Finite-element coupling
MeanFieldHomogenization used as a constitutive law inside a structural finite-element computation — the role an MFront behavior or an Abaqus UMAT plays. One microstructure stands for one material point: the FE code hands over a strain, the package hands back a stress and a consistent tangent.
Two opposite couplings — this is not the finite-element inclusion
| who calls whom | what it produces | |
|---|---|---|
| Finite-element inclusions | MFH calls the FE solver | one inclusion's response, when no closed form exists |
| This section | the FE code calls MFH | a material law at every Gauss point |
Why bother
A closed-form law is written once and fitted to data. A homogenized law is derived from the microstructure, so the same computation also tells you what each phase is doing — and lets the microstructure evolve. That is what makes the fractured-reservoir model of Barthélémy and Daniel (2011) possible: fracture apertures follow the effective stress, and the permeability follows the apertures.
Reading order
Three groups, read in this order: the equations, then how to build a model with them, then worked models.
| Page | |
|---|---|
| Getting started | |
| Quickstart: a structure with a nonlinear law | the whole path in one script: a thick tube of elastoplastic steel inflated to collapse |
| Step by step | the same script piece by piece, what goes wrong without each piece, troubleshooting |
| Theory | |
| Scale transition | the equations: incremental format, consistent tangent, tangent blocks |
| The coupled poroelastic problem | the same, with a fluid: two balances, the Biot blocks, the four tangents |
| Fractured permeability | flowing cracks and the effective conductivity of a fracture network |
| Manual | |
| Materials | the Gauss-point contract, in code |
| Building a fractured-rock material | the ARMA 2011 material: two gradients, two fluxes, evolving permeability |
| Ferrite backend | what the package and the Ferrite adapter each provide, and how to couple another code |
| Examples | |
| Thick-walled cylinder | worked model, checked against Lamé, then with closing cracks |
| A fractured-reservoir well test | the ARMA 2011 well test, end to end |
The Biot machinery the poroelastic coupling builds on is a property of a microstructure rather than of the coupling, so it lives on its own page: Poromechanics.