\boldsymbol{V}","\\bfW":"\\boldsymbol{W}","\\bfX":"\\boldsymbol{X}","\\bfY":"\\boldsymbol{Y}","\\bfZ":"\\boldsymbol{Z}"}});$ is the internal pressure, $var element = document.getElementById("moose-equation-e32d433a-66d7-4255-9aea-46e4437499ab");katex.render("n", element, {displayMode:false,throwOnError:false,macros:{"\\bs":"\\boldsymbol{#1}","\\normal":"\\bs{n}","\\grad":"\\bs{\\nabla}","\\divergence":"\\grad \\cdot","\\norm":"\\left\\lVert#1\\right\\rVert","\\abs":"\\left\\lvert#1\\right\\rvert","\\tr":"\\text{tr}","\\dev":"\\text{dev}","\\sym":"\\text{sym}","\\diff":"\\text{ d}#1","\\activepart":"{\\left< A \\right>}","\\inactivepart":"{\\left}","\\Gc":"{\\mathcal{G}_c}","\\strain":"\\bs{\\varepsilon}","\\stress":"\\bs{\\sigma}","\\macaulay":"\\left<#1\\right>","\\body":"\\Omega","\\bodyboundary":"{\\partial\\body}","\\ep":"{\\varepsilon^p}","\\ep0":"{\\varepsilon_0^p}","\\epdot":"{\\dot{\\varepsilon}}^p","\\epdot0":"{\\dot{\\varepsilon}}_0^p","\\bfa":"\\boldsymbol{a}","\\bfb":"\\boldsymbol{b}","\\bfc":"\\boldsymbol{c}","\\bfd":"\\boldsymbol{d}","\\bfe":"\\boldsymbol{e}","\\bff":"\\boldsymbol{f}","\\bfg":"\\boldsymbol{g}","\\bfh":"\\boldsymbol{h}","\\bfi":"\\boldsymbol{i}","\\bfj":"\\boldsymbol{j}","\\bfk":"\\boldsymbol{k}","\\bfl":"\\boldsymbol{l}","\\bfm":"\\boldsymbol{m}","\\bfn":"\\boldsymbol{n}","\\bfo":"\\boldsymbol{o}","\\bfp":"\\boldsymbol{p}","\\bfq":"\\boldsymbol{q}","\\bfr":"\\boldsymbol{r}","\\bfs":"\\boldsymbol{s}","\\bft":"\\boldsymbol{t}","\\bfu":"\\boldsymbol{u}","\\bfv":"\\boldsymbol{v}","\\bfw":"\\boldsymbol{w}","\\bfx":"\\boldsymbol{x}","\\bfy":"\\boldsymbol{y}","\\bfz":"\\boldsymbol{z}","\\bfA":"\\boldsymbol{A}","\\bfB":"\\boldsymbol{B}","\\bfC":"\\boldsymbol{C}","\\bfD":"\\boldsymbol{D}","\\bfE":"\\boldsymbol{E}","\\bfF":"\\boldsymbol{F}","\\bfG":"\\boldsymbol{G}","\\bfH":"\\boldsymbol{H}","\\bfI":"\\boldsymbol{I}","\\bfJ":"\\boldsymbol{J}","\\bfK":"\\boldsymbol{K}","\\bfL":"\\boldsymbol{L}","\\bfM":"\\boldsymbol{M}","\\bfN":"\\boldsymbol{N}","\\bfO":"\\boldsymbol{O}","\\bfP":"\\boldsymbol{P}","\\bfQ":"\\boldsymbol{Q}","\\bfR":"\\boldsymbol{R}","\\bfS":"\\boldsymbol{S}","\\bfT":"\\boldsymbol{T}","\\bfU":"\\boldsymbol{U}","\\bfV":"\\boldsymbol{V}","\\bfW":"\\boldsymbol{W}","\\bfX":"\\boldsymbol{X}","\\bfY":"\\boldsymbol{Y}","\\bfZ":"\\boldsymbol{Z}"}});$ is the moles of gas, $var element = document.getElementById("moose-equation-52f98c03-2835-4209-a7db-a3d2ea137ca5");katex.render("R", element, {displayMode:false,throwOnError:false,macros:{"\\bs":"\\boldsymbol{#1}","\\normal":"\\bs{n}","\\grad":"\\bs{\\nabla}","\\divergence":"\\grad \\cdot","\\norm":"\\left\\lVert#1\\right\\rVert","\\abs":"\\left\\lvert#1\\right\\rvert","\\tr":"\\text{tr}","\\dev":"\\text{dev}","\\sym":"\\text{sym}","\\diff":"\\text{ d}#1","\\activepart":"{\\left< A \\right>}","\\inactivepart":"{\\left}","\\Gc":"{\\mathcal{G}_c}","\\strain":"\\bs{\\varepsilon}","\\stress":"\\bs{\\sigma}","\\macaulay":"\\left<#1\\right>","\\body":"\\Omega","\\bodyboundary":"{\\partial\\body}","\\ep":"{\\varepsilon^p}","\\ep0":"{\\varepsilon_0^p}","\\epdot":"{\\dot{\\varepsilon}}^p","\\epdot0":"{\\dot{\\varepsilon}}_0^p","\\bfa":"\\boldsymbol{a}","\\bfb":"\\boldsymbol{b}","\\bfc":"\\boldsymbol{c}","\\bfd":"\\boldsymbol{d}","\\bfe":"\\boldsymbol{e}","\\bff":"\\boldsymbol{f}","\\bfg":"\\boldsymbol{g}","\\bfh":"\\boldsymbol{h}","\\bfi":"\\boldsymbol{i}","\\bfj":"\\boldsymbol{j}","\\bfk":"\\boldsymbol{k}","\\bfl":"\\boldsymbol{l}","\\bfm":"\\boldsymbol{m}","\\bfn":"\\boldsymbol{n}","\\bfo":"\\boldsymbol{o}","\\bfp":"\\boldsymbol{p}","\\bfq":"\\boldsymbol{q}","\\bfr":"\\boldsymbol{r}","\\bfs":"\\boldsymbol{s}","\\bft":"\\boldsymbol{t}","\\bfu":"\\boldsymbol{u}","\\bfv":"\\boldsymbol{v}","\\bfw":"\\boldsymbol{w}","\\bfx":"\\boldsymbol{x}","\\bfy":"\\boldsymbol{y}","\\bfz":"\\boldsymbol{z}","\\bfA":"\\boldsymbol{A}","\\bfB":"\\boldsymbol{B}","\\bfC":"\\boldsymbol{C}","\\bfD":"\\boldsymbol{D}","\\bfE":"\\boldsymbol{E}","\\bfF":"\\boldsymbol{F}","\\bfG":"\\boldsymbol{G}","\\bfH":"\\boldsymbol{H}","\\bfI":"\\boldsymbol{I}","\\bfJ":"\\boldsymbol{J}","\\bfK":"\\boldsymbol{K}","\\bfL":"\\boldsymbol{L}","\\bfM":"\\boldsymbol{M}","\\bfN":"\\boldsymbol{N}","\\bfO":"\\boldsymbol{O}","\\bfP":"\\boldsymbol{P}","\\bfQ":"\\boldsymbol{Q}","\\bfR":"\\boldsymbol{R}","\\bfS":"\\boldsymbol{S}","\\bfT":"\\boldsymbol{T}","\\bfU":"\\boldsymbol{U}","\\bfV":"\\boldsymbol{V}","\\bfW":"\\boldsymbol{W}","\\bfX":"\\boldsymbol{X}","\\bfY":"\\boldsymbol{Y}","\\bfZ":"\\boldsymbol{Z}"}});$ is the ideal gas constant, $var element = document.getElementById("moose-equation-69624377-74eb-4b15-8344-8146c9cd09d8");katex.render("T", element, {displayMode:false,throwOnError:false,macros:{"\\bs":"\\boldsymbol{#1}","\\normal":"\\bs{n}","\\grad":"\\bs{\\nabla}","\\divergence":"\\grad \\cdot","\\norm":"\\left\\lVert#1\\right\\rVert","\\abs":"\\left\\lvert#1\\right\\rvert","\\tr":"\\text{tr}","\\dev":"\\text{dev}","\\sym":"\\text{sym}","\\diff":"\\text{ d}#1","\\activepart":"{\\left< A \\right>}","\\inactivepart":"{\\left}","\\Gc":"{\\mathcal{G}_c}","\\strain":"\\bs{\\varepsilon}","\\stress":"\\bs{\\sigma}","\\macaulay":"\\left<#1\\right>","\\body":"\\Omega","\\bodyboundary":"{\\partial\\body}","\\ep":"{\\varepsilon^p}","\\ep0":"{\\varepsilon_0^p}","\\epdot":"{\\dot{\\varepsilon}}^p","\\epdot0":"{\\dot{\\varepsilon}}_0^p","\\bfa":"\\boldsymbol{a}","\\bfb":"\\boldsymbol{b}","\\bfc":"\\boldsymbol{c}","\\bfd":"\\boldsymbol{d}","\\bfe":"\\boldsymbol{e}","\\bff":"\\boldsymbol{f}","\\bfg":"\\boldsymbol{g}","\\bfh":"\\boldsymbol{h}","\\bfi":"\\boldsymbol{i}","\\bfj":"\\boldsymbol{j}","\\bfk":"\\boldsymbol{k}","\\bfl":"\\boldsymbol{l}","\\bfm":"\\boldsymbol{m}","\\bfn":"\\boldsymbol{n}","\\bfo":"\\boldsymbol{o}","\\bfp":"\\boldsymbol{p}","\\bfq":"\\boldsymbol{q}","\\bfr":"\\boldsymbol{r}","\\bfs":"\\boldsymbol{s}","\\bft":"\\boldsymbol{t}","\\bfu":"\\boldsymbol{u}","\\bfv":"\\boldsymbol{v}","\\bfw":"\\boldsymbol{w}","\\bfx":"\\boldsymbol{x}","\\bfy":"\\boldsymbol{y}","\\bfz":"\\boldsymbol{z}","\\bfA":"\\boldsymbol{A}","\\bfB":"\\boldsymbol{B}","\\bfC":"\\boldsymbol{C}","\\bfD":"\\boldsymbol{D}","\\bfE":"\\boldsymbol{E}","\\bfF":"\\boldsymbol{F}","\\bfG":"\\boldsymbol{G}","\\bfH":"\\boldsymbol{H}","\\bfI":"\\boldsymbol{I}","\\bfJ":"\\boldsymbol{J}","\\bfK":"\\boldsymbol{K}","\\bfL":"\\boldsymbol{L}","\\bfM":"\\boldsymbol{M}","\\bfN":"\\boldsymbol{N}","\\bfO":"\\boldsymbol{O}","\\bfP":"\\boldsymbol{P}","\\bfQ":"\\boldsymbol{Q}","\\bfR":"\\boldsymbol{R}","\\bfS":"\\boldsymbol{S}","\\bfT":"\\boldsymbol{T}","\\bfU":"\\boldsymbol{U}","\\bfV":"\\boldsymbol{V}","\\bfW":"\\boldsymbol{W}","\\bfX":"\\boldsymbol{X}","\\bfY":"\\boldsymbol{Y}","\\bfZ":"\\boldsymbol{Z}"}});$ is the temperature, and $var element = document.getElementById("moose-equation-77a2404c-9df3-4475-8482-4f09cea70adf");katex.render("V", element, {displayMode:false,throwOnError:false,macros:{"\\bs":"\\boldsymbol{#1}","\\normal":"\\bs{n}","\\grad":"\\bs{\\nabla}","\\divergence":"\\grad \\cdot","\\norm":"\\left\\lVert#1\\right\\rVert","\\abs":"\\left\\lvert#1\\right\\rvert","\\tr":"\\text{tr}","\\dev":"\\text{dev}","\\sym":"\\text{sym}","\\diff":"\\text{ d}#1","\\activepart":"{\\left< A \\right>}","\\inactivepart":"{\\left}","\\Gc":"{\\mathcal{G}_c}","\\strain":"\\bs{\\varepsilon}","\\stress":"\\bs{\\sigma}","\\macaulay":"\\left<#1\\right>","\\body":"\\Omega","\\bodyboundary":"{\\partial\\body}","\\ep":"{\\varepsilon^p}","\\ep0":"{\\varepsilon_0^p}","\\epdot":"{\\dot{\\varepsilon}}^p","\\epdot0":"{\\dot{\\varepsilon}}_0^p","\\bfa":"\\boldsymbol{a}","\\bfb":"\\boldsymbol{b}","\\bfc":"\\boldsymbol{c}","\\bfd":"\\boldsymbol{d}","\\bfe":"\\boldsymbol{e}","\\bff":"\\boldsymbol{f}","\\bfg":"\\boldsymbol{g}","\\bfh":"\\boldsymbol{h}","\\bfi":"\\boldsymbol{i}","\\bfj":"\\boldsymbol{j}","\\bfk":"\\boldsymbol{k}","\\bfl":"\\boldsymbol{l}","\\bfm":"\\boldsymbol{m}","\\bfn":"\\boldsymbol{n}","\\bfo":"\\boldsymbol{o}","\\bfp":"\\boldsymbol{p}","\\bfq":"\\boldsymbol{q}","\\bfr":"\\boldsymbol{r}","\\bfs":"\\boldsymbol{s}","\\bft":"\\boldsymbol{t}","\\bfu":"\\boldsymbol{u}","\\bfv":"\\boldsymbol{v}","\\bfw":"\\boldsymbol{w}","\\bfx":"\\boldsymbol{x}","\\bfy":"\\boldsymbol{y}","\\bfz":"\\boldsymbol{z}","\\bfA":"\\boldsymbol{A}","\\bfB":"\\boldsymbol{B}","\\bfC":"\\boldsymbol{C}","\\bfD":"\\boldsymbol{D}","\\bfE":"\\boldsymbol{E}","\\bfF":"\\boldsymbol{F}","\\bfG":"\\boldsymbol{G}","\\bfH":"\\boldsymbol{H}","\\bfI":"\\boldsymbol{I}","\\bfJ":"\\boldsymbol{J}","\\bfK":"\\boldsymbol{K}","\\bfL":"\\boldsymbol{L}","\\bfM":"\\boldsymbol{M}","\\bfN":"\\boldsymbol{N}","\\bfO":"\\boldsymbol{O}","\\bfP":"\\boldsymbol{P}","\\bfQ":"\\boldsymbol{Q}","\\bfR":"\\boldsymbol{R}","\\bfS":"\\boldsymbol{S}","\\bfT":"\\boldsymbol{T}","\\bfU":"\\boldsymbol{U}","\\bfV":"\\boldsymbol{V}","\\bfW":"\\boldsymbol{W}","\\bfX":"\\boldsymbol{X}","\\bfY":"\\boldsymbol{Y}","\\bfZ":"\\boldsymbol{Z}"}});$ is the volume of the cavity.

