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Notes: Abstract In this paper the mesophase developed between main phases in fibrous composites was studied assuming that it constitutes a diffuse boundary. This type of mesophase is normally developed in polymer-polymer adjacent phases and it it useful for the study of modern composites disposing a coupling agent between main phases. At the high temperature of reaction of phases during the casting process both neighboring phases are partly liquified, allowing a two-way movement of elements of either phase whose intensity and extent depends on the particular diffusion characteristics of either phase and the affinities between them. The characteristics of this diffusion reaction were studied and their influence on the development and the properties of the adhesion between phases were established, especially for fiber composites. Interesting results were derived concerning the extent of the diffusive mesophase and its mechanical properties, as well as its contribution on the global mechanical behavior of the composite. Finally, the results were found to be in agreement with previously established models.

Notes: Abstract An accurate relationship for the shear modulus of particulates is derived based on the Kerner model, but not using its approximate relations. Furthermore, the model takes into account the existence of the mesophase layer between the inclusions and the matrix, which acts as a smooth transition boundary layer between constituent materials. By applying Christensen's field to the Kerner model, modified by introducing the mesophase, the new model is liberated from any inconsistencies. Experimental evidence and application to a glass particle-epoxy resin-matrix composite indicated the superiority of the model over previous ones.

Notes: Summary The spectral decomposition of the compliance, stiffness, and failure tensors for transversely isotropic materials was studied and their characteristic values were calculated using the components of these fourth-rank tensors in a Cartesian frame defining the principal material directions. The spectrally decomposed compliance and stiffness or failure tensors for a transversely isotropic body (fiber-reinforced composite), and the eigenvalues derived from them define in a simple and efficient way the respective elastic eigenstates of the loading of the material. It has been shown that, for the general orthotropic or transversely isotropic body, these eigenstates consist of two double components, σ1 and σ2 which are shears (σ2 being a simple shear and σ1, a superposition of simple and pure shears), and that they are associated with distortional components of energy. The remaining two eigenstates, with stress components σ3, and σ4, are the orthogonal supplements to the shear subspace of σ1 and σ2 and consist of an equilateral stress in the plane of isotropy, on which is superimposed a prescribed tension or compression along the symmetry axis of the material. The relationship between these superimposed loading modes is governed by another eigenquantity, the eigenangle ω. The spectral type of decomposition of the elastic stiffness or compliance tensors in elementary fourth-rank tensors thus serves as a means for the energy-orthogonal decomposition of the energy function. The advantage of this type of decomposition is that the elementary idempotent tensors to which the fourth-rank tensors are decomposed have the interesting property of defining energy-orthogonal stress states. That is, the stress-idempotent tensors are mutually orthogonal and at the same time collinear with their respective strain tensors, and therefore correspond to energy-orthogonal stress states, which are therefore independent of each other. Since the failure tensor is the limiting case for the respective σx, which are eigenstates of the compliance tensor S, this tensor also possesses the same remarkable property. An interesting geometric interpretation arises for the energy-orthogonal stress states if we consider the “projections” of σx in the principal3D stress space. Then, the characteristic state σ2 vanishes, whereas stress states σ1, σ3 and σ4 are represented by three mutually orthogonal vectors, oriented as follows: The ε3 and ε4 lie on the principal diagonal plane (σ3δ12) with subtending angles equaling (ω−π/2) and (π-ω), respectively. On the positive principal σ3-axis, ω is the eigenangle of the orthotropic material, whereas the ε1-vector is normal to the (σ3δ12)-plane and lies on the deviatoric π-plane. Vector ε2 is equal to zero. It was additionally conclusively proved that the four eigenvalues of the compliance, stiffness, and failure tensors for a transversely isotropic body, together with value of the eigenangle ω, constitute the five necessary and simplest parameters with which invariantly to describe either the elastic or the failure behavior of the body. The expressions for the σx-vector thus established represent an ellipsoid centered at the origin of the Cartesian frame, whose principal axes are the directions of the ε1-, ε3- and ε4-vectors. This ellipsoid is a generalization of the Beltrami ellipsoid for isotropic materials. Furthermore, in combination with extensive experimental evidence, this theory indicates that the eigenangle ω alone monoparametrically characterizes the degree of anisotropy for each transversely isotropic material. Thus, while the angle ω for isotropic materials is always equal to ωi = 125.26° and constitutes a minimum, the angle |ω| progressively increases within the interval 90–180° as the anisotropy of the material is increased. The anisotropy of the various materials, exemplified by their ratiosE L/2GL of the longitudinal elastic modulus to the double of the longitudinal shear modulus, increases rapidly tending asymptotically to very high values as the angle ω approaches its limits of 90 or 180°.

