Mark Kachanov

Bio: Mark Kachanov is an academic researcher from Tufts University. The author has contributed to research in topics: Stress intensity factor & Isotropy. The author has an hindex of 48, co-authored 184 publications receiving 9684 citations. Previous affiliations of Mark Kachanov include Rutgers University & Saint Petersburg State Polytechnic University.

Elastic Solids with Many Cracks and Related Problems

Abstract: Publisher Summary This chapter discusses some basic problems in mechanics of elastic solids containing multiple cracks. A number of mathematical aspects that frequently constitute fields of their own (like various numerical techniques) are discussed very briefly in the chapter. The focus is on physically important effects produced by crack interactions and to present results in the simplest form possible. The problems considered in this chapter can be divided into two groups: (1) The impact of interactions on individual cracks, particularly on the stress intensity factors (SIFs), and (2) the effective elastic properties of solids with many cracks. Problems of the first group are, generally, relevant for the fracture-related considerations; solutions are sensitive to the positions of individual cracks. Problems of the second group deal with the volume average quantities; they are relatively insensitive to the information on individual cracks. The chapter discusses, in this connection, whether correlations exist between these two groups of quantities; in particular, whether microcracking can be reliably monitored by measuring changes in the effective elastic moduli.

Effective Elastic Properties of Cracked Solids: Critical Review of Some Basic Concepts

Abstract: The problem of effective moduli of cracked solids is critically reviewed. Various approaches to the problem are discussed; they are further assessed by comparing their predictions to results for sample deterministic arrays. These computer experiments indicate that the approximation of noninteracting cracks has a wider than expected range of applicability. Some of the deficiencies of various approximate schemes seem to be related to inadequacy of the conventionally used crack density parameter (insensitive to mutual positions of cracks). An alternative parameter that has this sensitivity, is suggested. Finally, the problem of effective moduli is discussed in the context of {open_quotes}damage mechanics{close_quotes}. It is argued that, contrary to the spirit of many damage models, there is no direct quantitative correlation between progression of a microcracking solid towards fracture and deterioration of its stiffness; thus, the effective moduli may not always serve as a reliable indicator of damage. 84 refs., 14 figs.

Microcrack-induced elastic wave anisotropy of brittle rocks

Abstract: The failure of brittle rocks during compression is preceded by the formation, growth, and coalescence of microcracks. Elastic wave velocities are reduced in the presence of open microcracks and fractures and may therefore be used to monitor the progressive damage of the rock. In general, these microcracks are not randomly oriented, and the rock displays an elastic anisotropy. The elastic anisotropy due to cracks can be expressed in terms of a second-rank and fourth-rank crack density tensor. For open cracks the contribution of the fourth-rank crack density tensor to the elastic wave velocities is small. These results are compared with recent measurements of the ultrasonic compressional and shear wave velocities for propagation parallel and perpendicular to an increasing axial stress applied at constant confining stress to Berea sandstone. Inversion of the velocity measurements indicates that the microcracks propagate parallel to the maximum compressive stress, in agreement with current rock mechanics theory. A reasonable fit to the data is obtained using only the second-rank crack density tensor even though, at high confining stress, the cracks are expected to be in partial contact along their length. This is consistent with the model of elastic wave propagation in a medium containing partially contacting fractures published by White. However, measurements of off-axis wave velocities are required to fully quantify the contribution of the fourth-rank crack density tensor.

Continuum Model of Medium with Cracks

Abstract: A continuum approach to an elastic medium containing cracks is developed. A crack density tensor describing the averaged geometry of a crack array is introduced and used to study the anisotropy of an effective elastic response due to the presence of cracks. The resulting continuum model turns out to be orthotropic, which is in good agreement with the results given by the small concentration approach and the self-consistent method. Anisotropy of the transport properties (fluid permeability, electric- and heat conductivity) is also considered.

Phd by thesis

Abstract: Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Effects of particle size, particle/matrix interface adhesion and particle loading on mechanical properties of particulate–polymer composites

Abstract: There have been a number of review papers on layered silicate and carbon nanotube reinforced polymer nanocomposites, in which the fillers have high aspect ratios. Particulate–polymer nanocomposites containing fillers with small aspect ratios are also an important class of polymer composites. However, they have been apparently overlooked. Thus, in this paper, detailed discussions on the effects of particle size, particle/matrix interface adhesion and particle loading on the stiffness, strength and toughness of such particulate–polymer composites are reviewed. To develop high performance particulate composites, it is necessary to have some basic understanding of the stiffening, strengthening and toughening mechanisms of these composites. A critical evaluation of published experimental results in comparison with theoretical models is given.

The Rock Physics Handbook: Tools for Seismic Analysis of Porous Media

Abstract: Preface 1. Basic tools 2. Elasticity and Hooke's law 3. Seismic wave propagation 4. Effective media 5. Granular media 6. Fluid effects on wave propagation 7. Empirical relations 8. Flow and diffusion 9. Electrical properties Appendices.

The Rock Physics Handbook

Abstract: Responding to the latest developments in rock physics research, this popular reference book has been thoroughly updated while retaining its comprehensive coverage of the fundamental theory, concepts, and laboratory results. It brings together the vast literature from the field to address the relationships between geophysical observations and the underlying physical properties of Earth materials - including water, hydrocarbons, gases, minerals, rocks, ice, magma and methane hydrates. This third edition includes expanded coverage of topics such as effective medium models, viscoelasticity, attenuation, anisotropy, electrical-elastic cross relations, and highlights applications in unconventional reservoirs. Appendices have been enhanced with new materials and properties, while worked examples (supplemented by online datasets and MATLAB® codes) enable readers to implement the workflows and models in practice. This significantly revised edition will continue to be the go-to reference for students and researchers interested in rock physics, near-surface geophysics, seismology, and professionals in the oil and gas industries.

Nonlocal integral formulations of plasticity and damage: Survey of progress

Abstract: Modeling of the evolution of distributed damage such as microcracking, void formation, and softening frictional slip necessitates strain-softening constitutive models. The nonlocal continuum concept has emerged as an effective means for regularizing the boundary value problems with strain softening, capturing the size effects and avoiding spurious localization that gives rise to pathological mesh sensitivity in numerical computations. A great variety of nonlocal models have appeared during the last two decades. This paper reviews the progress in the nonlocal models of integral type, and discusses their physical justifications, advantages, and numerical applications.