ComputeLagrangianStressCauchy

Overview

This class provides an interface to define a constitutive model in terms of the Cauchy stress stress $var element = document.getElementById("moose-equation-15373490-1463-40b3-a8e1-c5401fe4570e");katex.render("\\sigma_{ij}", element, {displayMode:false,throwOnError:false});$ and the associated algorithmic tangent $var element = document.getElementById("moose-equation-e3183c36-ca57-4d38-9a65-ff3638c1d88e");katex.render(" T_{ijkl} = \\frac{d \\sigma_{ij}}{d \\Delta l_{kl}}", element, {displayMode:true,throwOnError:false});$ See here for a complete description of the Lagrangian kernel material system and for detailed instructions on how to implement a new material model.

Conversion

This class converts the Cauchy stress and the algorithmic tangent to provide the 1st Piola Kirchhoff stress, where needed by the Lagrangian kernel system. The conversion formula are: $var element = document.getElementById("moose-equation-5bafd2a2-1982-4804-b06e-8c68691cf5d4");katex.render(" \\sigma_{ij}=\\frac{1}{J}P_{iK}F_{jK}", element, {displayMode:true,throwOnError:false});$ and $var element = document.getElementById("moose-equation-9d4b85d4-4c26-4117-8053-842a6708d8f6");katex.render(" T_{ijkl}=\\frac{d\\sigma_{ij}}{d\\Delta l_{kl}}=\\frac{1}{J}T_{iAmN}^{\\prime}F_{jA}F_{lN}f_{mk}+f_{jk}\\sigma_{il}-\\sigma_{ij}f_{lk}", element, {displayMode:true,throwOnError:false});$