Notes: Summary The present paper studies the influence of adhesives on the behaviour of cracks in two-dimensional linear elastic bodies. Especially the delamination and debonding effects are studied. The adhesive material is assumed to introduce non-monotone, possibly multivalued laws which can be described via non-convex superpotentials. The direct boundary integral equation method is extended for this problem. It gives rise to two equivalent multivalued integral equations holding on each crack. Numerical examples concerning the resulting stress intensity factors illustrate the theory.

Notes: Summary The optical method of reflected caustics was applied to beam buckling problems. The reflected rays of a light beam (either parallel, or convergent, or divergent) on the flanks of the strut create caustics which consist of two strongly illuminated straight lines, confining the luminous region of the strut. By measuring the distance between the extremities of the caustics, the perturbation parameters of the buckled beam can be defined. The accurate experimental evaluation ofs allows the solution of the respective Euler expansion equations for the critical buckling load and its higher order terms in the post-buckling state of the strut. The method is a versatile and sensitive technique for experimentally defining the mode of elastic buckling of struts and can be extended to study plastic buckling cases.

Notes: Summary Materials with specific microstructural characteristics and composite structures are able to exhibit negative Poisson's ratio. This fact has been shown to be valid for certain mechanisms, composites with voids and frameworks and has recently been verified for microstructures optimally designed by the homogenization approach. For microstructures composed of beams, it has been postulated that nonconvex shapes (with reentrant corners) are responsible for this effect. In this paper, it is numerically shown that mainly the shape, but also the ratio of shear-to-bending rigidity of the beams do influence the apparent (phenomenological) Poisson's ratio. The same is valid for continua with voids, or for composites with irregular shapes of inclusions, even if the constituents are quite usual materials, provided that their porosity is strongly manifested. Elements of the numerical homogenization theory and first attempts towards an optimal design theory are presented in this paper and applied for a numerical investigation of such types of materials.

Notes: Summary Materials with specific microstructural characteristics and composite structures are able to exhibit negative Poisson's ratio. This result has been proved for continuum materials by analytical methods in previous works of the first author, among others [1]. Furthermore, it also has been shown to be valid for certain mechanisms involving beams or rigid levers, springs or sliding collars frameworks and, in general, composites with voids having a nonconvex microstructure.Recently microstructures optimally designed by the homogenization approach have been verified. For microstructures composed of beams, it has been postulated that nonconvex shapes with re-entrant corners are responsible for this effect [2]. In this paper, it is numerically shown that mainly the shape of the re-entrant corner of a non-convex, star-shaped, microstructure influences the apparent (phenomenological) Poisson's ratio. The same is valid for continua with voids or for composities with irregular shapes of inclusions, even if the individual constituents are quite usual materials. Elements of the numerical homogenization theory are reviewed and used for the numerical investigation.

Notes: Summary The spectral decomposition of the fourth-rank compliance tensor S for transversely isotropic plates yields three eigenvalues, together with a new dimensionless parameter ω p , called the plane eigenangle. These constitute the essential parameters for an invariant description of the elastic behaviour of anisotropic plates. In this paper, a study of the variational bounds imposed by thermodynamical constraints on the values of the elastic constants is presented. Furthermore, a theoretical definition of the longitudinal shear modulus G L is introduced in terms of the elastic constants E L , E T and v L as a means of checking the validity of the experimentally measured value of G L . Finally, it is shown that the plane eigenangle ω p is the only necessary parameter required for a monoparametric indication of the elasticity and toughness of transversely isotropic plates.

