The Spherical Inclusion With Imperfect Interface

1991 ◽  
Vol 58 (2) ◽  
pp. 444-449 ◽  
Author(s):  
Z. Hashin
Keyword(s):  
Spherical Inclusion ◽  
Imperfect Interface ◽  
Interface Condition ◽  
Inclusion Problem ◽  
Homogeneous State ◽  
Interface Conditions ◽  
Spring Type ◽  
Strain Stress ◽  
Spring Constants ◽  
Perfect Interface

A rigorous solution of the spherical inclusion problem with remote uniform strain or stress and imperfect elastic spring-type interface conditions is presented. In the case of thin elastic interphase, the interface spring constants are expressed in terms of interphase elastic properties and thickness. The state of strain/stress in the inclusion is nonhomogeneous for imperfect interface conditions in contrast to the homogeneous state for perfect interface condition. Numerical results are given to demonstrate the significance of imperfect interface effects.

scholarly journals A circular inclusion with inhomogeneous non-slip imperfect interface in harmonic materials

2016 ◽  
Vol 472 (2190) ◽  
pp. 20160285 ◽  
Author(s):  
D. R. McArthur ◽  
L. J. Sudak
Keyword(s):  
Tangential Direction ◽  
Circular Inclusion ◽  
Imperfect Interface ◽  
Variable Coefficients ◽  
Interface Condition ◽  
Infinite Matrix ◽  
Linear Spring ◽  
Spring Type ◽  
Repeated Use ◽  
Plane Elastostatics

In this work, a rigorous study is presented for the problem associated with a circular inclusion embedded in an infinite matrix in finite plane elastostatics where both the inclusion and matrix are comprised a harmonic material. The inclusion/matrix boundary is treated as a circumferentially inhomogeneous imperfect interface that is described by a linear spring-type imperfect interface model where in the tangential direction, the interface parameter is infinite in magnitude and in the normal direction, the interface parameter is finite in magnitude (the so-called non-slip interface condition). Through the repeated use of the technique of analytic continuation, the boundary value problem for four analytic functions is reduced to solve a single first-order linear ordinary differential equation with variable coefficients for a single analytic function defined within the inclusion. The unknown coefficients of said function are then found via various analyticity requirements. The method is illustrated, using a specific example of a particular class of inhomogeneous non-slip imperfect interface. The results from these calculations are then contrasted with the results from the homogeneous imperfect interface. These comparisons indicate that the circumferential variation of interface damage has a pronounced effect on the average boundary stress.

Three-Dimensional Green’s Functions in Anisotropic Elastic Bimaterials With Imperfect Interfaces

2003 ◽  
Vol 70 (2) ◽  
pp. 180-190 ◽  
Author(s):  
E. Pan
Keyword(s):  
Green's Functions ◽  
Green’S Functions ◽  
Three Dimensional ◽  
Imperfect Interface ◽  
Boundary Integral ◽  
Stress Fields ◽  
Superposition Method ◽  
Interface Conditions ◽  
Complementary Part ◽  
Anisotropic Elastic

In this paper, three-dimensional Green’s functions in anisotropic elastic bimaterials with imperfect interface conditions are derived based on the extended Stroh formalism and the Mindlin’s superposition method. Four different interface models are considered: perfect-bond, smooth-bond, dislocation-like, and force-like. While the first one is for a perfect interface, other three models are for imperfect ones. By introducing certain modified eigenmatrices, it is shown that the bimaterial Green’s functions for the three imperfect interface conditions have mathematically similar concise expressions as those for the perfect-bond interface. That is, the physical-domain bimaterial Green’s functions can be obtained as a sum of a homogeneous full-space Green’s function in an explicit form and a complementary part in terms of simple line-integrals over [0,π] suitable for standard numerical integration. Furthermore, the corresponding two-dimensional bimaterial Green’s functions have been also derived analytically for the three imperfect interface conditions. Based on the bimaterial Green’s functions, the effects of different interface conditions on the displacement and stress fields are discussed. It is shown that only the complementary part of the solution contributes to the difference of the displacement and stress fields due to different interface conditions. Numerical examples are given for the Green’s functions in the bimaterials made of two anisotropic half-spaces. It is observed that different interface conditions can produce substantially different results for some Green’s stress components in the vicinity of the interface, which should be of great interest to the design of interface. Finally, we remark that these bimaterial Green’s functions can be implemented into the boundary integral formulation for the analysis of layered structures where imperfect bond may exist.

