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Peter Schiavone - One of the best experts on this subject based on the ideXlab platform.

  • need the uniform stress field inside multiple interacting inclusions be hydrostatic
    Journal of Elasticity, 2021
    Co-Authors: Ming Dai, Peter Schiavone
    Abstract:

    Since the pioneering work of Eshelby on a single ellipsoidal inclusion embedded in an infinite space, much attention has been devoted in the literature to the question of the uniformity of the stress field inside inclusions surrounded by an Elastic Matrix. Over the last decade or so, researchers have established the existence of multiple (interacting) inclusions enclosing uniform internal stress distributions when embedded in an infinite Elastic Matrix subjected to a uniform far-field loading and identified a variety of shapes of such inclusions. In the design of multiple inclusions with uniform internal stresses, it is customary to assume that the uniform stress field inside each inclusion (each with different shear modulus distinct from that of the Matrix) is hydrostatic. In this paper, we examine whether this assumption is actually necessary to ensure the required existence of multiple inclusions enclosing uniform stresses. By establishing several theorems in the theory of functions of a complex variable, we prove rigorously that for any collection of multiple inclusions enclosing uniform stresses in an infinite isotropic plane subjected to uniform remote in-plane loading, the internal uniform stress field must indeed be hydrostatic if the corresponding inclusion’s shear modulus is distinct from that of the Matrix.

  • the symmetry and loading independency of multiple inclusions enclosing uniform stresses in an infinite Elastic plane
    Applied Mathematics and Mechanics-english Edition, 2020
    Co-Authors: Ming Dai, Peter Schiavone
    Abstract:

    The identification of multiple interacting inclusions with uniform internal stresses in an infinite Elastic Matrix subjected to a uniform remote loading is of fundamental importance in the mechanics and design of particulate composite materials. In anti-plane shear and plane deformations, certain sufficient conditions have been established in the literature which guarantee uniform internal stresses inside multiple interacting inclusions displaying various symmetries when the Matrix is subjected to specific uniform remote loading. Correspondingly, sufficient conditions which allow for the design of multiple interacting inclusions independent of any specific form of (uniform) remote loading have also been established. In this paper, we demonstrate rigorously that, in all cases, these sufficient conditions are also necessary conditions and indeed allow for the identification of all possible collections of such inclusions.

  • neutrality of a partially debonded rigid inclusion in anti plane shear
    Archive of Applied Mechanics, 2019
    Co-Authors: Xu Wang, Peter Schiavone
    Abstract:

    We consider a coated rigid inclusion inserted into an Elastic Matrix subjected to uniform remote anti-plane shear stresses and examine whether the inclusion can be made neutral (meaning that its introduction will not disturb the original uniform stress field in the surrounding uncut Matrix) despite the presence of partial debonding along the inclusion–coating interface. Our analysis involves the introduction of a conformal mapping function (expressed in terms of a Laurent series) for the (thick) coating, a Laurent series expansion for the corresponding Plemelj function and simple Matrix algebra. Our method demonstrates that coated neutral inclusions continue to be available under these challenging yet more realistic physical conditions. Numerical results are presented to demonstrate the feasibility of the solution method.

  • a circular eshelby inclusion interacting with a coated non elliptical inhomogeneity with internal uniform stresses in anti plane shear
    Mechanics of Materials, 2019
    Co-Authors: Xu Wang, Peter Schiavone
    Abstract:

    Abstract We consider a coated non-elliptical inhomogeneity interacting with a nearby circular Eshelby inclusion inside an infinite Elastic Matrix subjected to anti-plane shear deformations and uniform remote stresses. Using conformal mapping techniques, we prove that despite the presence of the Eshelby inclusion, it is possible to design the system to achieve a uniform stress distribution inside the inhomogeneity. The conformal mapping function used in the analysis is constructed to give rise to an infinite number of first-order poles inside the unit circle in the image plane in order to satisfy all of the conditions required by the complex potential in the Matrix. Our analysis indicates that the inhomogeneity's internal uniform stress field is unaffected by the Eshelby inclusion whereas the non-elliptical shape of the coated inhomogeneity is attributed solely to the nearby Eshelby inclusion.

