Effect of defects to the band-gaps generation

Effect of defects to the band-gaps generation in sonic composites is investigated in this paper. Acoustic scatterers are composed by piezoceramic hollow spheres of functionally graded materials. Defects are vacancies or foreign interstitial atoms which are supported by the interfaces between the hollow spheres and the matrix. The presence of defects in sonic composites is related to the generation of localized modes in the vicinity of the point defect with a significant evanescent behavior of the waves outside the defect point. As result, the full band-gap is wider than in the case of no defects. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the acoustics of sonic composites

The primary goal of this paper is to propose an alternative method for obtaining the band structures of the 3D sonic composites without/ with point defects. The point defects are vacancies or foreign interstitial atoms which are supported by the interfaces between the hollow spheres and the matrix. The proposed method is used to simulate a sonic plate composed of an array of acoustic scatterers which are piezoceramic hollow spheres embedded in an epoxy matrix. The scatterers are made from functionally graded materials with radial polarization [1, 2]. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modeling of jointed structures using zero thickness interface elements

An important contribution to global damping of mechanical devices is structural damping due tomicroslip effects with friction in joint interfaces. In order to investigate the mechanical behaviour in these contact interfaces numerically, a contact element in the context of Finite Element Method (FEM) is presented. The suggested element is an isoparametric zero thickness element which is well suited for the present problem because the contact area is known and only small relative displacements occur. Arbitrary linear or nonlinear constitutive contact models for normal and tangential contact behaviour can be implemented. Using a proper parametrisation of the contact area, it is possible to apply the element in contact interfaces lying arbitrarily in space and in interfaces discretized with distorted elements. This method is described before a numerical example is compared with experimental results. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On one mathematical model of creep in superalloys

In [Sv1] a new micromechanical approach to the prediction of creep flow in composites with perfect matrix/particle interfaces, based on the nonlinear Maxwell viscoelastic model, taking into account a finite number of discrete slip systems in the matrix, has been suggested; high-temperature creep in such composites is conditioned by the dynamic recovery of the dislocation structure due to slip/climb motion of dislocations along the matrix/particle interfaces. In this article the proper formulation of the system of PDE's generated by this model is presented, some existence results are obtained and the convergence of Rothe sequences, applied in the specialized software CDS, is studied.     

On the sonic composites subjected to severe acoustic loads

Transformation acoustics opens a new avenue towards the fabrication of a new class of sonic composites with scatterers made of auxetic materials embedded in the epoxy matrix. The design of the acoustic scatterers is based on the property of Helmoltz equations to be invariant under coordinate transformations, i.e. a specific spatial compression is equivalent to a variation of the material parameters in the original space. In this paper, the noise suppression for a wide full band-gap of frequencies is discussed for spherical shell scatterers made of auxetic materials. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Homogenization of fibre composites using X-FEM

A successful material design process for novel textile reinforced composites requires an integrated simulation of the material behaviour and the estimation of the effective properties used in a macroscopic structural analysis. In this context the Extended Finite Element Method (X-FEM) is used to model the behavior of materials that show a complex structure on the mesoscale efficiently. A homogenization technique is applied to compute effective macroscopic stiffness parameters. This contribution gives an outline of the implementation of the X-FEM for complex multi-material structures. A modelling procedure is presented that allows for the automated generation of an extended finite element model for a specific representative volume element. Furthermore, the problem of branching material interfaces arising from complex textile reinforcement architectures in combination with high fibre volume fractions will be addressed and an appropriate solution is proposed. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Contact Homogenization Framework for Granular Interfaces

A computational contact homogenization framework is developed for contact interfaces with dry granular third bodies. The micro-to-macro transition procedure that forms the basis of this framework consists of projecting the macroscale contact pressure and slip velocity to the observable test surface of a representative contact element. The solution of the local microscale problem reveals a macroscale friction coefficient where inelastic effects are taken into account in a finite deformation setting. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Synthesis of averaging methods in stochastic boundary-value problems of the mechanics of microheterogeneous solids

The method of periodic components is further developed, which allows us, on unified positions, to predict the effective characteristics and structural strain fields in partially or fully disordered composites. The stochastic boundary-value problem of elasticity theory for microheterogeneous solids with a statistically homogeneous structure is treated. The heterogeneous solid is considered to be macroscopically homogeneous and macroanisotropic (or quasi-isotropic) with geometric form and properties of the structural components determined and given. The structural elements are assumed to have perfect interfaces, i.e., the displacements and tractions are continuous across the interface. The boundary-value problem was solved by the method of local approximation. Numerical results were obtained for composites with a stochastic structure.Perm' State Technical University, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 1, pp. 3–12, January–February, 1999.     

