We investigate the dynamic stability of a pipe that conveys fluid, clamped or pinned at one end and with an intermediate support, thus exhibiting an overhang. The model of the pipe incorporates both Euler–Bernoulli and Bresse–Timoshenko schemes as well as transverse inertia. Material and external damping mechanisms are taken into account, while the conveyed fluid is supposed to be in fully turbulent flow. The pipe can rest on a linear elastic Winkler soil. The influence of all the physical quantities and of the overhang length on the critical velocity of the fluid front is investigated. Some numerical results are presented and discussed.

This paper presents a multi-scale model for the analysis of the in-plane structural response of regular masonry. It is based on a computational periodic homogenization technique and is characterized by the adoption of the Cosserat continuum model at the macroscopic structural level, taking into account the influence of the microstructure on the global response and correctly describing the localization phenomena; at the microscopic representative volume element (RVE) level, where the nonlinear constitutive behavior, geometry, and arrangement of the masonry constituents are modeled in detail, a standard Cauchy model is employed. An isotropic nonsymmetric damage model is adopted for the bricks and mortar joints. The solution algorithm is based on a parallelization strategy and on the finite-element method. Some numerical applications on typical masonry structures are reported, showing both the global response curves and the stress and damage distributions on the RVEs

We present a simplified model of damaging porous material, obtained through consistent linearization from a recursive-faulting material model described in (Pandolfi et al. 2016). The brittle damage material model is characterized by special planar micro-structures, consisting of nested families of equi-spaced frictional-cohesive faults in an otherwise elastic matrix material. The linear kinematics model preserves the main microstructural features of the finite kinematics one but offers a far better computational performance. Unlike models commonly employed in geo-mechanical applications, the proposed model contains a small number of parameters, to wit, two elastic moduli, three frictional-cohesive parameters, and three hydraulic response parameters, all of which having clear physical meanings and amenable to direct experimental measurement through standard material tests. The model is validated by comparison to triaxial hydro-mechanical experimental data. Despite the paucity of material constants, the salient aspects of the observed behavior are well captured by the model, qualitatively and quantitatively. As an example of application of the model, we simulate the excavation of a borehole in a rocky embankment.

Computational homogenization is adopted to assess the homogenized two-dimensional response of periodic composite materials where the typical microstructural dimension is not negligible with respect to the structural sizes. A micropolar homogenization is, therefore, considered coupling a Cosserat medium at the macro-level with a Cauchy medium at the micro-level, where a repetitive Unit Cell (UC) is selected. A third order polynomial map is used to apply deformation modes on the repetitive UC consistent with the macro-level strain components. Hence, the perturbation displacement field arising in the heterogeneous medium is characterized. Thus, a newly defined micromechanical approach, based on the decomposition of the perturbation fields in terms of functions which depend on the macroscopic strain components, is adopted. Then, to estimate the effective micropolar constitutive response, the well known identification procedure based on the Hill-Mandel macro-homogeneity condition is exploited. Numerical examples for a specific composite with cubic symmetry are shown. The influence of the selection of the UC is analyzed and some critical issues are outlined.

The present paper deals with the homogenization problem of periodic composite materials, considering a Cosserat continuum at the macro-level and a Cauchy continuum at the micro-level. Consistently with the strain-driven approach, the two levels are linked by a kinematic map based on a third order polynomial expansion. Because of the assumed regular texture of the composite material, a Unit Cell (UC) is selected; then, the problem of determining the displacement perturbation fields, arising when second or third order polynomial boundary conditions are imposed on the UC, is investigated. A new micromechanical approach, based on the decomposition of the perturbation fields in terms of functions which depend on the macroscopic strain components, is proposed. The identification of the linear elastic 2D Cosserat constitutive parameters is performed, by using the Hill–Mandel technique, based on the macrohomogeneity condition. The influence of the selection of the UC is analyzed and some critical issues are outlined. Numerical examples for a specific composite with cubic symmetry are shown.

