Abstract: The dynamic power transmission characteristics of a finite stiffened Mindlin plate subject to different boundary conditions are analytically studied. The stiffened plate is modeled as a coupled structure comprising a plate and stiffeners. Dynamic responses calculated by the analytical solutions are verified through comparison of the results with those generated using the finite element method. The computed results show that Mindlin plate and Timoshenko beam theory is more suitable for studying dynamic power of the stiffened plate over a broad frequency range than classical plate and beam theory. The stiffness and inertia characteristics of the Mindlin plate can be enhanced using the stiffeners, which can significantly affect the dynamic response, especially in low-frequency range. It can be also noticed that the stop band in the low-frequency range can become wider by increasing the number and dimension (height and width) of the stiffeners, so vibratory power of the stiffened Mindlin plate in the low-frequency range can be greatly reduced. PubDate: 2019-03-20

Abstract: The inhomogeneous line inclusion problem has various backgrounds in practical application such as graphene sheet-reinforced composites, and hydrogen embrittlement, grain boundary segregation in metallic materials. Due to the long-standing mathematical difficulty, there is no explicit analytical solution obtained except for the thin ellipsoidal inhomogeneity and rigid line inhomogeneity. In this paper, to find the deformation state due to the presence of such kind of elastic inhomogeneities, the inhomogeneous line inclusion problem is tackled in the framework of plane deformation. Firstly, the fundamental solution for a point-wise residual strain is presented and its deformation strain field is derived. By using Green’s function method, the homogeneous line inclusion problem with non-uniform eigenstrain is formulated and an Eshelby tensor-like line inclusion tensor is derived. From the line inclusion concept, the classical edge dislocation is revisited. Also, by virtue of this model, some elementary line homogenous inclusion problems are explored. Secondly, based on the homogeneous line inclusion solution, the inhomogeneous line inclusion problem is formulated using the equivalent eigenstrain principle, and its general solution is derived. Then, an inhomogeneous edge dislocation model is proposed and its analytical solution is presented. Furthermore, to demonstrate the application of the proposed inhomogeneous line inclusion model, a typical thin inclusion under remote load is studied. This study provides a general solution for inhomogeneous thin inclusion problems. The models and their solutions introduced here will also find application in the mechanics of composites analysis, heterogeneous material modeling, etc. PubDate: 2019-03-16

Abstract: The paper concerns an analysis of equilibrium problems for elastic bodies with elastic Timoshenko inclusion in the presence of defects. Defects are characterized by a positive damage parameter. This parameter is responsible for a connection between defect faces. Asymptotic properties of solutions are investigated with respect to the damage parameters as well as with respect to a rigidity parameter of the inclusions. Limit models are investigated; in particular, different equivalent problem formulations are proposed. PubDate: 2019-03-14

Abstract: In this contribution, we analyze the properties of two-phase magneto-electric (ME) composites. Such ME composite materials have raised scientific attention in the last decades due to many possible applications in a wide range of technical devices. Since the effective magneto-electric properties significantly depend on the microscopic morphology, we investigate in more detail the changes in the in-plane polarization due to an applied magnetic field. It was shown in previous works that it is possible to grow vertically aligned nanopillars of magnetostrictive cobalt ferrite in a piezoelectric barium titanate matrix by pulsed laser deposition. Based on x-ray linear dichroism, the displacements of titanate ions in the matrix material can be measured due to an applied magnetic field near the boundary of the interface between the matrix and the nanopillars. Here, we focus on (1–3) fiber-induced composites, based on previous experiments, where cobalt ferrite nanopillars are embedded in a barium titanate matrix. In the numerical simulations, we adjusted the boundary value problem to match the experimental setup and compare the results with previously made assumptions of the in-plane polarizations. A further focus is taken on the deformation behavior of the nanopillar over its whole height. Such considerations validate the assumption of the distortion of the nanopillars under an external magnetic field. Furthermore, we analyze the resulting magneto-electric coupling coefficient. PubDate: 2019-03-07

Abstract: The present paper proposes an interphase model for the simulation of damage propagation in masonry walls in the framework of a mesoscopic approach. The model is thermodynamically consistent, with constitutive relations derived from a Helmholtz free potential energy. With respect to classic interface elements, the internal stress contribute is added to the contact stresses. It is considered that damage, in the form of loss of adhesion or cohesion, can potentially take place at each of the two blocks–mortar physical interfaces. Flow rules are obtained in the framework of the Theory of Plasticity, considering bilinear domains of ‘Coulomb with tension cut-off’ type. The model aims to be a first research step to solve the inverse problem of damage propagation in masonry generated by vertical ground movements, in order to ex-post identify the cause of a visible damage. The constitutive model is written in a discrete form for its implementation in a research-oriented finite element program. The response at the quadrature point is analyzed first. Then, the model is validated through comparisons with experimental results and finally employed to simulate the failure occurred in a wall of an ancient masonry building, where an arched collapse took place due to a lowering of the ground level under part of its foundation. PubDate: 2019-03-07