The moles of gas, the temperature, and the cavity volume in Eq. (1) are free to change with time. The moles of gas $var element = document.getElementById("moose-equation-8378cd5b-d9ed-4d48-9154-6c1c14bdbc82");katex.render("n", element, {displayMode:false,throwOnError:false,macros:{"\\bs":"\\boldsymbol{#1}","\\normal":"\\bs{n}","\\grad":"\\bs{\\nabla}","\\divergence":"\\grad \\cdot","\\norm":"\\left\\lVert#1\\right\\rVert","\\abs":"\\left\\lvert#1\\right\\rvert","\\tr":"\\text{tr}","\\dev":"\\text{dev}","\\sym":"\\text{sym}","\\diff":"\\text{ d}#1","\\activepart":"{\\left< A \\right>}","\\inactivepart":"{\\left}","\\Gc":"{\\mathcal{G}_c}","\\strain":"\\bs{\\varepsilon}","\\stress":"\\bs{\\sigma}","\\macaulay":"\\left<#1\\right>","\\body":"\\Omega","\\bodyboundary":"{\\partial\\body}","\\ep":"{\\varepsilon^p}","\\ep0":"{\\varepsilon_0^p}","\\epdot":"{\\dot{\\varepsilon}}^p","\\epdot0":"{\\dot{\\varepsilon}}_0^p","\\bfa":"\\boldsymbol{a}","\\bfb":"\\boldsymbol{b}","\\bfc":"\\boldsymbol{c}","\\bfd":"\\boldsymbol{d}","\\bfe":"\\boldsymbol{e}","\\bff":"\\boldsymbol{f}","\\bfg":"\\boldsymbol{g}","\\bfh":"\\boldsymbol{h}","\\bfi":"\\boldsymbol{i}","\\bfj":"\\boldsymbol{j}","\\bfk":"\\boldsymbol{k}","\\bfl":"\\boldsymbol{l}","\\bfm":"\\boldsymbol{m}","\\bfn":"\\boldsymbol{n}","\\bfo":"\\boldsymbol{o}","\\bfp":"\\boldsymbol{p}","\\bfq":"\\boldsymbol{q}","\\bfr":"\\boldsymbol{r}","\\bfs":"\\boldsymbol{s}","\\bft":"\\boldsymbol{t}","\\bfu":"\\boldsymbol{u}","\\bfv":"\\boldsymbol{v}","\\bfw":"\\boldsymbol{w}","\\bfx":"\\boldsymbol{x}","\\bfy":"\\boldsymbol{y}","\\bfz":"\\boldsymbol{z}","\\bfA":"\\boldsymbol{A}","\\bfB":"\\boldsymbol{B}","\\bfC":"\\boldsymbol{C}","\\bfD":"\\boldsymbol{D}","\\bfE":"\\boldsymbol{E}","\\bfF":"\\boldsymbol{F}","\\bfG":"\\boldsymbol{G}","\\bfH":"\\boldsymbol{H}","\\bfI":"\\boldsymbol{I}","\\bfJ":"\\boldsymbol{J}","\\bfK":"\\boldsymbol{K}","\\bfL":"\\boldsymbol{L}","\\bfM":"\\boldsymbol{M}","\\bfN":"\\boldsymbol{N}","\\bfO":"\\boldsymbol{O}","\\bfP":"\\boldsymbol{P}","\\bfQ":"\\boldsymbol{Q}","\\bfR":"\\boldsymbol{R}","\\bfS":"\\boldsymbol{S}","\\bfT":"\\boldsymbol{T}","\\bfU":"\\boldsymbol{U}","\\bfV":"\\boldsymbol{V}","\\bfW":"\\boldsymbol{W}","\\bfX":"\\boldsymbol{X}","\\bfY":"\\boldsymbol{Y}","\\bfZ":"\\boldsymbol{Z}"}});$ at any time is the original amount of gas (computed based on original pressure, temperature, and volume) plus the amount in the cavity due to any gas injected during the simulation.

