A Micromechanical Model and Reinforcing Distribution Optimisation in Fibre-Reinforced Materials

The use of composite materials has known a crescent interest in the last decades in many application fields due to their desirable mechanical characteristics such as high specific strength and stiffness, high fracture and fatigue resistance, high wear resistance, high damping durability performance, low thermal coefficient, and so on. For the above mentioned reasons composite materials replace or strategically compliment other traditional structural materials. The extensive use of advanced materials such as composite materials, requires to describe, with an appropriate accuracy, their overall mechanical behaviour to correctly assess the safety level of structural components in the design process. In the present chapter the problem of the description of the macroscopic mechanical characteristics of such a class of materials is considered. The behaviour of fibre-reinforced composites (FRC) is examined through the formulation of a micromechanical-based model. The macro constitutive equations for such a class of materials, composed by a matrix phase, for which an elastic-plastic behaviour is eventually allowed, and a fibre-reinforcing phase, is obtained through a micro mechanical model which takes into account the possibility of an imperfect bond between the matrix and the fibres. A two-parameters mechanical model, obtained from energetic considerations and by considering the evolution of the shear stress distribution along a single fibre during the loading process, is formulated to determine the entity of the debonding and its mechanical influence, from a macroscopic point of view, on the composite material. The detailed aspects of the mechanical model are presented and discussed and its implementation in a 2D FE code is finally illustrated. In the second part of the chapter the problem of the optimal content distribution of fibres in a fibre-reinforced composites, in order to maximise or minimise a given objective function and by assuming some suitable constraints, is investigated by using a biological-based procedure known as Genetic Algorithm (GA). The evolution process simulated by the developed algorithm, can be performed in order to get the maximisation or minimisation of some mechanical desired performance of the structure (stiffness, compliance, peak stress, etc) by keeping constant the total fibres content (optimal constrained problem). The proposed mechanical model with the optimisation algorithm is finally used in some numerical simulations in order to assess its reliability in material design composition with respect to some expected optimal performance, and quantitative comparisons – in term of the improvements with respect to classical homogeneously distributed fibres situations – is finally illustrated and quantified.