  • uniformity of stresses inside a non elliptical inhomogeneity interacting with a circular eshelby inclusion in anti plane shear
    Archive of Applied Mechanics, 2018
    Co-Authors: Xu Wang, Liang Chen, Peter Schiavone
    Abstract:

    We use conformal mapping techniques to examine the uniformity of stresses inside a non-elliptical inhomogeneity interacting with a circular Eshelby inclusion in an Elastic Matrix subjected to remote uniform stresses in anti-plane shear. We show that for a prescribed set of two real loading and two complex geometric parameters, it is possible to determine the single unknown complex coefficient in the mapping function and the (unique) shape of the corresponding inhomogeneity enclosing internal uniform stresses. Our results indicate that the shape of the inhomogeneity depends on the circular Eshelby inclusion whereas the uniform stress field inside the inhomogeneity does not. Finally, we note that the influence of the circular Eshelby inclusion in the vicinity of the inhomogeneity allows for the possibility of a sharp corner on the boundary of the inhomogeneity.

X L Gao - One of the best experts on this subject based on the ideXlab platform.

  • strain gradient solution for the eshelby type problem of an anti plane strain cylindrical inclusion in a finite Elastic Matrix
    Advances in Heterogeneous Material Mechanics 2011, 2011
    Co-Authors: H M, X L Gao
    Abstract:

    Eshelby’s equivalent eigenstrain method and fourth-order strain transformation tensor [1] are essential for homogenization schemes including the Mori-Tanaka and self-consistent methods. However, Eshelby’s tensor originally provided in [1] is based on classical Elasticity and is for an ellipsoidal inclusion embedded in an infinite Elastic Matrix. As a result, homogenization methods based on this classical Eshelby tensor cannot capture particle (inclusion) size effects or account for boundary effects. Hence, there has been a need to obtain Eshelby tensors for an inclusion in a finite Matrix using higher-order (non-classical) Elasticity theories. In this study, such an Eshelby tensor is provided for the finite-domain anti-plane strain inclusion problem of a finite Elastic Matrix containing a cylindrical inclusion prescribed with a uniform eigenstrain and a uniform eigenstrain gradient using a simplified strain gradient Elasticity theory (SSGET) [2]. This SSGET involves only one material length scale parameter and has been applied to analytically solve several Eshelby-type inclusion problems [3–7]. In the current formulation, the SSGET-based Green’s function for an infinite anti-plane strain Elastic body is first derived using the Fourier transform method. The extended Betti’s reciprocal theorem and Somigliana’s identity based on the SSGET and suitable for anti-plane strain problems are then used to determine the displacement field in the finite Matrix in terms of this Green’s function. The displacement solution reduces to that of the infinite-domain anti-plane inclusion problem when the boundary effect is suppressed.

  • strain gradient solution for a finite domain eshelby type plane strain inclusion problem and eshelby s tensor for a cylindrical inclusion in a finite Elastic Matrix
    International Journal of Solids and Structures, 2011
    Co-Authors: H M, X L Gao
    Abstract:

    Abstract A solution for the finite-domain Eshelby-type inclusion problem of a finite Elastic body containing a plane strain inclusion prescribed with a uniform eigenstrain and a uniform eigenstrain gradient is derived in a general form using a simplified strain gradient Elasticity theory (SSGET). The formulation is facilitated by an extended Betti’s reciprocal theorem and an extended Somigliana’s identity based on the SSGET and suitable for plane strain problems. The disturbed displacement field is obtained in terms of the SSGET-based Green’s function for an infinite plane strain Elastic body, which differs from that in earlier studies using the three-dimensional Green’s function. The solution reduces to that of the infinite-domain inclusion problem when the boundary effect is suppressed. The problem of a cylindrical inclusion embedded concentrically in a finite plane strain cylindrical Elastic Matrix of an enhanced continuum is analytically solved for the first time by applying the general solution, with the Eshelby tensor and its average over the circular cross section of the inclusion obtained in closed forms. This Eshelby tensor, being dependent on the position, inclusion size, Matrix size, and a material length scale parameter, captures the inclusion size and boundary effects, unlike existing ones. It reduces to the classical Elasticity-based Eshelby tensor for the cylindrical inclusion in an infinite Matrix if both the strain gradient and boundary effects are not considered. Numerical results quantitatively show that the inclusion size effect can be quite large when the inclusion is very small and that the boundary effect can dominate when the inclusion volume fraction is very high. However, the inclusion size effect is diminishing with the increase of the inclusion size, and the boundary effect is vanishing as the inclusion volume fraction becomes sufficiently low.

