A procedure for the stochastic characterization of the elastic moduli of plane irregular masonry structures is presented in this paper. It works in the field of the random composite materials by considering the masonry as a mixture of stones (or bricks) and mortars. Once that the elastic properties of each constituent are known (deterministically or stochastically), the definition of the overall masonry elastic properties requires the knowledge of the random field describing the irregular geometry distribution. This last one is obtained by a software, implemented ad hoc, that, starting from a colour digital photo of the masonry and using the instruments of the digital image processing techniques, gives the random features of this field in both the space and frequency domain. The definition of the stochastic properties of masonry structures may be very useful both for the application of the stochastic homogenization techniques and for the direct stochastic analysis of the structures.

The effect of microstructural properties on the wave dispersion in linear elastic membranes is addressed in this paper. A periodic spring-mass lattice at the lower level of observation is continualized and a gradient-enriched membrane model is obtained to account for the characteristic microstructural length scale of the material. In the first part of this study, analytical investigations show that the proposed model is able to correctly capture the physical phenomena of wave dispersion in microstructured membrane which is overlooked by classical continuum theories. In the second part, a finite-element discretization of microstructured membrane is formulated by introducing the pertinent inertia and stiffness terms. Importantly, the proposed modifications do not increase the size of the problem compared wiith classical elasticity. Numerical simulations confirm that the vibrational properties are affected by the microstructural characteristics of the material, particularly in the high-frequency regime.

SUMMARYContinuum theories can be equipped with additional inertia terms to make them capable of capturing wave dispersion effects observed in micro-structured materials. Such terms, often called micro-inertia, are convenient and straightforward extensions of classical continuum theories. Furthermore, the critical time step is usually increased via the inclusion of micro-inertia. However, the drawback exists that standard finite element discretisation leads to mass matrices that cannot be lumped without losing the micro-inertia terms. In this paper, we will develop a solution algorithm based on Neumann expansions by which this disadvantage is avoided altogether. The micro-inertia terms are translated into modifications of the residual force vector, so that the system matrix is the usual lumped mass matrix and all advantages of explicit time integration are maintained. The numerical stability of the algorithm and its effect on the dispersive properties of the model are studied in detail. Numerical examples are used to illustrate the various aspects of the algorithm.

Additional Information:• This is the author's version of a work that was accepted for publication in AbstractThe dynamic behaviour of periodic lattice materials is investigated using an equivalent higher-order continuum model obtained by homogenisation of the equations of motion. A gradient continuum enriched with higher-order inertia terms is developed using a combination of finite element discretisation of the unit cell and the continualisation approach. The analysis of the dispersion relations shows that the proposed model is able to capture correctly the physical phenomenon of wave dispersion in lattice structures which is overlooked by classical continuum theories.

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