| σ, σm, σe | Remotely applied stress tensor and corresponding mean and von-Mises effective stresses |
| Q, S | Remotely applied differential and deviatoric stresses |
| x | Stress triaxiality |
| ρc | Crack density as defined by Budiansky & O’Connell (1976) |
| Gi, G, Ki, K | Initial and current shear moduli, initial and current bulk moduli |
| G0, Gu, K0, Ku | Calcite and uncracked porous medium shear and bulk moduli |
| ν0, νu, νi | Calcite, uncracked porous medium, and initial Poisson’s ratios |
| KI, KIC | Stress intensity factor, and the critical value of the material |
| W | Strain energy density |
| ε, |$\dot{\varepsilon }$| | Remote strain and its rate of change |
| |$\dot{\varepsilon }_{ax}$| | Remotely imposed axial strain rate |
| |$\dot{\varepsilon }^p$| | Plastic strain rate |
| |$\dot{\varepsilon }^d$| | Strain rate induced by dislocations |
| εmd, |$\dot{\varepsilon }^{md}$| | Strain induced by mobile dislocation motions and its rate of change |
| |$\dot{\varepsilon }_{0}$| | Reference strain rate for the non-porous material |
| ε0 | Yield strain for macroscopic plasticity |
| εe, εcracks, εmp | Strain due to elasticity, cracks, and plasticity of the porous material |
| ρd, ρmd | Total and mobile dislocation densities |
| ρid, |$\rho_{id}^{ini}$|, |$\rho_{id}^{\rm new}$| | Immobile dislocation density, decomposed as initial and newly nucleated |
| b | Burgers vector |
| v | Dislocation average slip velocity |
| V0 | Reference dislocation slip velocity |
| m, n | Stress sensitivity of the dislocation slip velocity and of the plasticity in the material |
| M | Strain hardening exponent of the macroscopic plastic law of the non-porous material |
| σ0 | Reference stress for dislocation slip velocity |
| σp, |$\sigma _p^i$| | Reference stress for plasticity of the non-porous material and its initial value |
| σi | Internal stress |
| |$\sigma _i^i$|, |$\dot{\varepsilon }_0^p$|, |$\varepsilon _0^p$| | Constants depending on microplastic parameters and relevant to internal stress |
| Lg | Grain size |
| τd | Characteristic time for dislocation motions |
| Ap, Bp, Cp, Dp | Constants relevant to microplastic flow |
| V, |$\dot{V}$| | Void volume and its rate of change |
| x*, k, f* | Reference values in the porous medium plasticity law |
| L | Pile-up length |
| τ*, τa, τf | Dislocation driving shear stress, resolved shear stress, and lattice friction stress |
| Ndi, |$N_{di}^{pu}$| | Number of dislocations in a pile-up, and its average value |
| |$N_{di}^{cri}$| | Critical number of dislocations in a pile-up for new crack nucleation |
| Λpu | Number of pile-ups intersecting a reference surface |
| Lpu, ϱpu | Average spacing between pile-ups, and pile-up density |
| θ, ξ | Angle between wedge crack and pile-up plane, and angle between σ1 and the pile-up plane |
| lw | Wedge crack length |
| σw, τw | Normal and shear stresses acting on the wedge crack |
| γs | Surface energy of the material |
| σ, σm, σe | Remotely applied stress tensor and corresponding mean and von-Mises effective stresses |
| Q, S | Remotely applied differential and deviatoric stresses |
| x | Stress triaxiality |
| ρc | Crack density as defined by Budiansky & O’Connell (1976) |
| Gi, G, Ki, K | Initial and current shear moduli, initial and current bulk moduli |
| G0, Gu, K0, Ku | Calcite and uncracked porous medium shear and bulk moduli |
| ν0, νu, νi | Calcite, uncracked porous medium, and initial Poisson’s ratios |
| KI, KIC | Stress intensity factor, and the critical value of the material |
| W | Strain energy density |
| ε, |$\dot{\varepsilon }$| | Remote strain and its rate of change |
| |$\dot{\varepsilon }_{ax}$| | Remotely imposed axial strain rate |
| |$\dot{\varepsilon }^p$| | Plastic strain rate |
| |$\dot{\varepsilon }^d$| | Strain rate induced by dislocations |
| εmd, |$\dot{\varepsilon }^{md}$| | Strain induced by mobile dislocation motions and its rate of change |
