Soft Elastic Material Research Articles

Homogenization of an elastic medium reinforced by anisotropic fibers

We present results in this Note concerning a vector version in the framework of linearized elasticity (see A. Sili, Homogenization of an elastic medium reinforced by anisotropic fibers, in press), of our previous work in which we have studied the homogenization of a scalar nonlinear monotone problem posed on a fibered medium (see A. Sili, Homogenization of a nonlinear monotone problem in an anisotropic medium, in press). Here, we assume that parallel elastic anisotropic fibers, periodically distributed with a period of size ε in a cube Ω, are surrounded by a soft elastic material, the elasticity coefficients of this material being in the ratio ε 2 with those of the fibers. We prove that the homogenized problem is nonlocal and involves variables linked together with the anisotropy of the fibers. To cite this article: A. Sili, C. R. Mecanique 331 (2003).

Compression of Bonded Blocks of Soft Elastic Material: Variational Solution

The problem of a block of nearly incompressible elastic material, bonded on its top and bottom parallel faces to rigid end plates, against which any slip is prevented, and subjected to direct compression, is examined. Approximate solutions are obtained using the minimum potential energy and Hellinger-Reissner variational principles. Bulk compressibility is naturally included in these solutions. The necessity of avoiding a severe overestimation of the effective compressive stiffness of thin blocks is demonstrated. For such blocks, the results confirm solutions, extensively used in engineering design, which are based on the assumption of a pressure distribution within the block.

Mechanical effects in peel adhesion test

—Mechanical effects in the peel strength of a thin film have been studied both experimentally and theoretically. It has been found that the adhesion strength measured by the peel test is a practical adhesion (an engineering strength per unit width) and does not represent the true interface adhesion strength. The measured value may represent a multiplication of the true interface adhesion and other work expended in the plastic deformation of the thin film. The contribution of the latter to the peel strength is found to be, sometimes, of the order of 100 times higher than the former. It is found that the major controlling factors in the peel strength are the thickness, Young's modulus, the yield strength, the strain hardening coefficient of the film, and the compliance of the substrate as well as the interface adhesion strength. Even though the true interface adhesion strength is the same, a higher peel strength is obtained if the film is thinner or more ductile under the test conditions reported in this paper. The same effect can be obtained if the substrate is thinner in the case where the substrate is a soft elastic material, or if the substrate is thicker in the case where the substrate is a rigid material.

The Linear Magnetoelastic Problem of Two Coplanar Griffith Cracks in a Soft Ferromagnetic Elastic Strip

Following a linear theory for soft ferromagnetic elastic solids, we consider the problem of determining the stress-intensity factors in an infinite strip of a soft ferromagnetic elastic material containing two coplanar Griffith cracks. We assume that the solid is a homogeneous and isotropic one and it is permeated by a uniform magnetostatic field normal to the cracks surfaces and that the cracks are opened by a constant internal pressure. By the use of Fourier transforms we reduce the problem to that of solving two simultaneous triple integral equations. These equations are reduced to a singular integral equation of the first kind. By expanding the solution into the form of the product of the series of Chebyshev polynomials of the first kind and their weight function, the singular integral equation is further reduced to the infinite system of algebraic equations for the determination of the unknown coefficients. Numerical calculations are carried out and the influence of the magnetic fields on the stress-intensity factors is graphically shown in detail.

Plane strain rotation moduli for soft elastic blocks

Making assumptions similar to these used to obtain compression moduli, a simple relation is developed for the plane strain rotation moduli for blocks of soft elastic material bonded to rigid end plates. The deformation arises when one plate rotates relative to the other plane about an axis along the centre of its width. The approximate theoretical solution compares well with finite-element analysis data for materials with Poisson's ratios of 0.333, 0.483 87 and 0.499 83 and blocks having width-to-thickness ratios between 0.25 and 64.

Compression moduli for blocks of soft elastic material bonded to rigid end plates

Using simplifying assumptions based on a theoretical solution for incompressible materials, simple relations are developed for the plane strain and axisymmetric compression moduli for blocks of compressible soft elastic material bonded to rigid end plates. The approximate theoretical solutions compare well with finite-element analysis data for materials with Poisson's ratios between 0.125 and 0.499 83 and blocks having width-to-thickness or diameter-to-thickness ratios between 0.25 and 128.