Constructed MooseObjects

The Cavity Pressure Action system consists of three separate actions, listed in the Associated Actions block below, which are all created within the same block.

Table 1: Correspondence Among Action Functionality and MooseObjects for the CavityPressure Action

Functionality	Replaced Classes	Associated Parameters
Calculation of the initial moles quantity	CavityPressureUserObject	`volume`: the name of the internal volume postprocessor
`R`: the universal gas constant
`temperature` : the name of the average temperature postprocessor
Store the value of the initial moles	CavityPressurePostprocessor	`output_initial_moles`: the postprocessor name to used to report the initial moles of gas
Calculation of the current internal pressure	CavityPressureUserObject	`output`: the name of the cavity pressure postprocessor
Store the internal pressure value	CavityPressurePostprocessor	`output`: the name of the cavity pressure postprocessor
Apply the calculated internal pressure traction	Pressure	`boundary`: the list of boundary IDs to which the pressure should be applied
`displacements` : a string of the displacement variables to which the Pressure BC should be applied

Example Input Syntax

[BCs]
  [CavityPressure]
    [1]
      boundary = 100
      initial_pressure = 100
      material_input = materialInput
      R = 8.314472
      temperature = aveTempInterior
      volume = internalVolume
      startup_time = 0.5
      output = ppress
      save_in = 'pressure_residual_x pressure_residual_y pressure_residual_z'
    []
  []
[]

Postprocessors for both the average temperature and the internal volume are also required for the Cavity Pressure Action system. Note that the name of the postprocessors correspond to the arguments for the parameters temperature and internal_volume in the CavityPressure block.

[Postprocessors]
  [aveTempInterior]
    type = SideAverageValue
    boundary = 100
    variable = temp
    execute_on = 'initial linear'
  []
[]

[Postprocessors]
  [internalVolume]
    type = InternalVolume
    boundary = 100
    execute_on = 'initial linear'
  []
[]

Input Parameters

boundaryThe list of boundary IDs from the mesh where the pressure will be applied
C++ Type:std::vector<BoundaryName>
Unit:(no unit assumed)
Controllable:No
Description:The list of boundary IDs from the mesh where the pressure will be applied
displacementsThe nonlinear displacement variables
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The nonlinear displacement variables

Required Parameters

absolute_value_vector_tagsThe tags for the vectors this residual object should fill with the absolute value of the residual contribution
C++ Type:std::vector<TagName>
Unit:(no unit assumed)
Controllable:No
Description:The tags for the vectors this residual object should fill with the absolute value of the residual contribution
active__all__ If specified only the blocks named will be visited and made active
Default:__all__
C++ Type:std::vector<std::string>
Unit:(no unit assumed)
Controllable:No
Description:If specified only the blocks named will be visited and made active
extra_vector_tagsThe extra tags for the vectors this Kernel should fill
C++ Type:std::vector<TagName>
Unit:(no unit assumed)
Controllable:No
Description:The extra tags for the vectors this Kernel should fill
inactiveIf specified blocks matching these identifiers will be skipped.
C++ Type:std::vector<std::string>
Unit:(no unit assumed)
Controllable:No
Description:If specified blocks matching these identifiers will be skipped.
outputThe name to use for the cavity pressure value
C++ Type:std::string
Unit:(no unit assumed)
Controllable:No
Description:The name to use for the cavity pressure value
save_inAuxiliary variables to save the displacement residuals
C++ Type:std::vector<AuxVariableName>
Unit:(no unit assumed)
Controllable:No
Description:Auxiliary variables to save the displacement residuals
use_automatic_differentiationFalseFlag to use automatic differentiation (AD) objects when possible
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Flag to use automatic differentiation (AD) objects when possible
use_displaced_meshTrueWhether to use displaced mesh in the boundary condition
Default:True
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Whether to use displaced mesh in the boundary condition