scholarly journals MATHEMATICAL MODELLING AND COMPUTER SIMULATION OF TEMPERATURE DISTRIBUTION IN INHOMOGENEOUS COMPOSITE SYSTEMS WITH IMPERFECT INTERFACE

2014 ◽  
Vol 6 (2) ◽  
pp. 77-85
Author(s):  
Pratibha Joshi ◽  
Manoj Kumar
Keyword(s):  
Numerical Simulation ◽  
Heat Flux ◽  
Temperature Distribution ◽  
Imperfect Interface ◽  
Immersed Interface Method ◽  
Immersed Interface ◽  
Composite Systems ◽  
Steady State Temperature ◽  
Perfect Interface ◽  
Inhomogeneous Composite

Many studies have been done previously on temperature distribution in inhomogeneous composite systems with perfect interface, having no discontinuities along it. In this paper we have determined steady state temperature distribution in two inhomogeneous composite systems with imperfect interface, having discontinuities in temperature and heat flux using decomposed immersed interface method and performed the numerical simulation on MATLAB.

Stress Concentrations in Three-Dimensional Electrostriction

1967 ◽  
Vol 34 (2) ◽  
pp. 431-436 ◽  
Author(s):  
T. E. Smith
Keyword(s):  
Displacement Vector ◽  
Spherical Inclusion ◽  
Crack Problem ◽  
Three Dimensional ◽  
Theory Of Elasticity ◽  
Uniform Electric Field ◽  
Inclusion Problem ◽  
Stress Concentrations ◽  
Displacement Potential ◽  
Penny Shaped Crack

Using the techniques employed in developing a Papkovich-Neuber representation for the displacement vector in classical elasticity, a particular integral of the kinematical equations of equilibrium for the uncoupled theory of electrostriction is developed. The particular integral is utilized in conjunction with the displacement potential function approach to problems of the theory of elasticity to obtain closed-form solutions of several stress concentration problems for elastic dielectrics. Under a prescribed uniform electric field at infinity, the problems of an infinite elastic dielectric having first a spherical cavity and then a rigid spherical inclusion are solved. The rigid spheroidal inclusion problem and the penny-shaped crack problem are also solved for the case where the prescribed field is parallel to their axes of revolution.

Coupled Extensional and Flexural Motions of a Two-Layer Plate With Interface Slip

2018 ◽  
Vol 141 (2) ◽  
Author(s):  
Peng Li ◽  
Feng Jin ◽  
Weiqiu Chen ◽  
Jiashi Yang
Keyword(s):  
Plate Theory ◽  
Cutoff Frequency ◽  
Great Influence ◽  
Imperfect Interface ◽  
Mindlin Plate ◽  
Finite Plate ◽  
Mindlin Plate Theory ◽  
Interface Elasticity ◽  
Propagating Shear ◽  
Perfect Interface

The effect of imperfect interface on the coupled extensional and flexural motions in a two-layer elastic plate is investigated from views of theoretical analysis and numerical simulations. A set of full two-dimensional equations is obtained based on Mindlin plate theory and shear-slip model, which concerns the interface elasticity and tangential discontinuous displacements across the bonding imperfect interface. Some numerical examples are processed, including the propagation of straight-crested waves in an unbounded plate, the buckling of a finite plate, as well as the deflection of a finite plate under uniform load. It is revealed that the bending-evanescent wave in the composites with a perfect interface eventually cuts-on to a propagating shear-like wave with cutoff frequency when the two sublayers imperfectly bonded. The similar phenomenon has been verified once again for coupled face-shear and thickness-shear waves. It also has been pointed out that the interfacial parameter has a great influence on the performance of static buckling, in which the outcome can be reduced to classical buckling load of a simply supported plate when the interface is perfect.

