Thermoelastic effect on stress
Input(s)
\(\lambda\): Lame (psi)
\(\delta_{\mathrm{ij}}\): Kronecker Delta (dimensionless)
\(\varepsilon_{00}\): Initial Strain (dimensionless)
G: Modulus of Shear (psi)
\(\varepsilon_{\mathrm{ij}}\): Final Strain (dimensionless)
\(\alpha_{\mathrm{T}}\): Coefficient of Linear Thermal Expansion \((1 / \mathrm{K})\)
\(\mathrm{P}_{0}\): Pressure Applied (psi)
\(\mathrm{K}\): Bulk Modulus (psi)
\(\Delta \mathrm{T}\): Temperature Difference \((\mathrm{K})\)
Output(s)
\(\mathrm{S}_{\mathrm{ij}}\): Stress (psi)
Formula(s)
\[
\mathrm{S}_{\mathrm{ij}}=\lambda * \delta_{\mathrm{ij}} * \varepsilon_{00}+2 * \mathrm{G} * \varepsilon_{\mathrm{ij}}-\alpha_{\mathrm{T}} * \delta_{\mathrm{ij}} * \mathrm{P}_{0}-\mathrm{K} * \alpha_{\mathrm{T}} * \delta_{\mathrm{ij}} * \Delta \mathrm{T}
\]
Reference(s)
Mark D. Zoback, Reservoir Geomechanics, Cambridge University Express, UK, Page: 83.