Research Project B01

Modelling of hydromechanical fracturing across scales


Data sets published by project B01 can be found on the DaRUS website.

Publications in scientific journals

  1. (Journal-) Articles

    1. Schmidt, F., Krüger, M., Keip, M.-A., & Hesch, C. (2022). Computational homogenization of higher-order continua. International Journal for Numerical Methods in Engineering, n/a(n/a), Article n/a.
    2. Swamynathan, S., Jobst, S., Kienle, D., & Keip, M.-A. (2022). Phase-field modeling of fracture in strain-hardening elastomers: Variational formulation, multiaxial experiments and validation. Engineering Fracture Mechanics, 108303.
    3. Polukhov, E., & Keip, M.-A. (2021). On the Computational Homogenization of Deformation-Diffusion Processes. Proceedings in Applied Mathematics and Mechanics, 20(1), Article 1.
    4. Polukhov, E., & Keip, M.-A. (2021). On the Computational Homogenization of Deformation–Diffusion Processes. PAMM, 20(1), Article 1.
    5. Polukhov, E., & Keip, M.-A. (2020). Computational homogenization of transient  chemo-mechanical processes based on a variational minimization principle. Advanced Modeling and Simulation in Engineering Sciences, 7(1), Article 1.
    6. Polukhov, E., & Keip, M.-A. (2020). Computational homogenization of transient chemo-mechanical processes based on a variational minimization principle. Advanced Modeling and Simulation in Engineering Sciences, 7(1), Article 1.
    7. Kienle, D., & Keip, M.-A. (2019). Modeling of hydraulically induced fractures in elastic-plastic solids. PAMM, 19(1), Article 1.
    8. Kienle, D., Aldakheel, F., & Keip, M.-A. (2019). A finite-strain phase-field approach to ductile failure of frictional materials. International Journal of Solids and Structures.
    9. Teichtmeister, S., Mauthe, S., & Miehe, C. (2019). Aspects of finite element formulations for the coupled problem of poroelasticity based on a canonical minimization principle. Computational Mechanics.


About this Project

Hydraulically induced fractures usually initiate at very small (microscopic) length scales and then merge to larger (macroscopic) crack discontinuities. The goal of the project is to resolve this inherent characteristic through the development of computational scale-bridging techniques for hydraulic fracturing of porous media. The project is divided in three steps: (i) Development of a general basis for the homogenization of porous media; (ii) Incorporation of a fracture phase-field at micro-scale; (iii) Incorporation of elastic-plastic effects at micro-level. The result will be a new quality in the modelling of hydraulic fracturing across length scales.


We have developed variationally consistent approaches to the computational homogenisation of hydro-mechanically coupled processes in porous solids based on minimisation-type variational principles. The considered models follow a Biot approach with Darcy flow coupled to a phase-field model of fracturing and are formulated in rate-type variational settings. The numerical implementation is based on conforming Raviart-Thomas finite elements.

© SFB 1313 / University of Stuttgart

Progressive rupturing of porous-elastic microstructure with stiff inclusions under tension and shear.

Hydrualically driven crack propagation in porous-elastic and porous-elastic-plastic solids under different injection rates of fluids.

Further phase-field models developed in the present project comprise ductile fracture models with and without hydraulic effects. The first model describes finite elasto-plasticity based on a Drucker–Prager yield criterion and could be applied to the simulation of rupturing processes in soils. The second model is a small-strain extension of the mentioned ductile phase-field model to hydraulic effects by using Biot’s theory of consolidation and a Darcy-type fluid-transport model. Based on numerical simulations, we could show that the consideration of plastic effects has a major influence on hydraulically induced crack propagation. In a third step, we are improving the description of the elastic-plastic behavior by considering the plasticity model of Wolfgang Ehlers (Project B02), then yielding an alternative, more enhanced phase-field formulation of rupturing soils.

Next to finite-element discretisations, we have considered numerical realisations using Fast-Fourier-Transform-based implementations. Here, we have developed simulation environments for both brittle- as well as hydraulic-fracture scenarios.

© SFB 1313 / University of Stuttgart

Stepwise rupturing of a brittle representative elementary volume based on a Fast-Fourier-Transform discretisation.

Future Work

Future work will concentrate on enhancing and further developing the phase-field models of fracturing, by making the multilevel homogenisation procedure both more efficient and comprehensive. Ours goals will further enhance the modeling capabilities of the phase-field models as well as improve and extend the multiscale modeling frameworks. All mentioned further developments and extensions will be carried out in close collaboration within the CRC in Project Area B and beyond.

For further information please contact

This image shows Marc-André Keip

Marc-André Keip

Prof. Dr.-Ing.

Principal Investigator, Research Project B01

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