Numerical derivation of homogenized dynamic masonry material properties with strain rate effects

Masonry is a composite material composed of bricks and mortar disposed in a regular arrangement. It is commonly used as load bearing or partition walls in building structures. Owing to limitations of computer power, detailed distinctive modelling of brick and mortar of a realistic masonry structure or a structure with masonry infilled walls is usually not possible. Moreover, no dynamic masonry material model can be found in the open literature. Dynamic masonry material properties are important for an accurate prediction of masonry failure and fragmentation under dynamic loads. In this paper, a continuum damage model with strain rate effect is developed for masonry materials based on the homogenization method. The equivalent elastic properties, strength envelope and dynamic increase factors (DIFs) of strength and moduli for the homogenized masonry material are numerically derived from the simulated responses of a representative volume element (RVE). A numerical model of an RVE is analyzed with detailed distinctive modelling of brick and mortar with their respective dynamic material properties obtained from laboratory tests. The homogenized material model can be used to analyse large-scale masonry structures subjected to dynamic loading.     

New methods for estimating the torsional rigidity of composite bars

We obtain general bounds on the torsional rigidity and give examples on how these bounds can be used to obtain estimates and simple formulae which yield more accurate information than the classical treatment. Moreover, we use the homogenization theory to estimate the limit of the torsional rigidity when the characteristic length of the composite microstructures decreases.     

Acoustical and optical branches of wave propagation in random particulate composites

The work is dedicated to the analysis of acoustical and optical branches of longitudinal elastic wave propagation in the medium with a random set of spherical inclusions. The effective field method and quasicrystalline approximation are used for the construction of the dispersion equation for the wave number of the mean (coherent) wave field propagating in the composite. This dispersion equation serves for all frequencies of the incident field, properties and volume concentrations of inclusions. Different branches of the solutions of this equation are obtained and analyzed. Each of these branches may be interpreted as a specific mode of wave propagation, and its input in the mean (coherent) wave field is essential only in a certain frequency region. The predictions of the method are compared with some experimental data existing in the literature.     

Some numerical simulations of large deformations of heterogeneous hyperelastic media

Numerical experiments done on a two-dimensional stratified two-phase composite corroborate theoretical results on homogeneization of media capable of large deformations.     

Analysis of the effects of rough surfaces in compressible thin film flow by homogenization

A classical problem in lubrication theory is to predict the pressure distribution in a thin fluid film between two surfaces which are in relative motion. If one of the surfaces is rough, then the distance between the surfaces is rapidly oscillating. This leads to that the governing Reynolds partial differential equation involves rapidly oscillating coefficients. The branch in mathematics which considers such types of equations is known as homogenization. In this paper we study the effects of surface roughness for a special type of compressible fluid. In particular, we derive homogenization results connected to the friction force and the load carrying capacity.     

A multiscale extended finite element method for crack propagation

In this paper, we propose a multiscale strategy for crack propagation which enables one to use a refined mesh only in the crack’s vicinity where it is required. Two techniques are used in synergy: a multiscale strategy based on a domain decomposition method to account for the crack’s global and local effects efficiently, and a local enrichment technique (the X-FEM) to describe the geometry of the crack independently of the mesh. The focus of this study is the avoidance of meshing difficulties and the choice of an appropriate scale separation to make the strategy efficient. We show that the introduction of the crack’s discontinuity both on the microscale and on the macroscale is essential for the numerical scalability of the domain decomposition method to remain unaffected by the presence of a crack. Thus, the convergence rate of the iterative solver is the same throughout the crack’s propagation.     

Estimates of effective characteristics of random cell structures in terms of effective characteristics of periodic structures

The bounds of effective characteristics of random cell structures are obtained in terms of effective characteristics of periodic structures.     

Wavelet-based homogenization of unidirectional multiscale composites

The main aim is to present a homogenization algorithm for the multiscale heterogeneous (composite) materials, which is based on the wavelet representation of material properties and the relevant multiscale reduction. It is shown that classical homogenization method used before for two-scale composites (with micro and macro scales) is a special case of general multiresolutional strategy, where a single scale parameter tends to 0. The approach presented is applied to unidirectional wavelet-based homogenization of linear elasticity heterogeneous problem and to wave propagation, which may be applied in conjunction with various discrete numerical methods for efficient modeling of heterogeneous solids, fluids and multiphase media.