The lecture deals with the occurrence of self-similar and fractal patterns in the deformation, damage, and fatigue of cementitious and metallic materials, and with the consequent apparent scaling in their nominal mechanical properties. Such a scaling is negative (lacunar fractality) for tensile strength and fatigue limit, whereas it is positive (invasive fractality) for fracture energy, fracture toughness, and fatigue threshold. At the same time, corresponding fractal (or renormalized) quantities emerge, which are the true scale-invariant properties of the material. They appear to be the constant factor (the universal property) in the power-law relating the nominal canonical quantity to the size-scale of observation. In this fractal context, it is then possible to define a scale-invariant constitutive law: the so-called Fractal Cohesive Crack Model, in which stress and strain are defined over two orthogonal lacunar fractal sets and the fracture energy in an invasive fractal set that is the Cartesian product of the two previous lacunar sets. In addition, stress-intensity attenuation or mitigation with respect to the LEFM stress-singularity power ½ is considered, when the material is power-law strain-hardening, the sharp crack is replaced by a re-entrant corner (V-notch), and/or the crack faces are invasive (extremely rough) fractal sets. In all these cases, the stress-intensity factor assumes anomalous physical dimensions, which rule the scale-effect bilogarithmic diagrams with smaller slopes with respect to the most severe case of a sharp and smooth-faced crack in a linear elastic material. Particularly relevant applications are proposed to size effects on the fracture energy of concrete and the fatigue threshold of metals. As the former is demonstrated to be a power-law increasing with the specimen size, so the latter is shown to be a power-law decreasing by decreasing the crack length. A consistent explanation is provided to the short crack problem. As for rough cracks the invasive fractal sets are applied (dimension greater than 2), so for damaged cross-sections at peak load the lacunar fractal sets (dimension lower than 2) are considered. The tensile strength of concrete is proved to be a power-law with negative exponent, so that it decreases with the size of the specimen. Analogously, the fatigue limit of metals decreases by increasing the specimen size. All these trends are faithfully confirmed by extensive experimental results reported in the current literature.

High-fidelity damage assessment has potentially important applications in the design and retrofitting of civil engineering structures under service and extreme loading. Yet, despite huge advances in nonlinear structural analysis, empowered by developments in finite element analysis, constitutive modelling and damage mechanics, the utilisation of high-fidelity modelling for large-scale structures has been hampered by excessive computational demands in relation to both unrealistic run times and memory bottlenecks. This lecture presents recent developments undertaken by the author and his CSM Research Group at Imperial College London, which have been aimed at making high-fidelity damage assessment of real large-scale structural systems practicable. An advanced hierarchic domain decomposition method is described, which is shown to map directly onto the hierarchic nature of hardware resources in High Performance Computing systems, and which can effectively upgrade existing sequential finite element analysis programs with powerful parallel processing capabilities. This is supplemented with recent developments in macro- and meso-scale modelling of masonry structures, enabling the prediction of damage propagation in such structures, as well as phase-field modelling which is more generally applicable to other types of structure. Several applications of the developed capability, implemented within the nonlinear structural analysis program ADAPTIC, are presented to demonstrate the range of damage assessment problems that can be addressed effectively, with a particular focus on large-scale structural systems.

In this presentation, a detailed experimental investigation on the  uniaxial ratchetting-fatigue interaction  of extruded AZ31 Mg alloy is first conducted, including the macroscopic tests at room and elevated temperatures (i.e., 25°C, 100°C, 150°C, 200°C and 250°C)  and  with various stress levels by addressing the activation of single or multiple plastic deformation mechanisms (i.e., dislocation slipping, twinning, and detwinning), and  necessary microscopic  observations supporting  a mechanistic explanation for the complex ratchetting and corresponding fatigue failure of the alloy. Based on the microscopic and macroscopic experimental results, a new multi-mechanism damage-coupled constitutive model is then proposed to reproduce the whole-life ratchetting and predict the fatigue life of the AZ31 Mg alloy. During the construction of damage coupled constitutive model, a macroscopic multi-mechanism elastoplastic constitutive model is newly developed at first by considering the dislocation slipping and twinning/detwinning-induced plastic deformations, respectively, in the framework of small deformation; then, based on the observed characteristics of damage evolution at different temperatures and with various stress levels, a damage-coupled constitutive model is proposed by extending the developed multi-mechanism constitutive model within the framework of continuum damage mechanics, by considering pure fatigue damage and  an additional ratchetting  damage. This model gains a reasonable prediction to the whole-life ratchetting and fatigue life of the AZ31 Mg alloy at different temperatures, thus provides a theoretical guidance for the anti-fatigue design and safety assessment of Mg alloy components.