Optional Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Unit:(no unit assumed)
Controllable:No
Description:Adds user-defined labels for accessing object parameters via control logic.

Advanced Parameters

Associated Actions

Available Actions

Solid Mechanics App
CavityPressureActionAction to setup cavity pressure boundary condition
CavityPressurePPActionThis Action creates a CavityPressurePostprocessor.
CavityPressureUOActionAction to add user objects for cavity pressure

(moose/modules/combined/test/tests/cavity_pressure/3d.i)

#
# Cavity Pressure Test
#
# This test is designed to compute an internal pressure based on
#   p = n * R * T / V
# where
#   p is the pressure
#   n is the amount of material in the volume (moles)
#   R is the universal gas constant
#   T is the temperature
#   V is the volume
#
# The mesh is composed of one block (1) with an interior cavity of volume 8.
#   Block 2 sits in the cavity and has a volume of 1.  Thus, the total
#   initial volume is 7.
# The test adjusts n, T, and V in the following way:
#   n => n0 + alpha * t
#   T => T0 + beta * t
#   V => V0 + gamma * t
# with
#   alpha = n0
#   beta = T0 / 2
#   gamma = - (0.003322259...) * V0
#   T0 = 240.54443866068704
#   V0 = 7
#   n0 = f(p0)
#   p0 = 100
#   R = 8.314472 J * K^(-1) * mol^(-1)
#
# So, n0 = p0 * V0 / R / T0 = 100 * 7 / 8.314472 / 240.544439
#        = 0.35
#
# The parameters combined at t = 1 gives p = 301.
#

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
  volumetric_locking_correction = true
[]

[Mesh]
  file = 3d.e
[]

[Functions]
  [displ_positive]
    type = PiecewiseLinear
    x = '0 1'
    y = '0 0.0029069767441859684'
  []
  [displ_negative]
    type = PiecewiseLinear
    x = '0 1'
    y = '0 -0.0029069767441859684'
  []
  [temp1]
    type = PiecewiseLinear
    x = '0 1'
    y = '1 1.5'
    scale_factor = 240.54443866068704
  []
  [material_input_function]
    type = PiecewiseLinear
    x = '0    1'
    y = '0 0.35'
  []
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
  [disp_z]
  []
  [temp]
    initial_condition = 240.54443866068704
  []
  [material_input]
  []
[]

[AuxVariables]
  [pressure_residual_x]
  []
  [pressure_residual_y]
  []
  [pressure_residual_z]
  []
  [stress_xx]
    order = CONSTANT
    family = MONOMIAL
  []
  [stress_yy]
    order = CONSTANT
    family = MONOMIAL
  []
  [stress_zz]
    order = CONSTANT
    family = MONOMIAL
  []
  [stress_xy]
    order = CONSTANT
    family = MONOMIAL
  []
  [stress_yz]
    order = CONSTANT
    family = MONOMIAL
  []
  [stress_zx]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Kernels]
  [TensorMechanics]
    use_displaced_mesh = true
  []
  [heat]
    type = Diffusion
    variable = temp
    use_displaced_mesh = true
  []
  [material_input_dummy]
    type = Diffusion
    variable = material_input
    use_displaced_mesh = true
  []
[]

[AuxKernels]
  [stress_xx]
    type = RankTwoAux
    rank_two_tensor = stress
    index_i = 0
    index_j = 0
    variable = stress_xx
  []
  [stress_yy]
    type = RankTwoAux
    rank_two_tensor = stress
    index_i = 1
    index_j = 1
    variable = stress_yy
  []
  [stress_zz]
    type = RankTwoAux
    rank_two_tensor = stress
    index_i = 2
    index_j = 2
    variable = stress_zz
  []
  [stress_xy]
    type = RankTwoAux
    rank_two_tensor = stress
    index_i = 0
    index_j = 1
    variable = stress_xy
  []
  [stress_yz]
    type = RankTwoAux
    rank_two_tensor = stress
    index_i = 1
    index_j = 2
    variable = stress_yz
  []
  [stress_zx]
    type = RankTwoAux
    rank_two_tensor = stress
    index_i = 2
    index_j = 0
    variable = stress_zx
  []
[]

