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Phase-field modeling of fracture has gained popularity within the last decade due to the flexibility of the related computational framework in simulating three-dimensional arbitrarily complicated fracture processes. However, the numerical predictions are greatly affected by the presence of uncertainties in the mechanical properties of the material originating from unresolved heterogeneities and the use of noisy experimental data. The objective of this work is to apply the Bayesian approach to estimate bulk and shear moduli, tensile strength and fracture toughness of the phase-field model, thus improving accuracy of the simulations with the help of experimental data. Conventional approaches for estimating the Bayesian posterior probability density function adopt sampling schemes, which often require a large amount of model estimations to achieve the desired convergence, thus resulting in a high computational cost. In order to alleviate this problem, we employ a more efficient approach called sampling-free linear Bayesian update, which relies on the evaluation of the conditional expectation of parameters given experimental data. We identify the mechanical properties of cement mortar by conditioning on the experimental data of the three-point bending test (observations) in an online and offline manner. In the online approach the parameter values are sequentially updated on the fly as the new experimental information comes in. In contrast, the offline approach is used only when the whole history of experimental data is provided once the experiment is performed. Both versions of estimation are discussed and compared by validating the phase-field fracture model on an unused set of experimental data. [ABSTRACT FROM AUTHOR]

The difficulties in dealing with discontinuities related to a sharp crack are overcome in the phase-field approach for fracture by modeling the crack as a diffusive object being described by a continuous field having high gradients. The discrete crack limit case is approached for a small length-scale parameter that controls the width of the transition region between the fully broken and the undamaged phases. From a computational standpoint, this necessitates fine meshes, at least locally, in order to accurately resolve the phase-field profile. In the classical approach, phase-field models are computed on a fixed mesh that is a priori refined in the areas where the crack is expected to propagate. This on the other hand curbs the convenience of using phase-field models for unknown crack paths and its ability to handle complex crack propagation patterns. In this work, we overcome this issue by employing the multi-level hp-refinement technique that enables a dynamically changing mesh which in turn allows the refinement to remain local at singularities and high gradients without problems of hanging nodes. Yet, in case of complex geometries, mesh generation and in particular local refinement becomes non-trivial. We address this issue by integrating a two-dimensional phase-field framework for brittle fracture with the finite cell method (FCM). The FCM based on high-order finite elements is a non-geometry-conforming discretization technique wherein the physical domain is embedded into a larger fictitious domain of simple geometry that can be easily discretized. This facilitates mesh generation for complex geometries and supports local refinement. Numerical examples including a comparison to a validation experiment illustrate the applicability of the multi-level hp-refinement and the FCM in the context of phase-field simulations. [ABSTRACT FROM AUTHOR]

We propose a mechanical and computational model to describe the coupled problem of poromechanics and cracking in variably saturated porous media. A classical poromechanical formulation is adopted and coupled with a phase-field formulation for the fracture problem. The latter has the advantage of being able to reproduce arbitrarily complex crack paths without introducing discontinuities on a fixed mesh. The obtained simulation results show good qualitative agreement with desiccation experiments on soils from the literature. [ABSTRACT FROM AUTHOR]