A Spherical Inclusion with Inhomogeneous Interface in Conduction

2003 ◽  
Vol 19 (1) ◽  
pp. 1-8
Author(s):  
T. Chen ◽  
C. H. Hsieh ◽  
P. C. Chuang
Keyword(s):  
Infinite Number ◽  
Effective Conductivity ◽  
Spherical Inclusion ◽  
Cone Angle ◽  
Imperfect Interface ◽  
Infinite Matrix ◽  
Algebraic Equations ◽  
Legendre Series ◽  
Linear Set ◽  
The Matrix

ABSTRACTA series solution is presented for a spherical inclusion embedded in an infinite matrix under a remotely applied uniform intensity. Particularly, the interface between the inclusion and the matrix is considered to be inhomegeneously bonded. We examine the axisymmetric case in which the interface parameter varies with the cone angle θ. Two kinds of imperfect interfaces are considered: an imperfect interface which models a thin interphase of low conductivity and an imperfect interface which models a thin interphase of high conductivity. We show that, by expanding the solutions of terms of Legendre polynomials, the field solution is governed by a linear set of algebraic equations with an infinite number of unknowns. The key step of the formulation relies on algebraic identities between coefficients of products of Legendre series. Some numerical illustrations are presented to show the correctness of the presented procedures. Further, solutions of the boundary-value problem are employed to estimate the effective conductivity tensor of a composite consisting of dispersions of spherical inclusions with equal size. The effective conductivity solely depends on one particular constant among an infinite number of unknowns.

A Normal Mode Stability Analysis of Numerical Interface Conditions for Fluid/Structure Interaction

2011 ◽  
Vol 10 (2) ◽  
pp. 279-304 ◽  
Author(s):  
J. W. Banks ◽  
B. Sjögreen
Keyword(s):  
Stability Analysis ◽  
Normal Mode ◽  
Compressible Fluid ◽  
Elastic Solid ◽  
Interface Condition ◽  
Finite Difference Schemes ◽  
Interface Conditions ◽  
Characteristic Boundary ◽  
Mode Stability ◽  
The Stability

AbstractIn multi physics computations where a compressible fluid is coupled with a linearly elastic solid, it is standard to enforce continuity of the normal velocities and of the normal stresses at the interface between the fluid and the solid. In a numerical scheme, there are many ways that velocity- and stress-continuity can be enforced in the discrete approximation. This paper performs a normal mode stability analysis of the linearized problem to investigate the stability of different numerical interface conditions for a model problem approximated by upwind type finite difference schemes. The analysis shows that depending on the ratio of densities between the solid and the fluid, some numerical interface conditions are stable up to the maximal CFL-limit, while other numerical interface conditions suffer from a severe reduction of the stable CFL-limit. The paper also presents a new interface condition, obtained as a simplified characteristic boundary condition, that is proved to not suffer from any reduction of the stable CFL-limit. Numerical experiments in one space dimension show that the new interface condition is stable also for computations with the non-linear Euler equations of compressible fluid flow coupled with a linearly elastic solid.

scholarly journals A Model of Damage for Brittle and Ductile Adhesives in Glued Butt Joints

Technologies ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 19
Author(s):  
Maria Letizia Raffa ◽  
Raffaella Rizzoni ◽  
Frédéric Lebon
Keyword(s):  
Adhesive Layer ◽  
Imperfect Interface ◽  
Interface Condition ◽  
Stress Strain ◽  
Butt Joints ◽  
Adhesive Layers ◽  
Strain Behavior ◽  
Rate Dependent ◽  
Torsional Loads ◽  
Relative Errors

The paper presents a new analytical model for thin structural adhesives in glued tube-to-tube butt joints. The aim of this work is to provide an interface condition that allows for a suitable replacement of the adhesive layer in numerical simulations. The proposed model is a nonlinear and rate-dependent imperfect interface law that is able to accurately describe brittle and ductile stress–strain behaviors of adhesive layers under combined tensile–torsion loads. A first comparison with experimental data that were available in the literature provided promising results in terms of the reproducibility of the stress–strain behavior for pure tensile and torsional loads (the relative errors were less than 6%) and in terms of failure strains for combined tensile–torsion loads (the relative errors were less than 14%). Two main novelties are highlighted: (i) Unlike the classic spring-like interface models, this model accounts for both stress and displacement jumps, so it is suitable for soft and hard adhesive layers; (ii) unlike classic cohesive zone models, which are phenomenological, this model explicitly accounts for material and damage properties of the adhesive layer.

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