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.