Damage in solids in the form of fractures, deformation bands, and pore collapse, depends on both the material constitutive response and the finite deformation experienced by the solid. In this talk, I will present a new finite deformation theory for a transversely isotropic elasto-plastic solid employing a multiplicative decomposition of the deformation gradient. The anisotropy of the solid is defined by a microstructure tensor describing the orientation of the plane of isotropy, which is allowed to evolve with the deformation of the solid matrix through a push-forward by the deformation gradient. A novelty of the formulation is the use of the left Cauchy-Green deformation tensor and the microstructure tensor in the current configuration, which leverages existing constitutive theories developed for the solid in the small deformation range. The new formulation considers anisotropy in both the elastic and plastic responses. Through numerical examples, I will show how this new formulation can be used to simulate folding of transversely isotropic sedimentary rocks, an intriguing problem in structural geology characterized by finite stretching/compression as well as finite rotation.

Traditional structural design methods in Aeronautics explore a very large number of design variables using simple models, suitably calibrated following decades of experience, as well as extensive experimental and simulation data. More detailed finite element models are eventually created to verify the design, but only once the design space has been very significantly reduced, and vast aspects of the design have been fixed. This process creates an obvious problem when moving away from the design space for which the simple models used at the start of this process were calibrated. In this talk, we will explore various research avenues to mitigate this, including detailed finite element models of very large aircraft structures that have the capability to represent the detail required to predict likely damage hotspots in structural components such as a wing, models where the discretisation and the design variables can evolve during the  analysis as required, as well as surrogate models for damage in novel structural concepts using machine learning.

Fracture and damage mechanics are two main directions that are in use to understand failure of materials. Fracture mechanics requires a pre-existing macroscopic crack and structural failure is attributed to growth of single or several cracks. Hence, it makes it difficult to describe nucleation and subsequent coalescence of voids to form macrocracks. On the other hand, damage mechanics describes macrocracks as local loss of material integrity, which are due to the growth and coalescence of microdefects. Current numerical methods used to model damage/fracture in materials include finite element method, boundary element method, meshless methods and extended finite element, to name a few. When applied to fracture mechanics, the aforementioned requires conforming mesh combined with local adaptive refinement or enrichment functions to capture the fracture parameters. When applied to classical damage mechanics models, the numerical results suffer from mesh sensitivity. To alleviate this, nonlocal gradient and integral type damage models have been developed. Scaled boundary finite element is a semi-analytical approach introduced especially for unbounded problems. It shares the advantages of the boundary element method (BEM) and the finite element method (FEM). Like the BEM, only the boundary is discretized and like the FEM it does require Green's function. Due to its salient feature it is now adopted to a wider variety of bounded domain problems. Also, it can accommodate elements of arbitrary shapes and sizes. The presence of hanging nodes within quadtree/octree decomposition is handled by the SBFEM framework without requiring additional constraints/special shape functions. This talk will focus on the application of the scaled boundary finite element method to model cracks in materials based on fracture and damage mechanics. The computational advantage of the method, robustness and accuracy will be demonstrated with a few examples.

Structural reliability assessments critically depend on understanding material damage. Concrete, inherently heterogeneous with random features, exhibits stochastic constitutive behavior driven by these heterogeneities. Over the past two decades, we have pioneered the Stochastic Damage Mechanics (SDM) framework specifically for concrete. Rooted in continuum damage mechanics, the SDM framework explicitly incorporates material randomness across scales, utilizing multi-level uncertainty quantification to characterize the nuanced progression of damage. This presentation will highlight recent progress within the SDM framework, including time-dependent damage modeling, random fields on manifolds, and mechanics-based modeling of 3-D printed concrete structures. Finally, future perspectives for advancing stochastic damage mechanics of concrete will be outlined.

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