Micromechanical analysis of periodic composites by prescribing the average stress

Abstract

A new method for the micromechanical finite element analysis of unidirectional composites is presented. The method is especially effective in time-dependent analyses, as those involving viscoplasticity and viscoelasticity. The microstructure of the composites under consideration is characterized by periodicity and central symmetry, which allow analysing half of a unit cell for solving the micromechanical problem. Half of the unit cell contains only half of the continuous fibre and this makes the numerical analyses inexpensive in terms of computer memory usage and processing time. New boundary conditions are presented in order to prescribe the average stress on half of the unit cell of hexagonal and rectangular distributions of heterogeneities in the case of static analysis. Then, the new boundary conditions are used to prescribe the precise rate of the average stress in time-dependent analyses. With respect to other existing procedures, the proposed method is easy to adopt in commercial software and it does not require the modification of parts of the source code that are not usually accessible to the user. The proposed method is applied to the interesting case of composites with aligned long fibres imperfectly bonded to a viscoelastic matrix. The numerical simulations carried out in this work provide the loci of the average stress and strain corresponding to the initiation of the fibre-matrix debonding, which determines a considerable decay of the composite stiffness and strength. The influence of the geometrical properties of the microstructure is evaluated by analysing both hexagonal and rectangular distributions of fibres. The numerical results show how the inelastic behaviour of the matrix affects the loci corresponding to the initiation of the debonding.

Initiation of Failure for Masonry Subject to In-Plane Loads through Micromechanics

“…The following analyses are performed on the representative volume element. Instead of modelling the masonry as a random composite material (see, e.g., [31][32][33][34][35][36]), it is assumed that the constituents are arranged in a periodic way [37][38][39][40][41][42][43][44][45] and a unit cell is adopted as the representative volume element. The masonry considered in this work is shown in Figure 1, where a wall is depicted.…”

A micromechanical four-phase model to predict the compressive failure surface of cement concrete

“…icromechanical methods [1][2][3] have been widely used to homogenize fiber reinforced composites such as FRP, frequently employed to strengthen existing structures made of concrete [4][5][6][7][8]. Micromechanics has also been adopted for the analysis of different types of heterogeneous materials such as masonry arrangements [9,10] and cement concrete [11][12][13][14][15][16].…”