Furio Lorenzo Stazi

Computational aspects of the mechanics of complex materials

SummaryBodies with exotic properties display material substructural complexity from nano to meso-level. Various models have been built up in condensed matter physics to represent the behavior of special classes of complex bodies. In general, they fall within the setting of an abstract model building framework which is not only a unifying structure of existing models but—above all—atool to construct special models of new exotic materials. We describe here basic elements of this framework, the one ofmultifield theories, trying to furnish a clear idea of the subtle theoretical and computational problems arising within it. We present the matter in a form that allows one to construct appropriate algorithms in special cases of physical interest. We discuss also issues related to the construction of compatible and mixed finite elements in linearized setting, the extension of extended finite element methods to analyze the influnce of material substructures on crack growth, the evolution of sharp discontinuity surfaces in complex bodies. Concrete examples of complex bodies are also presented with a number of details.

Strain localization in elastic micro-cracked bodies

Elastic micro-cracked bodies are analyzed within the setting of multifield theories. The presence of micro-cracks is evaluated through a vector order-parameter describing the perturbation induced by the micro-cracks on the displacement field. Numerical analyses are developed in two dimensions. They show localization phenomena, induced by micro-cracks, even in the case of linear constitutive equations which have been deduced from a lattice model by means of an equivalence procedure in terms of power.

Microcracked bodies with random properties: a preliminary investigation on localization phenomena

Abstract In a previous paper [Comp. Meth. Appl. Mech. Eng. 2001;190:5657–5677], it has been shown that in microcracked bodies strain localization phenomena appear even if the constitutive relations are linear and the microcracks are in elastic phase and do not grow. In this paper the constitutive properties of the body are assumed random, although uniform over the body. An example case in two dimensions is presented: its properties are assumed to be the mean values or fractiles of the probability distributions of the relevant coefficients, resulting from assumed distributions of the parent quantities. In all cases, strain localization is evident; however, the influence of the random variations, at least under the set hypotheses, appears small.

Semi-Dense And Concentrated Fullerene-Based Composites: Microdeformation and Strain Gradient Effects

Fullerenes are carbon micro-aggregates with closed-cage structure made of pentagons or hexagons. They are obtained through condensation of carbon vapor at different values of temperature and pressure, values that determine the geometry of the resulting structure. Their importance in technology is currently increasing due to a wide class of possible applications allowed by their mechanical and chemical properties. Typically, fullerene-based composites are sol-gel structures. When they are characterized by polymeric matrices, they may combine the optical and electronic properties of semiconductors with the mechanical features of polymers [1]. Fullerene-based composites may have inorganic or/and organic nature. Among them we may select for example • FulIerene/SiO2, • Fullerene/SiOa TiO2,

Linear elastic fullerene-based composites with random properties

Publisher Summary This chapter presents a continuum model for fullerene-based composites. The distance between neighboring molecules in the matrix is considered to be a random field over the body. Fullerenes are carbon-based macromolecules reminding of the shapes of vaults of Buckemister Fuller. A great effort is done in material science to investigate their properties and to construct appropriate predictive models of their behavior. Constitutive equations from a lattice model of the material element, by using an identification procedure are obtained. They depend on some internal lengths describing the dimensions of the fullerenes and the distance between neighboring molecules. Numerical analyses that are developed on two-dimensional samples are reported, and they show the influence of the presence of the fullerenes on the macroscopic strain, generating strain localization zones when the matrix of the composite is softer than the fullerenes.

Laws of Evolution of Cracks in Plates in Terms of Stress Resultants

The laws of evolution of a crack that starts at the edge of a plate and progresses toward its interior are derived in terms of stress and moment resultants written in the reference configuration of the plate. A modified form of the J-integral in terms of stress and moment resultants is also derived.