[BCs]
  [no_x_exterior]
    type = DirichletBC
    variable = disp_x
    boundary = '7 8'
    value = 0.0
  []
  [no_y_exterior]
    type = DirichletBC
    variable = disp_y
    boundary = '9 10'
    value = 0.0
  []
  [no_z_exterior]
    type = DirichletBC
    variable = disp_z
    boundary = '11 12'
    value = 0.0
  []
  [prescribed_left]
    type = FunctionDirichletBC
    variable = disp_x
    boundary = 13
    function = displ_positive
  []
  [prescribed_right]
    type = FunctionDirichletBC
    variable = disp_x
    boundary = 14
    function = displ_negative
  []
  [no_y]
    type = DirichletBC
    variable = disp_y
    boundary = '15 16'
    value = 0.0
  []
  [no_z]
    type = DirichletBC
    variable = disp_z
    boundary = '17 18'
    value = 0.0
  []
  [no_x_interior]
    type = DirichletBC
    variable = disp_x
    boundary = '1 2'
    value = 0.0
  []
  [no_y_interior]
    type = DirichletBC
    variable = disp_y
    boundary = '3 4'
    value = 0.0
  []
  [no_z_interior]
    type = DirichletBC
    variable = disp_z
    boundary = '5 6'
    value = 0.0
  []
  [temperatureInterior]
    type = FunctionDirichletBC
    boundary = 100
    function = temp1
    variable = temp
  []
  [MaterialInput]
    type = FunctionDirichletBC
    boundary = '100 13 14 15 16'
    function = material_input_function
    variable = material_input
  []
  [CavityPressure]
    [1]
      boundary = 100
      initial_pressure = 100
      material_input = materialInput
      R = 8.314472
      temperature = aveTempInterior
      volume = internalVolume
      startup_time = 0.5
      output = ppress
      save_in = 'pressure_residual_x pressure_residual_y pressure_residual_z'
    []
  []
[]

[Materials]
  [elast_tensor1]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 1e1
    poissons_ratio = 0
    block = 1
  []
  [strain1]
    type = ComputeFiniteStrain
    block = 1
  []
  [stress1]
    type = ComputeFiniteStrainElasticStress
    block = 1
  []
  [elast_tensor2]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 1e6
    poissons_ratio = 0
    block = 2
  []
  [strain2]
    type = ComputeFiniteStrain
    block = 2
  []
  [stress2]
    type = ComputeFiniteStrainElasticStress
    block = 2
  []
[]

[Executioner]
  type = Transient

  petsc_options_iname = '-pc_type -sub_pc_type'
  petsc_options_value = 'asm       lu'

  nl_rel_tol = 1e-12
  l_tol = 1e-12

  l_max_its = 20

  dt = 0.5
  end_time = 1.0
  use_pre_SMO_residual = true
[]

[Postprocessors]
  [internalVolume]
    type = InternalVolume
    boundary = 100
    execute_on = 'initial linear'
  []
  [aveTempInterior]
    type = SideAverageValue
    boundary = 100
    variable = temp
    execute_on = 'initial linear'
  []
  [materialInput]
    type = SideAverageValue
    boundary = '7 8 9 10 11 12'
    variable = material_input
    execute_on = linear
  []
[]

[Outputs]
  exodus = true
[]

(moose/modules/combined/test/tests/cavity_pressure/3d.i)

#
# Cavity Pressure Test
#
# This test is designed to compute an internal pressure based on
#   p = n * R * T / V
# where
#   p is the pressure
#   n is the amount of material in the volume (moles)
#   R is the universal gas constant
#   T is the temperature
#   V is the volume
#
# The mesh is composed of one block (1) with an interior cavity of volume 8.
#   Block 2 sits in the cavity and has a volume of 1.  Thus, the total
#   initial volume is 7.
# The test adjusts n, T, and V in the following way:
#   n => n0 + alpha * t
#   T => T0 + beta * t
#   V => V0 + gamma * t
# with
#   alpha = n0
#   beta = T0 / 2
#   gamma = - (0.003322259...) * V0
#   T0 = 240.54443866068704
#   V0 = 7
#   n0 = f(p0)
#   p0 = 100
#   R = 8.314472 J * K^(-1) * mol^(-1)
#
# So, n0 = p0 * V0 / R / T0 = 100 * 7 / 8.314472 / 240.544439
#        = 0.35
#
# The parameters combined at t = 1 gives p = 301.
#

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
  volumetric_locking_correction = true
[]

[Mesh]
  file = 3d.e
[]

[Functions]
  [displ_positive]
    type = PiecewiseLinear
    x = '0 1'
    y = '0 0.0029069767441859684'
  []
  [displ_negative]
    type = PiecewiseLinear
    x = '0 1'
    y = '0 -0.0029069767441859684'
  []
  [temp1]
    type = PiecewiseLinear
    x = '0 1'
    y = '1 1.5'
    scale_factor = 240.54443866068704
  []
  [material_input_function]
    type = PiecewiseLinear
    x = '0    1'
    y = '0 0.35'
  []
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
  [disp_z]
  []
  [temp]
    initial_condition = 240.54443866068704
  []
  [material_input]
  []
[]

[AuxVariables]
  [pressure_residual_x]
  []
  [pressure_residual_y]
  []
  [pressure_residual_z]
  []
  [stress_xx]
    order = CONSTANT
    family = MONOMIAL
  []
  [stress_yy]
    order = CONSTANT
    family = MONOMIAL
  []
  [stress_zz]
    order = CONSTANT
    family = MONOMIAL
  []
  [stress_xy]
    order = CONSTANT
    family = MONOMIAL
  []
  [stress_yz]
    order = CONSTANT
    family = MONOMIAL
  []
  [stress_zx]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Kernels]
  [TensorMechanics]
    use_displaced_mesh = true
  []
  [heat]
    type = Diffusion
    variable = temp
    use_displaced_mesh = true
  []
  [material_input_dummy]
    type = Diffusion
    variable = material_input
    use_displaced_mesh = true
  []
[]