| |$\dot{\varepsilon }_{0}$| | Reference strain rate for the non-porous material |
| ε0 | Yield strain for macroscopic plasticity |
| εe, εcracks, εmp | Strain due to elasticity, cracks, and plasticity of the porous material |
| ρd, ρmd | Total and mobile dislocation densities |
| ρid, |$\rho_{id}^{ini}$|, |$\rho_{id}^{\rm new}$| | Immobile dislocation density, decomposed as initial and newly nucleated |
| b | Burgers vector |
| v | Dislocation average slip velocity |
| V0 | Reference dislocation slip velocity |
| m, n | Stress sensitivity of the dislocation slip velocity and of the plasticity in the material |
| M | Strain hardening exponent of the macroscopic plastic law of the non-porous material |
| σ0 | Reference stress for dislocation slip velocity |
| σp, |$\sigma _p^i$| | Reference stress for plasticity of the non-porous material and its initial value |
| σi | Internal stress |
| |$\sigma _i^i$|, |$\dot{\varepsilon }_0^p$|, |$\varepsilon _0^p$| | Constants depending on microplastic parameters and relevant to internal stress |
| Lg | Grain size |
| τd | Characteristic time for dislocation motions |
| Ap, Bp, Cp, Dp | Constants relevant to microplastic flow |
| V, |$\dot{V}$| | Void volume and its rate of change |
| x*, k, f* | Reference values in the porous medium plasticity law |
| L | Pile-up length |
| τ*, τa, τf | Dislocation driving shear stress, resolved shear stress, and lattice friction stress |
| Ndi, |$N_{di}^{pu}$| | Number of dislocations in a pile-up, and its average value |
| |$N_{di}^{cri}$| | Critical number of dislocations in a pile-up for new crack nucleation |
| Λpu | Number of pile-ups intersecting a reference surface |
| Lpu, ϱpu | Average spacing between pile-ups, and pile-up density |
| θ, ξ | Angle between wedge crack and pile-up plane, and angle between σ1 and the pile-up plane |
| lw | Wedge crack length |
| σw, τw | Normal and shear stresses acting on the wedge crack |
| γs | Surface energy of the material |
| σ, σm, σe | Remotely applied stress tensor and corresponding mean and von-Mises effective stresses |
| Q, S | Remotely applied differential and deviatoric stresses |
| x | Stress triaxiality |
| ρc | Crack density as defined by Budiansky & O’Connell (1976) |
| Gi, G, Ki, K | Initial and current shear moduli, initial and current bulk moduli |
| G0, Gu, K0, Ku | Calcite and uncracked porous medium shear and bulk moduli |
| ν0, νu, νi | Calcite, uncracked porous medium, and initial Poisson’s ratios |
| KI, KIC | Stress intensity factor, and the critical value of the material |
| W | Strain energy density |
| ε, |$\dot{\varepsilon }$| | Remote strain and its rate of change |
| |$\dot{\varepsilon }_{ax}$| | Remotely imposed axial strain rate |
| |$\dot{\varepsilon }^p$| | Plastic strain rate |
| |$\dot{\varepsilon }^d$| | Strain rate induced by dislocations |
| εmd, |$\dot{\varepsilon }^{md}$| | Strain induced by mobile dislocation motions and its rate of change |
| |$\dot{\varepsilon }_{0}$| | Reference strain rate for the non-porous material |
| ε0 | Yield strain for macroscopic plasticity |
| εe, εcracks, εmp | Strain due to elasticity, cracks, and plasticity of the porous material |
| ρd, ρmd | Total and mobile dislocation densities |
| ρid, |$\rho_{id}^{ini}$|, |$\rho_{id}^{\rm new}$| | Immobile dislocation density, decomposed as initial and newly nucleated |
| b | Burgers vector |
| v | Dislocation average slip velocity |
| V0 | Reference dislocation slip velocity |
| m, n | Stress sensitivity of the dislocation slip velocity and of the plasticity in the material |
| M | Strain hardening exponent of the macroscopic plastic law of the non-porous material |
| σ0 | Reference stress for dislocation slip velocity |
| σp, |$\sigma _p^i$| | Reference stress for plasticity of the non-porous material and its initial value |
| σi | Internal stress |
| |$\sigma _i^i$|, |$\dot{\varepsilon }_0^p$|, |$\varepsilon _0^p$| | Constants depending on microplastic parameters and relevant to internal stress |