We present a two–steps multiscale procedure suitable to describe the constitutive behavior of hierarchically structured particle composites. The complex material is investigated considering three nested scales, each one provided by a characteristic length. At the lowest scale (micro), a periodic lattice system describes in detail the mechanical response governed by interactions between rigid grains connected through elastic interfaces. At the intermediate scale (meso), the material is perceived as heterogeneous and characterized by deformable particles randomly distributed into a base matrix, either stiffer or softer. At the macroscopic scale, the material is represented as a micropolar continuum. The micro/meso transition is governed by an energy equivalence procedure, based on a generalized Cauchy–Born correspondence map between the discrete degrees of freedom and the continuum kinematic fields. The meso/macro equivalence exploits a statistically–based homogenization procedure, allowing us to estimate the equivalent micropolar elastic moduli. A numerical example illustrating the integrated multiscale procedure complements the paper.

Deterioration of mechanical and hydraulic properties of rock masses and subsequent problems are closely related to changes in the stress state, formation of new cracks, and increase of permeability in porous media saturated with freely moving fluids. We describe a coupled approach to model damage induced by hydro-mechanical processes in low permeability solids. We consider the solid as an anisotropic brittle material where deterioration is characterized by the formation of nested microstructures in the form of equi-distant parallel faults characterized by distinct orientation and spacing. The particular geometry of the faults allows for the analytical derivation of the porosity and of the anisotropic permeability of the solid. The approach can be used for a wide range of engineering problems, including the prevention of water or gas outburst in underground mines and the prediction of the integrity of reservoirs for underground CO2 sequestration or hazardous waste storage

We discuss a microstructural model of permeability in fractured solids, where fractures are modeled as recursive families of parallel, equidistant faults. Faults are originated by the attainment of a resistance threshold under the action of a confinement pressure over an initially undamaged, fully elastic matrix, not necessarily isotropic. The initially undamaged matrix might possess a natural permeability, which is modified by the progressive damage of the rock. The particular organization of the micro-faults considered in the model allows to define analytically the equivalent permeability of the solid. The model is particularly appealing to describe the permeability of rock undergoing the process of fracking, in a form that has great computational advantages, since the approach does not track explicitly the formation of individual macro-faults.

We present a microstructural model of permeability in fractured solids, where the fractures are described in terms of recursive families of parallel, equidistant cohesive faults. Faults originate upon the attainment of tensile or shear strength in the undamaged material. Secondary faults may form in a hierarchical organization, creating a complex network of connected fractures that modify the permeability of the solid. The undamaged solid may possess initial porosity and permeability. The particular geometry of the superposed micro-faults lends itself to an explicit analytical quantification of the porosity and permeability of the damaged material. The model is the finite kinematics version of a recently proposed porous material model, applied with success to the simulation of laboratory tests and excavation problems [De Bellis, M. L., Della Vecchia, G., Ortiz, M., Pandolfi, A., 2016. A linearized porous brittle damage material model with distributed frictional-cohesive faults. Engineering Geology 215, 10–24. Cited By 0. 10.1016/j.enggeo.2016.10.010]. The extension adds over and above the linearized kinematics version for problems characterized by large deformations localized in narrow zones, while the remainder of the solid undergoes small deformations, as typically observed in soil and rock mechanics problems. The approach is particularly appealing as a means of modeling a wide scope of engineering problems, ranging from the prevention of water or gas outburst into underground mines, to the prediction of the integrity of reservoirs for CO2 sequestration or hazardous waste storage, to hydraulic fracturing processes.

This article is focused on the identification of the size of the representative volume element (RVE) and the estimation of the relevant effective elastic moduli for particulate random composites modeled as micropolar continua. To this aim, a statistically-based scale-dependent multiscale procedure is adopted, resorting to a homogenization approach consistent with a generalized Hill’s type macrohomogeneity condition. At the fine level the material has two phases (inclusions/matrix). Two different cases of inclusions, either stiffer or softer than the matrix, are considered. By increasing the scale factor, between the size of intermediate control volume elements (Statistical Volume Elements, SVEs) and the inclusions size, series of boundary value problems are numerically solved and hierarchies of macroscopic elastic moduli are derived. The constitutive relations obtained are grossly isotropic and are represented in terms of classical bulk, shear and micropolar bending moduli. The “finite size scaling” of these relevant elastic moduli for the two different material contrasts (ratio of inclusion to matrix moduli) is reported. It is shown that regardless the scaling behavior, which depends on the material phase contrast, the RVE size is statistically detected. The results of the performed numerical simulations also highlight the importance of taking into account the spatial randomness of inclusions which intersect the SVEs boundary

