Abstract
The focus of the present contribution is on the numerical modelling of hydraulic fracture in fluid-saturated heterogeneous materials, which can be carried out on a macroscopic scale using extended continuum porous media theories. This accounts for the crack nucleation and propagation, deformation of the solid matrix and change in the flow of the interstitial fluid. In particular, fluid-saturated porous materials basically represent volumetrically interacting solid-fluid aggregates, which are modelled using the Theory of Porous Media. The hydraulic- or tension-induced fracture occurs in the solid matrix and is simulated using a diffusive phase-field modelling approach. This way of fracture treatment adds a partial differential equation of the phase-field evolution to the coupled solid-fluid problem, which requires special stabilisation techniques in the numerical calculation. A numerical example is also presented to demonstrate this way of fracture handling.
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Notes
- 1.
For a scalar value a, the Heaviside step function \(H(a) =\{\, 0\,\,\,\mbox{ if}\,\,\,a < 0,\,\,\mbox{ and}\,\,\,1\,\,\,\mbox{ if}\,a \geq 0\}\).
- 2.
A software for FE solutions of partial differential equations, see www.pdesolutions.com.
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Markert, B., Heider, Y. (2015). Coupled Multi-Field Continuum Methods for Porous Media Fracture. In: Mehl, M., Bischoff, M., Schäfer, M. (eds) Recent Trends in Computational Engineering - CE2014. Lecture Notes in Computational Science and Engineering, vol 105. Springer, Cham. https://doi.org/10.1007/978-3-319-22997-3_10
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