| Lg | Grain size |
| τd | Characteristic time for dislocation motions |
| Ap, Bp, Cp, Dp | Constants relevant to microplastic flow |
| V, |$\dot{V}$| | Void volume and its rate of change |
| x*, k, f* | Reference values in the porous medium plasticity law |
| L | Pile-up length |
| τ*, τa, τf | Dislocation driving shear stress, resolved shear stress, and lattice friction stress |
| Ndi, |$N_{di}^{pu}$| | Number of dislocations in a pile-up, and its average value |
| |$N_{di}^{cri}$| | Critical number of dislocations in a pile-up for new crack nucleation |
| Λpu | Number of pile-ups intersecting a reference surface |
| Lpu, ϱpu | Average spacing between pile-ups, and pile-up density |
| θ, ξ | Angle between wedge crack and pile-up plane, and angle between σ1 and the pile-up plane |
| lw | Wedge crack length |
| σw, τw | Normal and shear stresses acting on the wedge crack |
| γs | Surface energy of the material |
| σ, σm, σe | Remotely applied stress tensor and corresponding mean and von-Mises effective stresses |
| Q, S | Remotely applied differential and deviatoric stresses |
| x | Stress triaxiality |
| ρc | Crack density as defined by Budiansky & O’Connell (1976) |
| Gi, G, Ki, K | Initial and current shear moduli, initial and current bulk moduli |
| G0, Gu, K0, Ku | Calcite and uncracked porous medium shear and bulk moduli |
| ν0, νu, νi | Calcite, uncracked porous medium, and initial Poisson’s ratios |
| KI, KIC | Stress intensity factor, and the critical value of the material |
| W | Strain energy density |
| ε, |$\dot{\varepsilon }$| | Remote strain and its rate of change |
| |$\dot{\varepsilon }_{ax}$| | Remotely imposed axial strain rate |
| |$\dot{\varepsilon }^p$| | Plastic strain rate |
| |$\dot{\varepsilon }^d$| | Strain rate induced by dislocations |
| εmd, |$\dot{\varepsilon }^{md}$| | Strain induced by mobile dislocation motions and its rate of change |
| |$\dot{\varepsilon }_{0}$| | Reference strain rate for the non-porous material |
| ε0 | Yield strain for macroscopic plasticity |
| εe, εcracks, εmp | Strain due to elasticity, cracks, and plasticity of the porous material |
| ρd, ρmd | Total and mobile dislocation densities |
| ρid, |$\rho_{id}^{ini}$|, |$\rho_{id}^{\rm new}$| | Immobile dislocation density, decomposed as initial and newly nucleated |
| b | Burgers vector |
| v | Dislocation average slip velocity |
| V0 | Reference dislocation slip velocity |
| m, n | Stress sensitivity of the dislocation slip velocity and of the plasticity in the material |
| M | Strain hardening exponent of the macroscopic plastic law of the non-porous material |
| σ0 | Reference stress for dislocation slip velocity |
| σp, |$\sigma _p^i$| | Reference stress for plasticity of the non-porous material and its initial value |
| σi | Internal stress |
| |$\sigma _i^i$|, |$\dot{\varepsilon }_0^p$|, |$\varepsilon _0^p$| | Constants depending on microplastic parameters and relevant to internal stress |
| Lg | Grain size |
| τd | Characteristic time for dislocation motions |
| Ap, Bp, Cp, Dp | Constants relevant to microplastic flow |
| V, |$\dot{V}$| | Void volume and its rate of change |
| x*, k, f* | Reference values in the porous medium plasticity law |
| L | Pile-up length |
| τ*, τa, τf | Dislocation driving shear stress, resolved shear stress, and lattice friction stress |
| Ndi, |$N_{di}^{pu}$| | Number of dislocations in a pile-up, and its average value |
| |$N_{di}^{cri}$| | Critical number of dislocations in a pile-up for new crack nucleation |
| Λpu | Number of pile-ups intersecting a reference surface |
| Lpu, ϱpu | Average spacing between pile-ups, and pile-up density |
| θ, ξ | Angle between wedge crack and pile-up plane, and angle between σ1 and the pile-up plane |
| lw | Wedge crack length |
| σw, τw | Normal and shear stresses acting on the wedge crack |
| γs | Surface energy of the material |
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