The so-called Complexity Sciences are a topic of fast growing interest inside the scientific community. Actually, researchers did not come to a definition of complexity, since it manifests itself in so many different ways [1]. This field itself is not a single discipline, but rather a heterogeneous amalgam of different techniques of mathematics and science. In fact, under the label of Complexity Sciences we comprehend a large variety of approaches: nonlinear dynamics, deterministic chaos theory, nonequilibrium thermodynamics, fractal geometry, intermediate asymptotics, complete and incomplete similarity, renormalization group theory, catastrophe theory, self-organized criticality, neural networks, cellular automata, fuzzy logic, etc. Aim of this paper is at providing insight into the role of complexity in the field of Materials Science and Fracture Mechanics [2-3]. The presented examples will be concerned with the snap-back instabilities in the structural behaviour of composite structures (Carpinteri [4-6]), the occurrence of fractal patterns and self-similarity in material damage and deformation of heterogeneous materials, and the apparent scaling on the nominal mechanical properties of disordered materials (Carpinteri [7,8]). Further examples will deal with criticality in the acoustic emissions of damaged structures and with scaling in the time-to-failure (Carpinteri et al. [9]). Eventually, results on the transition towards chaos in the dynamics of cracked beams will be reported (Carpinteri and Pugno [10,11]).

The use of a gasket made in soft material is not recommended for large size centrifugal compressor case flanges. The two case halves are assembled with bolted flanges and the leakage is prevented by the “metal–to–metal” contact of the flange surfaces. The prediction of the leakage condition is an important engineering challenge for this technology. A new model to predict the leakage condition, based on Fracture Mechanics, is here presented. The partially open flange surfaces interface can be regarded as a partially open crack. The Stress Intensity Factor of a partially open crack is zero, since the flange surfaces can not transfer tensile traction, being just in contact (not “glue” or “welded”). The extension of the open zone, i.e. the crack length, can be obtained imposing the zero Stress Intensity Factor condition. The leakage is expected as the flange surface open front reaches the bolt hole, that produces a way out path for the internal pressurized fluid. By means of the weight functions analytical technique, the leakage pressure can be calculated. The proposed model was then successfully validated by means of both numerical simulations and full scale and small scale experimental tests. The proposed analytical model can be used to compare different flange geometries and then it is a useful design tool.

The theory of critical distances (TCD) has been applied to predict notch-based fracture and fatigue in a wide range of materials and components. The present paper describes a series of projects in which we applied this approach to human bone. Using experimental data from the literature, combined with finite element analysis, we showed that the TCD was able to predict the effect of notches and holes on the strength of bone failing in brittle fracture due to monotonic loading, in different loading regimes. Bone also displays short crack effects, leading to R-curve data for both fracture toughness and fatigue crack propagation thresholds; we showed that the TCD could predict this data. This analysis raised a number of questions for discussion, such as the significance of the L value itself in this and other materials. Finally, we applied the TCD to a practical problem in orthopaedic surgery: the management of bone defects, showing that predictions could be made which would enable surgeons to decide on whether a bone graft material would be needed to repair a defect, and to specify what mechanical properties this material should have.

In this study, a generalized Barenblatt and Botvina dimensional analysis approach to fatigue crack growth is proposed in order to highlight and explain the deviations from the classical power-law equations used to characterize the fatigue behaviour of quasi-brittle materials. According to this theoretical approach, the microstructural-size (related to the volumetric content of fibres in fibre-reinforced concrete), the crack-size, and the size-scale effects on the Paris’ law and the Wöhler equation are presented within a unified mathematical framework. Relevant experimental results taken from the literature are used to confirm the theoretical trends and to determine the values of the incomplete self-similarity exponents. All these information are expected to be useful for the design of experiments, since the role of the different dimensionless numbers governing the phenomenon of fatigue is herein elucidated.

In this research work by changing different parameters of soil foundation like density, cohesion and foundation depth and width of square foundation at angle of friction of 0? to 50? with increment of 5?, numerically safe bearing capacity of soil foundation is calculated and it is attempted to assess economical dimension of foundation as well as understanding variation range of bearing capacity at different degree. It could help of civil engineering in design of foundations at any situation.

The high ductility of Fiber Reinforced Self-consolidating concrete (called Sismabeton) can be developed not only in tension but also in compression. This aspect is evidenced in the present paper by measuring the mechanical response of normal concrete (NC), plain self-compacting concrete (SC) and Sismabeton cylindrical specimens under uniaxial and triaxial compression. The post-peak behaviour of these specimens is defined by a non-dimensional function that relates the inelastic displacement and the relative stress during softening. Both for NC and SC, the increase of the fracture toughness with the confinement stress is observed. Conversely, Sismabeton shows, even in absence of confinement, practically the same ductility measured in normal and self-compacting concretes with a confining pressure. Thus, the presence of Sismabeton in compressed columns is itself sufficient to create a sort of active distributed confinement.

Metal-ceramic composites represent a class of quasi-brittle materials for advanced structural applications that require adequate mechanical characterization. Difficulties and costs associated with material production and specimen extraction prevent the execution of a statistically meaningful number of standard laboratory tests. Parameter calibration methodologies based on instrumented indentation and inverse analysis represent fast and reliable identification procedures in the present context, as shown by the present contribution, based on some experience achieved in the framework of the European Network of Excellence on ‘Knowledge-based Multi-component Materials for durable and safe performance’ (KMM-NoE).

In this work, Cohesive Zone Modelling (CZM) was used to simulate failure of T-peel bonded joints with 1.5mm thick adherends, respectively, bonded toghether with Loctite Multibond 330 adhesive. The fracture toughness and load-opening behaviour recorded in previous experiments on bonded Double Cantilever Beam (DCB) specimens were taken as reference to calibrate CZM parameters. Two-dimensional models were analysed using the FE code ABAQUS. The failing interface was modeled with the cohesive elements available in this software. The influence of: i) different cohesive law shapes, ii) modeling the presence of the adhesive layer explicitly, was studied.

This paper is concerned with the fracture of composite materials containing stress concentration features such as notches and holes. In particular, it addresses the question of the use of the Theory of Critical Distances (TCD) – a method which is widely used for predicting notch effects in fatigue and fracture. The TCD makes use of a length constant, L, known as the critical distance, which is normally assumed to be a material property. However, many workers in the field of composite materials have suggested that the critical distance is not a constant, but rather is a function of notch size. I examined the evidence for this assertion, and concluded that it arises for four different reasons, two of which (process zone size and constraint) are real material effects whilst the other two (choice of test specimen and estimation of the stress field) arise due to errors in making the assessments. From a practical point of view, the assumption of a constant value for L leads to only small errors, so it is recommended for engineering design purposes.