Notes: Summary The elastic problem of an infinite orthotropic plate with different roots of its characteristic equation, when the fibers are oriented perpendicularly to an internal crack, and is weakened by an elliptic hole, is solved using Lekhnitskii's theory. The plate is subjected to prescribed stresses at infinity, while the boundary conditions are given at the flanks of the crack, at the rim of the perforation and at infinity. Using the complex-variable method, the solution of the problem is reduced to the evaluation of Cauchy-type integrals concerning the analytic functions of the problem. The numerical solution of the problem revealed an intense variation of mode-I stress intensity factors (SIF) at the crack tips due to the increase of either the crack length, or the distance of the near-by rack tip from the center of the hole. Furthermore, it was found that orthotropy strongly influences the intensity of stresses at the crack tips. These findings are in complete agreement with results given in a previous work by the authors, concerning a similar problem for an orthotropic plate, which, however, constitutes a special case, where the material presents equal roots for its characteristic equation [1].

Notes: Summary  The spectral decomposition of the compliance, stiffness, and failure tensors for transversely isotropic materials was studied and their characteristic values were calculated using the components of these fourth-rank tensors in a Cartesian frame defining the principal material directions. The spectrally decomposed compliance and stiffness or failure tensors for a transversely isotropic body (fiber-reinf orced composite), and the eigenvalues derived from them define in a simple and efficient way the respective elastic eigenstates of the loading of the material. It has been shown that, for the general orthotropic or transversely isotropic body, these eigenstates consist of two double components, σ 1 and σ 2, which are shears (σ 2 being a simple shear and σ 1, a superposition of simple and pure shears), and that they are associated with distortional components of energy. The remaining two eigenstates, with stress components σ 3 and σ 4, are the orthogonal supplements to the shear subspace of σ 1 and σ 2 and consist of an equilateral stress in the plane of isotropy, on which is superimposed a prescribed tension or compression along the symmetry axis of the material. The relationship between these superimposed loading modes is governed by another eigenquantity, the eigenangle ω. The spectral type of decomposition of the elastic stiffness or compliance tensors in elementary fourth-rank tensors thus serves as a means for the energy-orthogonal decomposition of the energy function. The advantage of this type of decomposition is that the elementary idempotent tensors to which the fourth-rank tensors are decomposed have the interesting property of defining energy-orthogonal stress states. That is, the stress-idempotent tensors are mutually orthogonal and at the same time collinear with their respective strain tensors, and therefore correspond to energy-orthogonal stress states, which are therefore independent of each other. Since the failure tensor is the limiting case for the respective σ x-tensors, which are eigenstates of the compliance tensor S, this tensor also possesses the same remarkable property. An interesting geometric interpretation arises for the energy-orthogonal stress states if we consider the “projections” of σ x in the principal 3D stress space. Then, the characteristic state σ 2 vanishes, whereas stress states σ 1, σ 3 and σ 4 are represented by three mutually orthogonal vectors, oriented as follows: The ε 3- and ε 4-vectors lie on the principal diagonal plane (σ3∂12) with subtending angles equaling (ω−π/2) and (π− ; ω), respectively. On the positive principal σ3-axis, ω is the eigenangle of the orthotropic material, whereas the ε 1-vector is normal to the (σ3∂12)-plane and lies on the deviatoric π-plane. Vector ε 2 is equal to zero. It was additionally conclusively proved that the four eigenvalues of the compliance, stiffness, and failure tensors for a transversely isotropic body, together with value of the eigenangle ω, constitute the five necessary and simplest parameters with which invariantly to describe either the elastic or the failure behavior of the body. The expressions for the σ x-vector thus established represent an ellipsoid centered at the origin of the Cartesian frame, whose principal axes are the directions of the ε 1, ε 3- and ε 4-vectors. This ellipsoid is a generalization of the Beltrami ellipsoid for isotropic materials. Furthermore, in combination with extensive experimental evidence, this theory indicates that the eigenangle ω alone monoparametrically characterizes the degree of anisotropy for each transversely isotropic material. Thus, while the angle ω for isotropic materials is always equal to ω i =125.26° and constitutes a minimum, the angle |ω| progressively increases within the interval 90–180° as the anisotropy of the material is increased. The anisotropy of the various materials, exemplified by their ratios E L /2G L of the longitudinal elastic modulus to the double of the longitudinal shear modulus, increases rapidly tending asymptotically to very high values as the angle ω approaches its limits of 90 or 180°.