A combined finite/discrete element algorithm for delamination analysis of composites

A combined finite/discrete element method is developed to model delamination behaviour in laminated composites. A penalty based algorithm is employed to evaluate the interlaminar stress state. The failure surface for delamination is defined by a Chang-Springer criterion, and the interlaminar crack propagation is achieved by a standard discrete element contact/release algorithm. The ability of the method for simulation of this behaviour is assessed by solving standard test cases available from the literature.     

On the non-periodic multilayer films

The non-periodic multilayer film is studied in order to discern some of the most important features of periodic sonic composites, such as the full band-gaps and modes that are localized around defects. The band-gap for different number of Cantor elements into the film is analysed by taken into account the role of the fracton and phonon vibration regimes in the wave propagation. The film can prohibit the propagation of Lamb waves in the Ox₁ direction. The band-gap is generated in the band structure of the structure, meaning that the surface waves are forbidden to propagate with certain frequencies in the Ox₁ direction. The structure of the band-gaps for different number of Cantor elements into the film is analysed. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Evaluation of the physicochemical properties of boron-aluminum composite by the method of acoustic emission

Conclusion With the aid of the described method processes occurring in composites at the early stages of loading can be judged. The method yields a comparative characteristic of the strength of the bond at interfaces and makes it possible to judge initial defectiveness of the composite and residual thermal stress due to different production technologies of the composite. Moreover, the method makes it possible to differentiate between the kinds of defect of the composite. For a more detailed study of the properties of composites it is necessary to carry out experiments with composites obtained by different technologies. For a better understanding of the physics of the process it is necessary to obtain the spectral components of the signals, the amplitude distribution in time, and also to use additional research methods.Translated from Mekhanika Kompozitnykh Materialov, No. 6, pp. 1106–1109, November–December, 1988.     

Stress State of Multilayer Thin-Walled Elements with Interfacial Defects of Structure

Based on the discrete-structural theory of thin plates and shells, a calculation model for thin-walled elements consisting of a number of rigid anisotropic layers is put forward. It is assumed that the transverse shear and compression stresses are equal on the interfaces. Elastic slippage is allowed over the interfaces between adjacent layers. The solution to the problem is obtained in a geometrically nonlinear statement with account of the influence of transverse shear and compression strains. The stress-strain state of circular two-layer transversely isotropic plates, both without defects and with a local area of adhesion failure at their center, is investigated numerically and experimentally. It is found that the kinematic and static contact conditions on the interfaces of layered thin-walled structural members greatly affect the magnitude of stresses and strains. With the use of three variants of calculation models, in the cases of perfect and weakened contact conditions between layers, the calculation results for circular plates are compared. It is revealed that the variant suggested in this paper adequately reflects the behavior of layered thin-walled structural elements under large deformations. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 41, No. 6, pp. 761–772, November–December, 2005.     

Buckling stability of multilayer plates and shells with interfacial structural defects under axial compression

Based on the discrete-structural theory of thin plates and shells, a variant of the equations of buckling stability, containing a parameter of critical loading, is put forward for the thin-walled elements of a layered structure with a weakened interfacial contact. It is assumed that the transverse shear and compression stresses are equal on the interfaces. Elastic slippage is allowed over the interfaces between adjacent layers. The stability equations include the components of geometrically nonlinear moment subcritical buckling conditions for the compressed thin-walled elements. The buckling of two-layer transversely isotropic plates and cylinders under axial compression is investigated numerically and experimentally. It is found that variations in the kinematic and static contact conditions on the interfaces of layered thin-walled structural members greatly affect the magnitude of critical stresses. In solving test problems, a comparative analysis of the results of stability calculations for anisotropic plates and shells is performed with account of both perfect and weakened contacts between adjacent layers. It is found that the model variant suggested adequately reflects the behavior of layered thin-walled structural elements in calculating their buckling stability. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 4, pp. 513–530, July–August, 2007.     