Andreas M Menzel - One of the best experts on this subject based on the ideXlab platform.

  • reversible magnetomechanical collapse virtual touching and detachment of rigid inclusions in a soft Elastic Matrix
    arXiv: Soft Condensed Matter, 2018
    Co-Authors: Mate Puljiz, Shilin Huang, Karl A Kalina, Johannes Nowak, Stefan Odenbach, Markus Kastner, Gunter K Auernhammer, Andreas M Menzel
    Abstract:

    Soft Elastic composite materials containing particulate rigid inclusions in a soft Elastic Matrix are candidates for developing soft actuators or tunable damping devices. The possibility to reversibly drive the rigid inclusions within such a composite together to a close-to-touching state by an external stimulus would offer important benefits. Then, a significant tuning of the mechanical properties could be achieved due to the resulting mechanical hardening. For a long time, it has been argued whether a virtual touching of the embedded magnetic particles with subsequent detachment can actually be observed in real materials, and if so, whether the process is reversible. Here, we present experimental results that demonstrate this phenomenon in reality. Our system consists of two paramagnetic nickel particles embedded at finite initial distance in a soft Elastic polymeric gel Matrix. Magnetization in an external magnetic field tunes the magnetic attraction between the particles and drives the process. We quantify the scenario by different theoretical tools, i.e., explicit analytical calculations in the framework of linear Elasticity theory, a projection onto simplified dipole-spring models, as well as detailed finite-element simulations. From these different approaches, we conclude that in our case the cycle of virtual touching and detachment shows hysteretic behavior due to the mutual magnetization between the paramagnetic particles. Our results are important for the design and construction of reversibly tunable mechanical damping devices. Moreover, our projection on dipole-spring models allows the formal connection of our description to various related systems, e.g., magnetosome filaments in magnetotactic bacteria.

  • reversible magnetomechanical collapse virtual touching and detachment of rigid inclusions in a soft Elastic Matrix
    Soft Matter, 2018
    Co-Authors: Mate Puljiz, Shilin Huang, Karl A Kalina, Johannes Nowak, Stefan Odenbach, Markus Kastner, Gunter K Auernhammer, Andreas M Menzel
    Abstract:

    Soft Elastic composite materials containing particulate rigid inclusions in a soft Elastic Matrix are candidates for developing soft actuators or tunable damping devices. The possibility to reversibly drive the rigid inclusions within such a composite together to a close-to-touching state by an external stimulus would offer important benefits. Then, a significant tuning of the mechanical properties could be achieved due to the resulting mechanical hardening. For a long time, it has been argued whether a virtual touching of the embedded magnetic particles with subsequent detachment can actually be observed in real materials, and if so, whether the process is reversible. Here, we present experimental results that demonstrate this phenomenon in reality. Our system consists of two paramagnetic nickel particles embedded at finite initial distance in a soft Elastic polymeric gel Matrix. Magnetization in an external magnetic field tunes the magnetic attraction between the particles and drives the process. We quantify our experimental results by different theoretical tools, i.e., explicit analytical calculations in the framework of linear Elasticity theory, a projection onto simplified dipole-spring models, as well as detailed finite-element simulations. From these different approaches, we conclude that in our case the cycle of virtual touching and detachment shows hysteretic behavior due to the mutual magnetization between the paramagnetic particles. Our results are important for the design and construction of reversibly tunable mechanical damping devices. Moreover, our projection on dipole-spring models allows the formal connection of our description to various related systems, e.g., magnetosome filaments in magnetotactic bacteria.

  • bridging from particle to macroscopic scales in uniaxial magnetic gels
    arXiv: Soft Condensed Matter, 2014
    Co-Authors: Andreas M Menzel
    Abstract:

    Connecting the different length scales of characterization is an important, but often very tedious task for soft matter systems. Here we carry out such a procedure for the theoretical description of anisotropic uniaxial magnetic gels. The so-far undetermined material parameters in a symmetry-based macroscopic hydrodynamic-like description are determined starting from a simplified mesoscopic particle-resolved model. This mesoscopic approach considers chain-like aggregates of magnetic particles embedded in an Elastic Matrix. Our procedure provides an illustrative background to the formal symmetry-based macroscopic description. There are presently other activities to connect such mesoscopic models as ours with more microscopic polymer-resolved approaches; together with these activities, our study complements a first attempt of scale-bridging from the microscopic to the macroscopic level in the characterization of magnetic gels.