A multi-scale nonlinear homogenization procedure is presented for the analysis of the inplane structural response of masonry panels characterized by a regular texture. A Cosserat continuum model is adopted at the macroscopic level, while a classical Cauchy model is employed at the microscopic scale; proper bridging conditions are stated to connect the two scales. The constitutive behaviour of bricks and mortar at the microscopic level is based on a scalar damage model, non symmetric in tension and compression. As for the regularization of the strain softening response, the standard fracture energy method is used at micro-level, while at the macro-level the inner capabilities of Cosserat continuum are exploited. A numerical example is presented and a comparison with an experimental test is performed

The use of multifunctional composite materials adopting piezo-electric periodic cellular lattice structures with auxetic elastic behavior is a recent and promising solution in the design of piezoelectric sensors. In the present work, periodic anti-tetrachiral auxetic lattice structures, characterized by different geometries, are taken into account and the mechanical and piezoelectrical response are investigated. The equivalent piezoelectric properties are obtained adopting a first order computational homogenization approach, generalized to the case of electro-mechanical coupling, and various polarization directions are adopted. Two examples of in-plane and out-of-plane strain sensors are proposed as design concepts. Moreover, a piezo-elasto-dynamic dispersion analysis adopting the Floquet–Bloch decomposition is performed. The acoustic behavior of the periodic piezoelectric material with auxetic topology is studied and possible band gaps are detected.

A comprehensive characterization of the novel class of anti-tetrachiral cellular solids, both considering the static and the dynamic response, is provided in the paper.The heterogeneous material is characterized by a periodic microstructure made of equi-spaced rings each interconnected by four ligaments. In the most general case, rings and ligaments are surrounded by a softer matrix and the rings can be filled by a different material.First, the first order linear elastic homogenized constitutive response is estimated resorting to two different microstructural models: a discrete model, in which the ligaments are modeled as beams and the presence of the matrix is neglected and the equivalent elastic properties are evaluated through a simplified analytical approach, and a more detailed continuous model, where the actual properties of matrix, ligaments and rings, varying in the 2D domain, are considered and the first order computational homogenization is adopted. Special attention is given to the dependence of the 2D overall Cauchy-type elastic constants on the mechanical and geometrical parameters characterizing the microstructure. The results, indeed, show the existence of large variations in the linear elastic constants and degree of anisotropy. A comparison with available experimental results confirms the validity of the analytical and numerical approaches adopted.Finally, the rigorous Floquet-Bloch approach is applied to the periodic cell of the cellular solid to evaluate the dispersion of propagation waves along the orthotropic axes in the framework of elasticity and to detect band gaps characterizing the material. A numerical approach, based on the first order computational homogenization, is also adopted and the rigorous and approximate solutions are compared.

A multitude of composite materials ranging from polycrystals up to concrete and masonry-like materials overwhelmingly display random morphologies. In this work we propose a statistically-based multiscale procedure which allow us to simulate the actual microstructure of a two-dimensional and two-phase random medium and to estimate the elastic moduli of the energy equivalent homogeneous micropolar continuum. This procedure uses finite-size scaling of Statistical Volume Elements (SVEs) and approaches the so-called Representative Volume Element (RVE) through two hierarchies of constitutive bounds, respectively stemming from the numerical solution of Dirichlet and Neumann non-classical boundary value problems, set up on mesoscale material cells. The results of the performed numerical simulations point out the worthiness of accounting spatial randomness as well as the additional degrees of freedom of the Cosserat continuum.

This article considers the behaviour of a fluid conveying pipe on a partial elastic foundation. The model of the pipe is that of a Timoshenko beam; the foundation response is of Wieghardt type. Both material and environmental damping are taken into account. The critical value of the velocity of the fluid inducing dynamical instability of the system is evaluated as a function of the attachment ratio of the foundation for various values of the physical quantities involved. It is shown that this dependance is not always monotonic.