[AuxKernels]
  [stress_xx]
    type = RankTwoAux
    rank_two_tensor = stress
    index_i = 0
    index_j = 0
    variable = stress_xx
  []
  [stress_yy]
    type = RankTwoAux
    rank_two_tensor = stress
    index_i = 1
    index_j = 1
    variable = stress_yy
  []
  [stress_zz]
    type = RankTwoAux
    rank_two_tensor = stress
    index_i = 2
    index_j = 2
    variable = stress_zz
  []
  [stress_xy]
    type = RankTwoAux
    rank_two_tensor = stress
    index_i = 0
    index_j = 1
    variable = stress_xy
  []
  [stress_yz]
    type = RankTwoAux
    rank_two_tensor = stress
    index_i = 1
    index_j = 2
    variable = stress_yz
  []
  [stress_zx]
    type = RankTwoAux
    rank_two_tensor = stress
    index_i = 2
    index_j = 0
    variable = stress_zx
  []
[]

[BCs]
  [no_x_exterior]
    type = DirichletBC
    variable = disp_x
    boundary = '7 8'
    value = 0.0
  []
  [no_y_exterior]
    type = DirichletBC
    variable = disp_y
    boundary = '9 10'
    value = 0.0
  []
  [no_z_exterior]
    type = DirichletBC
    variable = disp_z
    boundary = '11 12'
    value = 0.0
  []
  [prescribed_left]
    type = FunctionDirichletBC
    variable = disp_x
    boundary = 13
    function = displ_positive
  []
  [prescribed_right]
    type = FunctionDirichletBC
    variable = disp_x
    boundary = 14
    function = displ_negative
  []
  [no_y]
    type = DirichletBC
    variable = disp_y
    boundary = '15 16'
    value = 0.0
  []
  [no_z]
    type = DirichletBC
    variable = disp_z
    boundary = '17 18'
    value = 0.0
  []
  [no_x_interior]
    type = DirichletBC
    variable = disp_x
    boundary = '1 2'
    value = 0.0
  []
  [no_y_interior]
    type = DirichletBC
    variable = disp_y
    boundary = '3 4'
    value = 0.0
  []
  [no_z_interior]
    type = DirichletBC
    variable = disp_z
    boundary = '5 6'
    value = 0.0
  []
  [temperatureInterior]
    type = FunctionDirichletBC
    boundary = 100
    function = temp1
    variable = temp
  []
  [MaterialInput]
    type = FunctionDirichletBC
    boundary = '100 13 14 15 16'
    function = material_input_function
    variable = material_input
  []
  [CavityPressure]
    [1]
      boundary = 100
      initial_pressure = 100
      material_input = materialInput
      R = 8.314472
      temperature = aveTempInterior
      volume = internalVolume
      startup_time = 0.5
      output = ppress
      save_in = 'pressure_residual_x pressure_residual_y pressure_residual_z'
    []
  []
[]

[Materials]
  [elast_tensor1]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 1e1
    poissons_ratio = 0
    block = 1
  []
  [strain1]
    type = ComputeFiniteStrain
    block = 1
  []
  [stress1]
    type = ComputeFiniteStrainElasticStress
    block = 1
  []
  [elast_tensor2]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 1e6
    poissons_ratio = 0
    block = 2
  []
  [strain2]
    type = ComputeFiniteStrain
    block = 2
  []
  [stress2]
    type = ComputeFiniteStrainElasticStress
    block = 2
  []
[]

[Executioner]
  type = Transient

  petsc_options_iname = '-pc_type -sub_pc_type'
  petsc_options_value = 'asm       lu'

  nl_rel_tol = 1e-12
  l_tol = 1e-12

  l_max_its = 20

  dt = 0.5
  end_time = 1.0
  use_pre_SMO_residual = true
[]

[Postprocessors]
  [internalVolume]
    type = InternalVolume
    boundary = 100
    execute_on = 'initial linear'
  []
  [aveTempInterior]
    type = SideAverageValue
    boundary = 100
    variable = temp
    execute_on = 'initial linear'
  []
  [materialInput]
    type = SideAverageValue
    boundary = '7 8 9 10 11 12'
    variable = material_input
    execute_on = linear
  []
[]

[Outputs]
  exodus = true
[]

(moose/modules/combined/test/tests/cavity_pressure/3d.i)

#
# Cavity Pressure Test
#
# This test is designed to compute an internal pressure based on
#   p = n * R * T / V
# where
#   p is the pressure
#   n is the amount of material in the volume (moles)
#   R is the universal gas constant
#   T is the temperature
#   V is the volume
#
# The mesh is composed of one block (1) with an interior cavity of volume 8.
#   Block 2 sits in the cavity and has a volume of 1.  Thus, the total
#   initial volume is 7.
# The test adjusts n, T, and V in the following way:
#   n => n0 + alpha * t
#   T => T0 + beta * t
#   V => V0 + gamma * t
# with
#   alpha = n0
#   beta = T0 / 2
#   gamma = - (0.003322259...) * V0
#   T0 = 240.54443866068704
#   V0 = 7
#   n0 = f(p0)
#   p0 = 100
#   R = 8.314472 J * K^(-1) * mol^(-1)
#
# So, n0 = p0 * V0 / R / T0 = 100 * 7 / 8.314472 / 240.544439
#        = 0.35
#
# The parameters combined at t = 1 gives p = 301.
#

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
  volumetric_locking_correction = true
[]

[Mesh]
  file = 3d.e
[]

