Bernardino Chiaia

Incipient sliding of rough surfaces in contact: a multiscale numerical analysis

In this paper, the Cattaneo theory of frictional contact is extended to elastic half-spaces in contact through rough disordered interfaces. The discrete version of the Cattaneo theorem is provided, and represents the basis of a multiscale numerical contact algorithm. Mathematical surfaces with imposed roughness, as well as experimentally digitised ones, are analysed. By means of a numerical method, the evolution of the contact domain, at different resolution, is investigated. Roughness of the interfaces provides lacunarity of the contact domains, whose fractal dimension is always smaller than 2.0. When a tangential force is applied, the extent of the stick area decreases in the same way as the contact area develops with increasing pressure, and the slip area is found to be proportional to the tangential force, as predicted by Cattaneo theory. The evolution of the shear centroid, as well as the amount of dissipated energy up to full-sliding, are provided. Finally, it is shown that, at a sufficient level of discretization, the distribution of contact pressures is multifractal.

Fracture mechanisms induced in a brittle material by a hard cutting indenter

The process of indentation of brittle and quasi-brittle materials has been extensively investigated both from the experimental and the theoretical point of view. Also, the elastic stress fields induced by sliding bodies are well known and have been used to predict fracture patterns below moving contacts. Quite surprisingly, only a few studies have tried to explain the mechanics of cutting due to an indenter which penetrates inside the material. In this paper, an attempt is made to find some general relations for the cutting process in quasi-brittle materials, under different hypotheses for the microscopic failure behaviour, namely a simple frictional mechanism, plastic crushing and linear elastic fracture mechanics. These mechanisms interact with each other, and provide a particular load-penetration law and a peculiar cutting advancement. Some numerical simulations by the lattice model have been also carried out, in order to verify the assumptions. Dimensional analysis permits to highlight remarkable size-scale effects on the cutting strength and provides some hints for enhancing the performances of cutting tools.

On the sliding instabilities at rough surfaces

Abstract In this paper, the onset of sliding between two elastic half-spaces in contact, subjected to a tangential force, is studied within the framework of critical phenomena. First, it is shown that the contact domain between two rough surfaces is a lacunar set and that the distribution of contact stresses is multifractal. By applying an increasing tangential force, under constant normal load, the so-called regime of partial-slip comes into play. However, the continuous and smooth transition to full sliding, predicted by the classical Cattaneo–Mindlin theory, is not confirmed by the experiments, which show marked frictional instabilities. A numerical multi-scale procedure is proposed, taking into account the redistribution of stress, consequent to partial-slip, among the contact areas at all scales. It is shown that the lacunarity of the contact domain delays the onset of instability, when compared to compact Euclidean domains. Independently of the assumptions made for the frictional behaviour at the scale of the asperities (Coulomb friction for meso-scale asperities, adhesion for micro-scales), renormalization permits the critical value of the tangential force which provides the instability to be found. Moreover, the multifractal analysis of the domains where the shear resistance is activated captures the size-scale effects on the friction coefficient, currently evidenced by the experiments.

Embrittlement and decrease of apparent strength in large-sized concrete structures

The problem of scale-effects on the performances of concrete structures is discussed. Experimentally observed decrease of nominal tensile strength, accompanied by structural embrittlement, occurring in large structures is of crucial importance in modern concrete engineering. Most of the previous approaches to the problem are restricted to notched structures and they often fail to predict mechanical behaviour in real situations. The physical approach put forward by us takes into adequate account the effects of microstructural disorder and seems to be valid in the whole size range, at least for unnotched structures. Thereby, reliable predictions can be made of the material properties in large-sized concrete structures.

Golden ratio in the crack pattern of reinforced concrete structures

Among all the proportions, the golden ratio has been taken into consideration for its geometrical and morphological properties, which can be found in a huge number of natural patterns, and therefore has been always considered as a model of beauty. Nevertheless, as discussed for the first time in the present paper, the cracking phenomenon of quasi-brittle materials also brings the golden ratio into play. In particular, such an irrational number appears when the average crack spacing of RC ties and beams is evaluated at different scales. This conjecture is corroborated by the results of a tension-stiffening model capable of predicting both the crack width and the crack spacing measured by the tests. In other words, it can be argued that the centrality of the golden ratio in the crack pattern of concrete members has profound physical meanings and reveals the existence of a size-effect law of crack spacing. The practical interest of this law lies in the possibility of predicting the crack pattern of large structures without knowing the material performances but by testing prototypes of the lower dimensions.

Hierarchical Structures for a Robustness-Oriented Capacity Design

In this paper, we study the response of 2D framed structures made of rectangular cells, to the sudden removal of columns. We employ a simulation algorithm based on the Discrete Element Method, where the structural elements are represented by elasto-plastic Euler Bernoulli beams with elongation-rotation failure threshold. The effect of structural cell slenderness and of topological hierarchy on the dynamic residual strength after damage

Energy-Based Study of Structures Under Accidental Damage

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Scaling in structural complexity

is investigated. Topologically textit{hierarchical} frames have a primary structure made of few massive elements, while textit{homogeneous} frames are made of many thin elements. We also show how

Stochastic reliability based design criteria for linear structure subject to random vibrations

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Robustness-Oriented Design of a Panel-Based Shelter System in Critical Sites

depends on the activated collapse mechanisms, which are determined by the mechanical hierarchy between beams and columns, i.e. by their relative strength and stiffness. Finally, principles of robustness-oriented capacity design which seem to be in contrast to the conventional anti-seismic capacity design are addressed.