Thermoelastic effect on stress

Input(s)

λ\lambda: Lame (psi)

δij\delta_{\mathrm{ij}}: Kronecker Delta (dimensionless)

ε00\varepsilon_{00}: Initial Strain (dimensionless)

G: Modulus of Shear (psi)

εij\varepsilon_{\mathrm{ij}}: Final Strain (dimensionless)

αT\alpha_{\mathrm{T}}: Coefficient of Linear Thermal Expansion (1/K)(1 / \mathrm{K})

P0\mathrm{P}_{0}: Pressure Applied (psi)

K\mathrm{K}: Bulk Modulus (psi)

ΔT\Delta \mathrm{T}: Temperature Difference (K)(\mathrm{K})

Output(s)

Sij\mathrm{S}_{\mathrm{ij}}: Stress (psi)

Formula(s)

Sij=λδijε00+2GεijαTδijP0KαTδijΔT\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.


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