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+### Compression cap hardening
+
+The standard Mohr–Coulomb yield surface characterizes shear failure in geomaterials by relating the shear stress $\tau$ on a potential failure plane to the corresponding normal stress $\sigma$. While suitable for frictional materials, the standard Mohr-Coulomb envelope lacks a mechanism to limit the admissible stress space under high compressive pressure. As a result, the standard Mohr-Coulomb model cannot represent the compaction, crushing, and plastic volumetric hardening that occur in soils and rocks under high confining stresses.
+
+To address this limitation, a compression cap is introduced. The cap provides a smooth closure of the yield surface in the high-compression regime. Here we describe the combined Mohr-Coulomb and cap yield surfaces.
+
+### Mohr–Coulomb yield surface
+
+In the $`(\sigma, \tau)`$ stress space, the Mohr-Coulomb yield surface is expressed as:
+
+```math
+ F_{MC}(\sigma, \tau) = \tau + \sigma \sin{\phi} - c \cos{\phi} = 0
+```
+where:
+
+- $`\sigma`$ = normal stress component
+- $`\tau`$ = shear stress component
+- $`c`$ = cohesion of material
+- $`\phi`$ = friction angle
+
+In stress-invariant form, the MC yield function is typically written as:
+
+```math
+ F_{MC}(p, q) = q - \frac{6 \sin{\phi}}{3 - \sin{\phi}} p - \frac{6 c \cos{\phi}}{3 - \sin{\phi}}
+```
+where:
+
+- $`p = \frac{1}{3} tr(\sigma)`$ is the mean effective stress
+- $`q = \sqrt{\frac{3}{2}\sigma':\sigma'}`$ is the norm of deviatoric stress tensor, where $`\sigma' = \sigma - p`$.
+
+This defines a hexagonal pyramid in principal stress space, but is shown as a straight line in the $`(\sigma, \tau)`$ stress space.
+
+### Compression cap concept
+At high confining pressures, real geomaterials exhibit compaction and crushing rather than unlimited strength. The Mohr-Coulomb envelope alone allows unbounded compressive stresses. A cap yield surface introduces a limit to admissible volumetric compression and establishes a mechanism for volumetric plastic deformation.
+
+In $`p-q`$ stress-invariant space, the cap is defined as an ellipse (or a smooth rounded surface) closing the Mohr-Coulomb yield surface in the compressive regime.
+
+### Cap yield surface
+An elliptical cap can be defined as:
+
+```math
+ F_{cap}(p, q) = \left( \frac{q}{X} \right)^2 + p^2 - p_c^2
+```
+where:
+
+- $`p_c`$ = cap position (preconsolidation pressure),
+- $`X`$ = cap size parameter
+
+The cap intersects the MC surface. A linear hardening relation for the cap position can be written as:
+
+```math
+ p_c = p_{c0} + H \epsilon^p
+```
+where:
+- $`p_{c0}`$ = the initial cap position
+- $`H`$ = the hardening modulus
+- $`\epsilon^p`$ = the plastic volumetric strain
+
+
+### Combined Mohr–Coulomb + cap yield surface
+
+The figure below shows a typical Mohr–Coulomb yield surface extended with tension cutoff and compression cap yield surfaces. In $(\sigma, \tau)$ coordinates:
+
+
+
+Here, we need to convert the compression cap yield surface from $(p, q)$ coordinates to $(\sigma, \tau)$ coordinates. The conversion is to be followed ...
+
+
+### Plastic Potential for the compression cap
+
+For the cap branch, plastic deformation is primarily volumetric (compaction), and the plastic potential is usually taken to be associated. The flow function is then:
+
+```math
+ G_{cap} \left(p, q \right) = F_{cap} \left(p, q \right)
+```
+The derivative of the flow function is the:
+
+```math
+ \frac{\partial G_{cap}}{\partial \sigma} = \frac{2 q}{X^2} \frac{\partial q}{\partial \sigma} + 2 p \frac{\partial p}{\partial \sigma}
+```
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diff --git a/applications/GeoMechanicsApplication/custom_constitutive/documentation_data/mohr-coulomb-with-tension-cutoff-and-cap_zones.svg b/applications/GeoMechanicsApplication/custom_constitutive/documentation_data/mohr-coulomb-with-tension-cutoff-and-cap_zones.svg
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+
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+
+Here, we need to convert the compression cap yield surface from $(p, q)$ coordinates to $(\sigma, \tau)$ coordinates. The conversion is to be followed ...
+
+
+### Plastic Potential for the compression cap
+
+For the cap branch, plastic deformation is primarily volumetric (compaction), and the plastic potential is usually taken to be associated. The flow function is then:
+
+```math
+ G_{cap} \left(p, q \right) = F_{cap} \left(p, q \right)
+```
+The derivative of the flow function is the:
+
+```math
+ \frac{\partial G_{cap}}{\partial \sigma} = \frac{2 q}{X^2} \frac{\partial q}{\partial \sigma} + 2 p \frac{\partial p}{\partial \sigma}
+```
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+
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