Nonlinear homogenization techniques to solve masonry structures problems

The behaviour of masonry material subjected to different in-plane loading combination is studied in this work. The masonry is considered as a periodic composite material composed by a regular distribution of brick and mortar and it is analyzed using a homogenization technique. The mechanical properties of the masonry, as an orthotropic homogeneous material, depend on the geometrical and mechanical properties of the components based on the study of the equilibrium and compatibility of a basic cell. The masonry is a frictional material and its behaviour depends on the loading direction, for these reasons, a unilateral damage model is chosen for the analysis. This model describes the behaviour of brittle materials subjected to tension-compression cyclic loads based on the introduction of two damage variables and it assumes that the damage is due to the beginning and growth of cracks only in the mortar joints. It is considered that the bricks have a linear elastic constitutive relationship. Numerical applications are performed with a nonlinear finite element code in order to test the proposed procedure by comparing the results with those available in the literature and also with experimental data.     

Trefftz approximations in complex media: Accuracy and applications

Approximations by Trefftz functions are rapidly gaining popularity in the numerical solution of boundary value problems of mathematical physics. By definition, these functions satisfy locally, in weak form, the underlying differential equations of the problem, which often results in high-order or even exponential accuracy with respect to the size of the basis set. We highlight two separate examples in applied electromagnetics and photonics: (i) homogenization of periodic structures, and (ii) numerical simulation of electromagnetic waves in slab geometries. Extensive numerical evidence and theoretical considerations show that Trefftz approximations can be applied much more broadly than is traditionally done: they are effective not only in physically homogeneous regions but also in complex inhomogeneous ones. Two mechanisms underlying the high accuracy of Trefftz approximations in such complex cases are pointed out. The first one is related to trigonometric interpolation and the second one – somewhat surprisingly – to well-posedness of random matrices.     

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.     

徐家围子断陷沙河子组致密砂砾岩气藏的成藏期次及类型划分

下白垩统沙河子组是松辽盆地徐家围子断陷最为重要的气源岩之一,但过去对其致密砂砾岩气藏的油气充注时期及成藏期次等研究较少,制约了对该区致密储层成因机制等的认识。为此,基于19块岩石样品273个流体包裹体的均一温度、盐度等测试数据,结合沉积埋藏史和热演化史分析结果,厘定了该区致密砂砾岩气藏的成藏期次;进而通过分析沙河子组储层致密期与成藏期之间的关系,确定了致密气藏的类型。结果表明:(1)该区流体包裹体的均一温度和盐度分布范围较宽,气藏具有长期充注的特点;(2)徐西—徐东地区第1期天然气充注时期在距今94~100 Ma,第2期在距今80~90 Ma,而安达—宋站地区第1期天然气充注时期在距今82~94 Ma,第2期在距今68~82 Ma;(3)安达—宋站地区沙河子组主要发育"先成型"致密气藏,在东斜坡发育"复合型"致密气藏,而徐西—徐东地区沙河子组则以"复合型"致密气藏为主。     

An inverse procedure for determination of material constants of a periodic multilayer using Floquet wave homogenization

An inverse numerical method for periodic composite characterization is reported. The method utilizes the velocity data based on Floquet wave homogenization. The optimization procedure is performed on the basis of the gradient method. An efficient polynomial function is derived from Christoffel equation. The numerical procedure leads to an analytical form of the minimized function which is related to the whole Floquet data. The set of input data is collected from different azimuthal plane orientations inside the homogenization domain. The output results mainly include the effective elastic constants of the multidirectional composite and the reliability factor. The initialization of the elastic stiffness matrix is obtained by averaging the rigidity tensor corresponding to each layer orientation. This procedure is examined for [0/90] and [0/60/−60] composites; some of the obtained elastic constants are significantly dependent on the frequency. The agreement between the adopted Floquet velocities and the calculated ones is good; the reliability factor does not exceed 1%. Slight deviations are pointed out in the vicinity of the homogenization limits.