Abstract: This paper focuses on development of a new mathematical model and its analytical solution for the buckling analysis of elastic columns with preexisted longitudinal cracks and finite adhesion between the cracked sections. Consequently, the analytical solution for the buckling loads is derived for the first time. The critical buckling loads are calculated for two different types of connections between the cracked sections, namely for slipping only and simultaneous slipping and uplifting between them. The parametric study is performed to analyze the effect of the crack length on the critical buckling loads. It is shown that the critical buckling load can be greatly affected by the crack length and type of the connection between the cracked sections. Finally, the presented results obtained can be used as a benchmark solution. PubDate: 2019-03-06

Abstract: In this paper, we present an asymptotic model describing localised flexural vibrations along a structured ring containing point masses or spring–mass resonators in an elastic plate. The values for the required masses and stiffnesses of resonators are derived in a closed analytical form. It is shown that spring–mass resonators can be tuned to produce a “negative inertia” input, which is used to enhance localisation of waveforms around the structured ring. Theoretical findings are accompanied by numerical simulations, which show exponentially localised and leaky modes for different frequency regimes. PubDate: 2019-03-01

Abstract: We relate two problems which arise from different branches of mechanics of materials: construction of limiting phase transformation surfaces in strain space and stress–strain diagrams for stress-induced phase transitions and optimal design of two-phase 3D composites in the sense of minimizing its energy. In Antimonov et al. (Int J Eng Sci 98:153–182, 2015) for the case of isotropic phases, it was shown that given a new phase volume fraction and depending on average strain, the strain energy of a two-phase linear-elastic composite is minimized by either direct or inclined simple laminates, direct or skew second-rank laminates or third-rank laminates. Then these results were applied for the construction of direct and reverse transformations limiting surfaces in strain space for elastic solids undergoing phase transformations by additional minimization with respect to the new phase volume fraction and finding the strains at which minimizing volume fraction equals zero or one. In the present paper we construct stress–strain diagrams on various straining paths at which a material undergoes the phase transformation. We demonstrate that an additional degree of freedom—new phase volume fraction—may crucially result in instability of two-phase microstructures even if the microstructures are energy minimizers for composites with given volume fractions of phases. This in turn may lead to incompleteness of monotonic phase transformations and broken stress–strain diagrams. We study how such a behavior depends on a loading path and chemical energies of the phases. PubDate: 2019-03-01

Abstract: The paper studies damage propagation in brittle elastic beam lattices, using the quasistatic approach. The lattice is subjected to a remote tensile loading; the beams in the lattice are bent and stretched. An introduced initial flaw in a stressed lattice causes an overstress of neighboring beams. When one of the overstressed beams fails, it is eliminated from the lattice; then, the process repeats. When several beams are overstressed, one has to choose which beam to eliminate. The paper studies and compares damage propagation under various criteria of the elimination of the overstressed beams. These criteria account for the stress level, randomness of beams properties, and decay of strength due to micro-damage accumulation during the loading history. A numerical study is performed using discrete Fourier transform approach. We compare damage patterns in triangular stretch-dominated and hexagonal bending-dominated lattices. We discuss quantitative characterization of the damage pattern for different criteria. We find that the randomness in the beam stiffness increases fault tolerance, and we outline conditions restricting the most dangerous straight linear crack-like pattern. PubDate: 2019-03-01

Abstract: A closed finite-dimensional system of dynamical equations for an unbounded periodic set of edge dislocations obtained previously from homogenization reasoning (Berdichevsky in J Mech Phys Solids 106:95–132, 2017) is rederived in this paper using some elementary means. PubDate: 2019-03-01

Abstract: This paper is concerned with the well posedness and homogenization for a multiscale parabolic problem in a cylinder Q of \({\mathbb {R}}^N \) . A rapidly oscillating non-smooth interface inside Q separates the cylinder in two heterogeneous connected components. The interface has a periodic microstructure, and it is situated in a small neighborhood of a hyperplane which separates the two components of Q. The problem models a time-dependent heat transfer in two heterogeneous conducting materials with an imperfect contact between them. At the interface, we suppose that the flux is continuous and that the jump of the solution is proportional to the flux. On the exterior boundary, homogeneous Dirichlet boundary conditions are prescribed. We also derive a corrector result showing the accuracy of our approximation in the energy norm. PubDate: 2019-03-01

Abstract: The equilibrium problem of a nonlinearly elastic medium with a given dislocation distribution is considered. The system of equations consists of the equilibrium equations for the stresses, the incompatibility equations for the distortion tensor, and the constitutive equations. Deformations are considered to be finite. For a special distribution of screw and edge dislocations, an exact spherically symmetric solution of these equations is found. This solution is universal in the class of isotropic incompressible elastic bodies. With the help of the obtained solution, the eigenstresses in a solid elastic sphere and in an infinite space with a spherical cavity are determined. The interaction of dislocations with an external hydrostatic load was also investigated. We have found the dislocation distribution that causes the spherically symmetric quasi-solid state of an elastic body, which is characterized by zero stresses and a nonuniform elementary volumes rotation field. PubDate: 2019-03-01