On the composites consisting of randomly distributed fibers

The results highlight and interpret the testing and properties of natural fibre composites including, non-destructive and high strain rate testing. The potential of this material for noise enclosures is investigated by using a coupled method cnoidal – Extended Finite Element Method (XFEM). XFEM enables the accurate approximation of solutions with jumps, discontinuities or general high gradients across interfaces. The dissipation of the sound power into a plate/cavity system shows the efficiency of this composite to achieve noise reduction better to that obtained at low and higher frequencies with traditional foams. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Environmental degradation of carbon nanotube-modified composite laminates: a study of electrical resistivity

The environmental durability of carbon nanotube (CNT)-modified carbon-fibre-reinforced polymers (CFRPs) is investigated. The key problem of these new-generation composites is the modification of their polymer matrix with nanoscaled fillers. It was recently demonstrated that the damage tolerance of these materials, as manifested by their fracture toughness, impact properties, and fatigue life, can be improved by adding CNTs at weight fractions as low as 0.5%. This improvement is mainly attributed to the incorporation of an additional interfacial area between the CNTs and the matrix, which is active at the nanoscale. However, this additional interface could have a negative effect on the environmental durability of the aforementioned systems, since it is well known that the moisture absorption ability of a matrix is enhanced by the presence of multiple interfaces, which serve as an ingress route to water. To examine this problem, CNT-modified CFRPs were exposed to hydrothermal loadings. At specified intervals, the composites were weighted, and the water uptake vs. time was recorded for both the modified and a reference systems. The electrical conductivity of the composites was registered at the same time intervals. After the environmental exposure, the interlaminar shear properties of the conditioned composite systems were measured and compared with those of unmodified composites, as well as with the shear properties of unexposed laminates. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 45, No. 1, pp. 31–48, January–February, 2009.     

Intersections of Hugoniot curves with the sonic surface in the wave manifold

Local 1-shock curve arcs and local reverse 2-shock curve arcs were constructed, in the geometric context of the wave manifold, in a previous paper. In that geometric context, sonic and sonic’ surfaces are the boundaries of admissible shock curve arcs; in order to introduce the concept of non-local 1-shock curve arcs and non-local reverse 2-shock curve arcs it is necessary to understand how a hugoniot curve intersects the sonic and sonic’ surfaces; intersections of such curves with sonic’ surface are well known. In this paper we present a complete study on how Hugoniot curves intersect the sonic surface for a quadratic system of two conservation laws.     

Difference approximations for wave equations via finite elements. I. Construction and performance

Many practical applications of wave equations involve media in which there are interfaces, or discontinuities in material properties. The accurate numerical representation of these interfaces is important in mathematical models. One can develop generalizations of standard finite-difference methods that accommodate sharp interfaces by modifying a straightforward finite-element approach. In two space dimensions, these methods yield explicit, 5-point or 9-point difference schemes that accurately capture reflection, transmission, and refraction at interfaces. The approach also extends readily to the simulation of waves in elastic media. A companion article presents an error analysis for the approach. © 1995 John Wiley & Sons, Inc.     

Analysis of the Forced Vibration of Two Bolted Half-Pipes with Extended Friction Contacts

The present paper deals with the forced vibration analysis of a test structure. The test structure consists of two parts, an upper and a lower half pipe, joint in two bolted flanges which represent the extended friction contacts. Depending on the clamping loads different normal pressure distributions can be established in the contact interfaces. Since the test structure is loaded with a harmonic external force relative displacements occur in the contact interface. This leads to microslip effects affecting the dynamic behaviour. The experimental validation of the calculation method accounting for these effects is shown by comparing measured and calculated frequency response functions (FRF). (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

GLOBAL EXISTENCE OF SOLUTIONS FOR A MULTI-PHASE FLOW: A BUBBLE IN A LIQUID TUBE AND RELATED CASES

In this paper we study the problem of the global existence(in time) of weak,entropic solutions to a system of three hyperbolic conservation laws, in one space dimension,for large initial data. The system models the dynamics of phase transitions in an isothermal fluid; in Lagrangian coordinates, the phase interfaces are represented as stationary contact discontinuities. We focus on the persistence of solutions consisting in three bulk phases separated by two interfaces. Under some stability conditions on the phase configuration and by a suitable front tracking algorithm we show that, if the BV-norm of the initial data is less than an explicit(large) threshold, then the Cauchy problem has global solutions.     

A Two Dimensional Model for the Dynamical Contact of Elastic Rough Surfaces

To model the contact behavior including dynamical effects, a two dimensional mechanical model of elastic rough contact is developed. This model can simulate the contact behaviour between two rough surfaces depending on normal pressure, sliding speed and roughness profiles. The contact between two rough surfaces is reduced to a rough rigid and a rough elastic layer. The elastic layer is modeled by point masses connected by spring-damper elements. The total system is described by coupled ODEs. The number of ODEs and thus the degree of freedom of the model depends on the varying contact conditions. The contact conditions are monitored during the simulation and the simulation interrupts, in case the contact conditions change. The equations of motion are then adapted with respect to the contact constraints. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)