X Wang - One of the best experts on this subject based on the ideXlab platform.

  • influences of longitudinal magnetic field on wave propagation in carbon nanotubes embedded in Elastic Matrix
    Applied Mathematical Modelling, 2010
    Co-Authors: Hao Wang, K Dong, F Men, Y J Yan, X Wang
    Abstract:

    This paper reported the result of an investigation into the effect of magnetic field on wave propagation in carbon nanotubes (CNTs) embedded in Elastic Matrix. Dynamic equations of CNTs under a longitudinal magnetic field are derived by considering the Lorentz magnetic forces. The results obtained show that wave propagation in CNTs embedded in Elastic Matrix under longitudinal magnetic field appears in critical frequencies at which the velocity of wave propagation drops dramatically. The velocity of wave propagation in CNTs increases with the increase of longitudinal magnetic field exerted on the CNTs in some frequency regions. The critical/cut-off frequency increases with the increase of Matrix stiffness, and the influence of Matrix on wave velocity is little in some frequency regions. This investigation may give a useful help in applications of nano-oscillators, micro-wave absorbing and nano-electron technology.

Yi Ze Wang - One of the best experts on this subject based on the ideXlab platform.

  • nonlinear vibration of carbon nanotube embedded in viscous Elastic Matrix under parametric excitation by nonlocal continuum theory
    Physica E-low-dimensional Systems & Nanostructures, 2016
    Co-Authors: Yi Ze Wang, Yuesheng Wang, Liaoliang Ke
    Abstract:

    Abstract In the present work, the nonlinear vibration of a carbon nanotube which is subjected to the external parametric excitation is studied. By the nonlocal continuum theory and nonlinear von Karman beam theory, the governing equation of the carbon nanotube is derived with the consideration of the large deformation. The principle parametric resonance of the nanotube is discussed and the approximation explicit solution is presented by the multiple scale method. Numerical calculations are performed. It can be observed that when the mode number is 1, the stable region can be significantly changed by the parametric excitation, length-to-diameter ratio and Matrix stiffness. This phenomenon becomes different to appear if the mode number increases. Moreover, the small scale effects have great influences on the positive bifurcation point for the short carbon nanotube, and the nonlocal continuum theory can present the proper model.

  • effects of axial load and Elastic Matrix on flexural wave propagation in nanotube with nonlocal timoshenko beam model
    Journal of Vibration and Acoustics, 2012
    Co-Authors: Yi Ze Wang, Kikuo Kishimoto
    Abstract:

    In this paper, the effects of the axial load and the Elastic Matrix on the flexural wave in the carbon nanotube are studied. Based on the nonlocal continuum theory and the Timoshenko beam model, the equation of the flexural wave motion is derived. The dispersion relation between the frequency and the wave number is illustrated. The characteristics of the flexural wave propagation in the carbon nanotube embedded in the Elastic Matrix with the axial load are analyzed. The wave frequency and the phase velocity are presented with different wave numbers. Furthermore, the small scale effects on the wave properties are discussed.

  • scale effects on flexural wave propagation in nanoplate embedded in Elastic Matrix with initial stress
    Applied Physics A, 2010
    Co-Authors: Yi Ze Wang, Kikuo Kishimoto
    Abstract:

    In this paper, the small-scale effects on the flexural wave in the nanoplate are studied. Based on the nonlocal continuum theory, the equation of wave motion is derived and the dispersion relation is presented. Numerical simulations are performed to investigate the influences of the scale coefficient, the surrounding Elastic Matrix and the initial stress on the wave propagation properties. The results show that the nonlocal model provides an appropriate method to investigate the characteristics of the flexural wave in the nanoplate. Furthermore, the direction and amplitude of the biaxial load, the stiffness of the shearing layer and the Winkler foundation can change the wave properties, significantly.