Abstract: We study thermally activated unzipping, which is modeled as a debonding process. The system is modeled as a parallel bundle of elastically interacting breakable units loaded through a series spring. Using equilibrium statistical mechanics, we compute the reversible response of this mechanical system under quasi-static driving. Depending on the stiffness of the series spring, the system exhibits either ductile behavior, characterized by noncooperative debonding, or brittle behavior, with a highly correlated detachment of the whole bundle. We show that the ductile to brittle transition is of the second order and that it can also be controlled by temperature. PubDate: 2019-03-01

Abstract: The present paper studies non-uniform plastic deformations of crystals undergoing anti-plane constrained shear. The asymptotically exact energy density of crystals containing a moderately large density of excess dislocations is found by the averaging procedure. This energy density is extrapolated to the cases of extremely small or large dislocation densities. Taking into account the configurational temperature and the density of redundant dislocations, we develop the thermodynamic dislocation theory for non-uniform plastic deformations and use it to predict stress–strain curves and dislocation densities. PubDate: 2019-03-01

Abstract: For centuries, statics and dynamics of two-phase heterogeneous systems were and remain to be in the focus of multiple academic and engineering disciplines. Phase transformations phenomena include both strong reversible and irreversible effects. Many of the irreversible effects, such as friction, viscosity, heat conduction, etc., are the same as in the single-phase systems. In addition to those, the two-phase systems are known for one more irreversible effect. It is the effect entailed by finite rate of kinetics of phase transformation. Below, we explore this irreversible phenomenon for two two-phase heterogeneous systems: (i) the layered system of incompressible phases in the external gravity field and (ii) the two-phase, two-layered self-gravitating planet. PubDate: 2019-03-01

Abstract: The paper demonstrates a rational design of an isotropic heterogeneous beam lattice that is fault-tolerant and energy-absorbing. Combining triangular and hexagonal structures, we calculate elastic moduli of obtained hybrid heterogeneous structures; simulate the development of flaws in that composite lattice subjected to a uniform uniaxial deformation; investigate its damage evolution; measure various characteristics of damage that estimate fault tolerance; discuss the trade-off between stiffness and fault tolerance. A design is found that develops a cloud of small evenly spread flaws instead of a crack. PubDate: 2019-03-01

Authors:Lichun Bian; Jiuming Guo; Jing Pan Abstract: In the present investigation, a new equivalent micromechanics method is proposed, and then, an analysis model has been developed to estimate the nonlinear coefficients of thermal expansion (CTEs) of three-phase composites. As Compared with previous analytical models, the innovative point of this paper is that the influence of the debonding surface thickness is investigated. It is noted that the parameters of thickness of debonding surface have a significant effect on both the longitudinal CTEs and transverse CTEs. The CTEs of composites are also very sensitive to the different inclusion aspect ratios. The constitutive equation curves for different variable parameters can describe the influence of debonding damage on thermal expansion coefficients (CTEs) of the composites. The new model provides a direct prediction of CTEs and can account for the effects of inclusion aspect ratio, volume fractions and thickness of debonding surface. PubDate: 2019-02-26 DOI: 10.1007/s00419-019-01533-0

Authors:Ani P. Velo; George A. Gazonas Abstract: Here we analyze by means of the z-transform a system of recursive relations for stress and particle velocity, previously developed to study impact problems in Goupillaud-type layered elastic media. As a result, we are able to obtain finite series representations of the stress and particle velocity sequences. This representation provides insight into the monotonic behavior and damped oscillations observed about the steady-state values of the stress and particle velocity. The convergence of both stress and particle velocity sequences requires for the roots of the determinant of the system matrix in the z-space to lie inside the unit circle, except for a single root of unity. The analytical expectations are confirmed for the one- and two-layered target and demonstrated through various numerical experiments. PubDate: 2019-02-19 DOI: 10.1007/s00419-019-01515-2

Authors:Elena Cherkaev Abstract: Mathematical model for viscous internal friction is suggested. The model relates the viscous phenomena on the grain boundaries in a polycrystalline composite to the spectral measure in the analytic representation of the effective viscoelastic properties. This spectral measure contains all information about the geometry of a finely structured material. The spectral measure can be recovered from the measurements of viscoelastic effective properties over a range of frequencies. The Stieltjes analytic representation of the effective modulus is derived for the two-dimensional viscoelastic problem. It is shown that the spectral function in this representation determines the internal memory variables and the viscous internal friction. PubDate: 2019-02-16 DOI: 10.1007/s00419-019-01514-3