In the framework of the computational homogenization procedures, the problem of coupling a Cosserat continuum at the macroscopic level and a Cauchy medium at the microscopic level, where a heterogeneous periodic material is considered, is addressed. In particular, non-homogeneous higher-order boundary conditions are defined on the basis of a kinematic map, properly formulated for taking into account all the Cosserat deformation components and for satisfying all the governing equations at the micro-level in the case of a homogenized elastic material. Furthermore, the distribution of the perturbation fields, arising when the actual heterogeneous nature of the material is taken into account, is investigated. Contrary to the case of the first-order homogenization where periodic fluctuations arise, in the analyzed problem more complex distributions emerge.

In this work we present a collocation method for the structural analysis of shells of revolution based on Non-Uniform Rational B-Spline (NURBS) interpolation. The method is based on the strong formulation of the equilibrium equations according to Reissner-Mindlin theory, with Fourier series expansion of dependent variables, which makes the problem 1D. Several numerical tests validate convergence, accuracy, and robustness of the proposed methodology, and its feasibility as a tool for the analysis and design of complex shell structures.

In the present paper the homogenization problem of periodic composites is investigated, in the case of a Cosserat continuum at the macro-level and a Cauchy continuum at the micro-level. In the framework of a strain-driven approach, the two levels are linked by a kinematic map based on a third order polynomial expansion. The determination of the displacement perturbation fields in the Unit Cell (UC), arising when second or third order polynomial boundary conditions are imposed, is investigated. A new micromechanical approach, based on the decomposition of the perturbation fields in terms of functions which depend on the macroscopic strain components, is proposed. The identification of the linear elastic 2D Cosserat constitutive parameters is performed, by using a Hill-Mandel-type macrohomogeneity condition. The influence of the selection of the UC is analyzed and some critical issues are outlined. Numerical examples referred to a specific composite with cubic symmetry are shown.

Many composite materials, widely used in different engineering fields, are characterized by random distributions of the constituents. Examples range from polycrystals to concrete and masonry-like materials. In this work we propose a statistically-based scale-dependent multiscale procedure aimed at the simulation of the mechanical behavior of a two-phase particle random medium and at the estimation of the elastic moduli of the energy-equivalent homogeneous micropolar continuum. The key idea of the procedure is to approach the so-called Representative Volume Element (RVE) using finite-size scaling of Statistical Volume Elements (SVEs). To this end properly defined Dirichlet, Neumann, and periodic-type non-classical boundary value problems are numerically solved on the SVEs defining hierarchies of constitutive bounds. The results of the performed numerical simulations point out the importance of accounting for spatial randomness as well as the additional degrees of freedom of the continuum with rigid local structure.

A multitude of composite materials ranging from polycrystals to rocks, concrete, and masonry overwhelmingly display random morphologies. While it is known that a Cosserat (micropolar) medium model of such materials is superior to a Cauchy model, the size of the Representative Volume Element (RVE) of the effective homogeneous Cosserat continuum has so far been unknown. Moreover, the determination of RVE properties has always been based on the periodic cell concept. This study presents a homogenization procedure for disordered Cosserat-type materials without assuming any spatial periodicity of the microstructures. The setting is one of linear elasticity of statistically homogeneous and ergodic two-phase (matrix-inclusion) random microstructures. The homogenization is carried out according to a generalized Hill-Mandel type condition applied on mesoscales, accounting for non-symmetric strain and stress as well as couple-stress and curvature tensors. In the setting of a two-dimensional elastic medium made of a base matrix and a random distribution of disk-shaped inclusions of given density, using Dirichlet-type and Neumann-type loadings, two hierarchies of scale-dependent bounds on classical and micropolar elastic moduli are obtained. The characteristic length scales of approximating micropolar continua are then determined. Two material cases of inclusions, either stiffer or softer than the matrix, are studied and it is found that, independent of the contrast in moduli, the RVE size for the bending micropolar moduli is smaller than that obtained for the classical moduli. The results point to the need of accounting for: spatial randomness of the medium, the presence of inclusions intersecting the edges of test windows, and the importance of additional degrees of freedom of the Cosserat continuum.