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🚧 Under development

This section of the documentation is currently under development. More detailed content and model descriptions will be added soon.

Mechanical models describe the stress-strain behaviour of soils and are a core component of numerical geotechnical analysis. In numgeo, these models are responsible for updating the (effective) stress at time \(t = t_0 + \Delta t\), based on the imposed strain increment \(\Delta \boldsymbol{\varepsilon}\) and the internal state of the material.

In its simplest form, the stress at the current time step is computed as:

\[ \boldsymbol{\sigma}^t = \boldsymbol{\sigma}^{t_0} + \Delta \boldsymbol{\sigma}, \quad \text{with} \quad \Delta \boldsymbol{\sigma} = \Delta \boldsymbol{\sigma}(\Delta \boldsymbol{\varepsilon}) \]

However, many models incorporate additional dependencies on:

  • Void ratio \(e\)
  • Current stress state \(\boldsymbol{\sigma}\)
  • Degree of saturation \(S\)
  • Internal state variables (e.g., plastic strains, fabric tensors, accumulated cycles)

These models enable the simulation of non-linear, inelastic, and path-dependent soil behaviour.

Available Mechanical Models in numgeo

  • Linear elasticity
  • Barotropic elasticity
  • Mohr-Coulomb
  • Matsuoka Nakai
  • Modified Cam Clay
  • Hypoplasticity + Intergranular Strain (IGS)
  • Hypoplasticity + Intergranular Strain Anisotropy (ISA)
  • Sanisand
  • Sanisand-MSf
  • Sanisand-F
  • Anisotropic Viscous ISA (AVISA)
  • Anisotropic Visco-Hypoplasticity (AVHP)
  • High Cycle Accumulation model for sand (HCA-Sand)
    • coupled with Hypoplasticity + Intergranular Strain
    • coupled with Sanisand
    • coupled with Elasticity
  • High Cycle Accumulation model for clay (HCA-Clay)

Model Superposition

In addition to stand-alone constitutive models, numgeo supports the superposition of mechanical responses by adding:

  • Viscous stress components, via:

  • Additional elastic contributions, via:

    • Linear Elasticity