[Functions]
  [displ_positive]
    type = PiecewiseLinear
    x = '0 1'
    y = '0 0.0029069767441859684'
  []
  [displ_negative]
    type = PiecewiseLinear
    x = '0 1'
    y = '0 -0.0029069767441859684'
  []
  [temp1]
    type = PiecewiseLinear
    x = '0 1'
    y = '1 1.5'
    scale_factor = 240.54443866068704
  []
  [material_input_function]
    type = PiecewiseLinear
    x = '0    1'
    y = '0 0.35'
  []
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
  [disp_z]
  []
  [temp]
    initial_condition = 240.54443866068704
  []
  [material_input]
  []
[]

[AuxVariables]
  [pressure_residual_x]
  []
  [pressure_residual_y]
  []
  [pressure_residual_z]
  []
  [stress_xx]
    order = CONSTANT
    family = MONOMIAL
  []
  [stress_yy]
    order = CONSTANT
    family = MONOMIAL
  []
  [stress_zz]
    order = CONSTANT
    family = MONOMIAL
  []
  [stress_xy]
    order = CONSTANT
    family = MONOMIAL
  []
  [stress_yz]
    order = CONSTANT
    family = MONOMIAL
  []
  [stress_zx]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Kernels]
  [TensorMechanics]
    use_displaced_mesh = true
  []
  [heat]
    type = Diffusion
    variable = temp
    use_displaced_mesh = true
  []
  [material_input_dummy]
    type = Diffusion
    variable = material_input
    use_displaced_mesh = true
  []
[]

[AuxKernels]
  [stress_xx]
    type = RankTwoAux
    rank_two_tensor = stress
    index_i = 0
    index_j = 0
    variable = stress_xx
  []
  [stress_yy]
    type = RankTwoAux
    rank_two_tensor = stress
    index_i = 1
    index_j = 1
    variable = stress_yy
  []
  [stress_zz]
    type = RankTwoAux
    rank_two_tensor = stress
    index_i = 2
    index_j = 2
    variable = stress_zz
  []
  [stress_xy]
    type = RankTwoAux
    rank_two_tensor = stress
    index_i = 0
    index_j = 1
    variable = stress_xy
  []
  [stress_yz]
    type = RankTwoAux
    rank_two_tensor = stress
    index_i = 1
    index_j = 2
    variable = stress_yz
  []
  [stress_zx]
    type = RankTwoAux
    rank_two_tensor = stress
    index_i = 2
    index_j = 0
    variable = stress_zx
  []
[]

[BCs]
  [no_x_exterior]
    type = DirichletBC
    variable = disp_x
    boundary = '7 8'
    value = 0.0
  []
  [no_y_exterior]
    type = DirichletBC
    variable = disp_y
    boundary = '9 10'
    value = 0.0
  []
  [no_z_exterior]
    type = DirichletBC
    variable = disp_z
    boundary = '11 12'
    value = 0.0
  []
  [prescribed_left]
    type = FunctionDirichletBC
    variable = disp_x
    boundary = 13
    function = displ_positive
  []
  [prescribed_right]
    type = FunctionDirichletBC
    variable = disp_x
    boundary = 14
    function = displ_negative
  []
  [no_y]
    type = DirichletBC
    variable = disp_y
    boundary = '15 16'
    value = 0.0
  []
  [no_z]
    type = DirichletBC
    variable = disp_z
    boundary = '17 18'
    value = 0.0
  []
  [no_x_interior]
    type = DirichletBC
    variable = disp_x
    boundary = '1 2'
    value = 0.0
  []
  [no_y_interior]
    type = DirichletBC
    variable = disp_y
    boundary = '3 4'
    value = 0.0
  []
  [no_z_interior]
    type = DirichletBC
    variable = disp_z
    boundary = '5 6'
    value = 0.0
  []
  [temperatureInterior]
    type = FunctionDirichletBC
    boundary = 100
    function = temp1
    variable = temp
  []
  [MaterialInput]
    type = FunctionDirichletBC
    boundary = '100 13 14 15 16'
    function = material_input_function
    variable = material_input
  []
  [CavityPressure]
    [1]
      boundary = 100
      initial_pressure = 100
      material_input = materialInput
      R = 8.314472
      temperature = aveTempInterior
      volume = internalVolume
      startup_time = 0.5
      output = ppress
      save_in = 'pressure_residual_x pressure_residual_y pressure_residual_z'
    []
  []
[]

[Materials]
  [elast_tensor1]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 1e1
    poissons_ratio = 0
    block = 1
  []
  [strain1]
    type = ComputeFiniteStrain
    block = 1
  []
  [stress1]
    type = ComputeFiniteStrainElasticStress
    block = 1
  []
  [elast_tensor2]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 1e6
    poissons_ratio = 0
    block = 2
  []
  [strain2]
    type = ComputeFiniteStrain
    block = 2
  []
  [stress2]
    type = ComputeFiniteStrainElasticStress
    block = 2
  []
[]

[Executioner]
  type = Transient

  petsc_options_iname = '-pc_type -sub_pc_type'
  petsc_options_value = 'asm       lu'

  nl_rel_tol = 1e-12
  l_tol = 1e-12

  l_max_its = 20

  dt = 0.5
  end_time = 1.0
  use_pre_SMO_residual = true
[]

[Postprocessors]
  [internalVolume]
    type = InternalVolume
    boundary = 100
    execute_on = 'initial linear'
  []
  [aveTempInterior]
    type = SideAverageValue
    boundary = 100
    variable = temp
    execute_on = 'initial linear'
  []
  [materialInput]
    type = SideAverageValue
    boundary = '7 8 9 10 11 12'
    variable = material_input
    execute_on = linear
  []
[]

[Outputs]
  exodus = true
[]