The paper describes a simple identification procedure that can be used to construct a function relating the increased diffusivity or permeability to the current mechanical state of the material, based on an experimentally determined relation between the excess flux along the crack and the crack opening. The underlying mechanical model belongs to the class of phase-field formulations (or variational damage models) for quasibrittle materials, but the procedure would be applicable to other types of regularized failure models as well.

Interfacial properties in layered microstructures such as composites, rocks, and 3D-printed brittle materials play a significant role in bulk fracture and failure mechanisms, and are critical for the purposeful design of toughening mechanisms in architected materials. Capturing the role of the interface in crack propagation of layered materials is challenging due to the need to incorporate interface elements within the bulk while accounting for bulk fracture. A coupled phase-field and CZM framework, previously developed by authors for crack impinging on an interface, was used to numerically examine the significance of including vs. excluding the weak interface for accurate prediction of crack propagation in layered and functionally graded materials. The crack penetration and deflection scenarios were examined and compared with LEFM theory for a crack tip present in the bulk. It was found that the framework accurately captures the fracture and crack-interface interaction when the crack is present in the bulk, while exclusion of the interface led to inaccurate fracture response. Interfacial failure (i.e., debonding) in the case of crack deflection provides significant energy dissipation (toughness) —17 times greater compared to penetration and 4 times greater compared to the case where the interface is excluded. These dissipative mechanisms from crack-interface interaction can help engineer tougher layered composites. A strategically engineered weak interface can effectively redirect crack propagation, transforming a catastrophic penetration failure into a more controlled deflection mechanism.

The behaviour of concrete is greatly influenced by its internal composition. Unlike brittle materials, concrete and other quasi-brittle materials have a larger fracture process zone due to the presence of microcracks. Traditional analysis methods may fail to account for the effects of its heterogeneous structure. Experimentally, this heterogeneity results in variabilities in the global response, such as peak load and post-peak behaviour. To address this, we propose a novel cohesive phase field model for analyzing quasi-brittle fractures in concrete, treating the material behaviour as a generalized continuum. This model considers the deformation of the material’s internal structure at the continuum level, assuming it can undergo finite rigid rotation, characteristic of a micropolar continuum. This framework can be extended to more complex behaviours such as micro stretch and micromorphic continuum. The model’s elastic response is insensitive to the smoothing length scale, which is introduced to approximate the sharp crack topology with a continuous scalar field variable. Our model introduces additional length scales related to bending and torsional rigidity, allowing for a better representation of size-dependent effects in concrete. We demonstrate the impact of various parameters in our formulation on matching experimental data. The variation of these parameters highlights the variations in internal structure, offering insights into how the additional parameters relate to the material’s varying internal structure.

The modelling of cracking behaviour of reinforced concrete (RC) structures represents an intricate challenge because of the heterogeneity of the concrete properties and the complex relationship between concrete and its reinforcement. While experimental methods are limited to inspecting deformations and cracks merely on the concrete’s surface, analytical approaches usually assume simplifications as homogeneity of the concrete properties or constant deformation along the concrete section. Concrete’s heterogeneous nature, where crack nucleation and propagation are governed by local material properties, introduces uncertainty in mechanical behaviour affecting structural safety, making finite element modelling with varying material properties more suitable for accurately capturing these effects.

The focus of this study is to develop a numerical tool capable of predicting the cracking behaviour of concrete elements reinforced with steel bars subjected to tension. To that aim, finite element models were developed in ABAQUS using a phase field approach to simulate a RC tie element with a single centred steel bar. A stochastic random field was implemented to account for the variability of the concrete’s tensile strength. Furthermore, the effectiveness of several techniques to model the concrete-to-steel bond such as a bilinear cohesive interface interaction and a rib-scale model was evaluated. Numerical models with different material field configurations were used to investigate the in-depth variability in cracking patterns and deformations. The numerical results were compared with available experimental results in the literature to validate the proposed model, confirming that the method can effectively model the mechanical behaviour and predict the crack formation stage of RC elements under tensile loading.

Understanding crack propagation in concrete across different length scales is essential for capturing the intricate failure mechanisms that arise from its highly heterogeneous structure. However, fracture simulations in concrete often have significant computational costs and implementation difficulties. Phase-field models address these challenges by capturing crack phenomena, such as nucleation and propagation while maintaining easiness in implementation. Despite the advantages of phase-field models, their application to fracture analysis of concrete at multiple length scales is limited. Existing phase field models often face substantial computational costs while accounting for material heterogeneity. To address these challenges, a multiscale phase-field fracture study is presented in this work. The focus of the study is to model heterogeneity while maintaining computational efficiency. The first part of this work focuses on generating the meso-scale structure of concrete. This includes considering meso-scale features such as aggregate volume fraction, the interfacial transition zone, and air voids. The second part addresses formulating the multiscale phase-field fracture problem. A three-point bending test is conducted to investigate the fracture phenomena in
detail. meso-scale crack toughening mechanisms, such as aggregate bridging and crack deflection, were observed in the model. The fracture energy and tensile strength values are investigated in detail. Finally, the accuracy of the presented model is evaluated by comparing the load-displacement data with experimental results. The findings of this study provide valuable insights for developing more efficient and scalable phase field modelling approaches for fracture phenomena in concrete.