Research Project B01

This project aims at the development of multi-scale continuum models of fluid-driven thermo-elasto-plastic fracturing porous media. Our objective is to investigate, understand, and predict fluid-flow processes and fluid-driven fracturing in heterogeneous porous solids by means of efficient and reliable computational frameworks. To accomplish this, we have developed a phase-field model for the description of the hydraulic fracturing of porous materials exhibiting non-linear and non-associative poro-elasto-plastic response. Furthermore, we established variationally consistent first- and second-order computational-homogenisation schemes for the description of transient hydro-mechanical processes. By means of these frameworks, we are able to describe complex inelastic hydro-mechanical coupling responses of fracturing porous materials across scales.

During FP 1, we contributed phenomenological and multi-scale methods for the description of deformable porous media with a focus on the fracturing of elastic-plastic porous solids. On the phenomenological side, our project group developed computational models for porous media at large strains as well as for the hydraulic fracturing of brittle and ductile materials. The proposed models were derived within a variational minimisation structure, so that they are not subject to inf-sup instabilities and yield numerically efficient implementations. On the side of multi-scale modelling, we developed a first-order homogenisation framework for the description of transient deformation-diffusion processes at finite strains and fracturing across scales (see Figure 1).

In a continuing effort, in FP 2 we have been extending the multi-scale frameworks to higher-order formulations of fluid flow through heterogeneous porous media. In this context, we have established a second-grade phenomenological model and contributed two higher-order multi-scale models: (i) a two-scale model for generalized materials at large strains in collaboration with colleagues from the University of Siegen; (ii) a two-scale model for the nonlinear fluid flow through heterogeneous porous media across non-separated scales. Given the relaxed principle of scale separation and the associated gradient extensions, the latter models are essential to describe fracture propagation across scales and materials that have heterogeneities of size comparable to the scale of application. In addition to the mentioned activities, we contributed a phase-field model for fracture propagation in soft materials in collaboration with colleagues from the Robert Bosch GmbH and proposed a phase-field model for stochastic crack propagation in collaboration with B04. A more recent milestone has been reached by establishing a poro-elasto-dynamic model with variational minimisation structure. The latter framework enables us to investigate wave propagation in porous materials and will be extended to fracture propagation under dynamic loading within the current funding period. It furthermore serves as a fundamental step in the direction of the research planned for FP 3.

In FP 3, our objective is to develop efficient and predictive computational multi-scale models for the dynamic thermo-hydro-mechanical response of porous media across pore and REV scales. The conceptual basis will be formed by a finite-strain thermo-poro-elastic model that we have been developing in collaboration with B02. In FP 3 we will embed the developed model in a variationally consistent setting and extend it to a second-grade formulation of a phase-field model of fracturing.

Furthermore, we will employ the second-order multi-scale model for the homogenisation of the pore scale. The resulting model will enable us to account for the hydro-mechanical characterisation of REVs at different stages of salt precipitation. Potential salt-nucleation sites will be explored in collaboration with A01. The pore-scale properties and morphologies will be obtained from the experiments conducted by Z02. The insights gained from the homogenised mechanical and hydraulic properties will be valuable for understanding calcite precipitation during bio-cementation explored in C04.

In a final step, we intend to establish a gradient-extended dynamic model coupled with a phase-field model of fracturing. Here, we plan to collaborate with B03 on the modelling of wave propagation in fracturing porous materials using diffuse- and sharp-interface models. A wide range of excitation frequencies will be investigated and compared to experimental studies of B05.