Victor A. Gotlib

Effect of structure on environmentally assisted subcritical crack growth in brittle materials

Subcritical crack growth in brittle materials is considered when it is thermally activated and water vapor affected. Effects of material structure on the crack growth were investigated. Special case of subcritical crack growth is examined when the crack growth is decided by water vapor enhanced rupture of some particulate strength controlling elements of material structure. The water vapor is assumed to be transported to these elements through the material by diffusion in a gas filling a system of interconnected open pore channels in the material volume. Calculated crack velocity plots versus the stress intensity factor, temperature and humidity are presented.

Continuum versus discontinuum damage mechanics of creep caused by microcracking

The effect of evolution of damage, mainly microcrack damage, on creep and creep fracture of brittle materials (or materials exhibiting brittle-like behavior under certain temperature and loading conditions) is treated theoretically. A comparative analysis of two basic approaches is given:(i) continuum damage mechanics (CDM), and(ii) discontinuum damage mechanics (DDM). The first approach deals, from the very beginning, with continuum abstract description of damage with the help of field quantities.The second approach considers the macroscopic mechanical behavior of the material affected by damage evolution in terms of individual damage units, such as microcracks or/and microvoids. A serious conceptual deficiency of the CDM approach is pointed out and analyzed. This deficiency is associated with the CDM basic notion of the effective stress, understood as the stress (referred to undamaged area) which governs the deformation of the material per se in the presence of damage. This deficiency becomes apparent in the case when damage is caused by a multitude of cracks (microcracks). In this case, the damaged area, as it is defined by CDM, is actually the area occupied by cracks. As this area is negligible, the effect of damage on the mechanical behavior of the material, according to CDM, would be negligible either, irrespective of the cracks concentration, which is in deep contradiction with reality. It is shown how the situation can be improved with the aid of DDM and how the macroscopic creep behavior relates to the structure and strength parameters of the material when considering the mechanism of damage evolution in terms of thermal activation.

Neural computing of effective properties of random composite materials

Abstract The effective response of disordered heterogeneous materials, in general, is not amenable to the exact analysis because the phase geometry may not be completely specified. The present paper deals with the problem of effective properties such as thermal conductivity, electrical conductivity, dielectric constant, magnetic permeability, and diffusivity in the realm of disordered composites. Even though all these properties are analogous, their numerical treatment in the same unified frameworks may be difficult. In fact, depending on the physical quantity involved, there may be a large discrepancy in the order of magnitude of relevant material parameters. This paper reports a methodology for investigating the effective scalar parameter of disordered composites with the help of the same neural network, regardless of the above physical context. Particular results are obtained for effectively isotropic and macroscopically homogeneous two-phase materials.

Neural computations of effective response of random composites

Abstract The effective response of disordered heterogeneous materials, in general, is not amenable to exact analysis because the phase geometry may not be completely specified. Besides the bounds for the effective moduli, most reported results are essentially approximate, may contradict each other or even violate the bounds. With increasing number of phases, and therefore increasing uncertainty inherent in the very statement of the problem, the investigation of effective response becomes less amenable to analytical treatment, in particular, by methods of boundary-value problems of mathematical physics. The present paper reports a methodology for investigating the effective response of disordered composites with the help of neural networks as well as particular results obtained for effectively isotropic and macroscopically homogeneous two-phase materials. It is shown that, after incorporating the bounds and proper training, simple neural networks may describe a wide variety of the effective response for two-phase composites, though in general more complicated networks appear necessary.

Assessment of Informational Properties of Finite Elements

The very variety of finite elements available, which is perhaps the most attractive feature of the finite element method, poses a problem of their comparative “quality”. This problem may be approached from various points of view, such as simplicity of the finite element, its conformability, etc. The present work deals with the definition and evaluation of the information “stored” by a finite element. This quantity may adequately describe what is usually called the versatility of the element, in a sense that a more versatile element “stores” more information. Accordingly, it may provide an additional parameter for evaluation of the quality of a finite element. The treatment below is based on the maximum-entropy (or minimum bias) principle, which states that the most likely probability distribution follows from maximization of the entropy subjected to the given constraints. Jaynes [1,2] provided a particularly elegant formalism for implementing this principle to physical systems. Applications to evaluation of the accuracy of approximate methods (Ritz, Bubnov-Galerkin) were given by Beltzer in [3,4] to which the present work is a sequel. For an extensive exposition of the entropy concept and related subjects the reader is referred to the monograph by Kapur [5].

Subcritical crack growth in brittle material at gas turbulence effect on aggressive species transport to crack tip

In the case when the replacing gas flow is turbulent, the turbulence can affect the water vapor transport to the crack tip via turbulent eddy penetration through the laminar sublayer and, therefore, influence the subcritical crack growth

Delayed fracture of damaged zone in fibrous composite

This approach to solving a problem which involves only two scales of cracking and fracture (the one associated with a fiber and another one associated with many fibers bridging the damaged zone in a composite), illustrates a general idea of how one can cope with problems involving a multitude of such scales as is the case with ceramics and, to an even greater extent, the case of rock