Volume 20, Nº 2 (2017)

The present paper embraces mainly the three-year period of 1966 to 1968 when the invariant integral of fracture mechanics appeared and became popular, and the last two years of 2015 to 2016 when the neoclassic cosmology based on the invariant integral came up. A mention is given to the previous works of Euler, Cauchy, Maxwell, Nother, Gunther and Eshelby who dealt with invariant integrals in mathematics, hydrodynamics, electrodynamics, and the theory of dislocations. A brief review is given of the creation of the invariant integral of fracture mechanics under static and dynamic conditions for a solid continuum including elastic, plastic and viscoelastic materials, as well as of some of its most important applications, ramifications and generalizations for other physical fields. The initial phase of the expansion and revolution of the large-scale universe is studied in the framework of the neoclassic approach, including the Big Bang and the Dark Energy; it is shown that the spheroidal shape of the universe assumed at the Big Bang retains its eccentricity constant in the initial phase. The assumption of a superphoton as a primordial universe was analyzed.

The effect of the nonequilibrium structure of 2D aluminum hydroxide-based objects on the macroscopic response (adsorption properties) is studied in the physical mesomechanics framework. Molecular dynamics simulation is performed to examine the nature of selective adsorption of the considered low-dimensional structures. The role of defects and structural elements, such as polar functional groups, is analyzed. Model ions and endotoxin are used to illustrate the selective character of adsorption. Prospects for biomedical applications of the obtained results are discussed.

In this work, some recent mixed mode I/II fracture toughness results obtained from Perspex (or polymethylmethacrylate (PMMA)) with four simple cracked specimens subjected to the conventional three-point bend loading are reanalysed based on local energy concept. Although all the mentioned samples have been tested under the same and similar mode mixities, different fracture toughness envelopes were obtained for mixed mode I/II fracture of PMMA. The averaged strain energy density (SED) criterion has been applied in the past for different types of notched specimens (including U, V, O and keyhole notches). It is shown that the mixed mode tensile-in plane shear fracture toughness data obtained from the semicircular and triangular crack type specimens are successfully predicted for sharp cracked PMMA samples using the SED criterion.

This paper completes the review of recent (last 15 years) publications on experimental and theoretical methods and approaches for studying damage accumulation and fracture in crystalline solids. It summarizes the works that describe damage and fracture using an approach based on crystal plasticity. These works study the propagation of trans- and intergranular cracks, microvoid nucleation and evolution in two-phase steel specimens, crack growth in low- and high-cycle fatigue, and analyze the deformation behavior of various materials under high radiation that strongly affects mechanical properties. Much attention is given to the papers on the numerical implementation of crystal plasticity models, particularly, modifications of finite element models used in application packages for damage and fracture description.

The paper reports the results of field experiments on studying different modes of gravitational sliding of a block on the natural fault surface. Various materials were used as interface filler to model the whole range of deformation events that can be arbitrarily divided into three groups: accelerated creep, slow slip, and dynamic slip. The experiments show that the type of modeled deformation events is defined by both structural parameters of contact between blocks and material composition of the contact filler.

Foundations for a new geomechanical model of occurrence of different-type dynamic events were developed. The model is based on the idea that “contact spots” form subnormally to the crack edges during shear deformation; the “spots” are clusters of force mesostructures whose evolution governs the deformation mode. The spatial configuration of “contact spots” remains unchanged during the entire “loading-slip” cycle but changes after the dynamic event occurrence. The destroyed force mesostructures can be replaced by similar structures under intergranular interaction forces when the external influence is fully compensated. Unless “contact spots” are incompletely destroyed, the deformation process dynamics is defined by their rheology. The migration of “contact spots” during deformation of a crack filled with heterogeneous material causes changes in deformation parameters and transformation of the mode itself due to changing rheology of local contact areas between blocks.

It is found by fractal analysis that in order for dynamic slip to occur, spatially structured “contact spots” characterized by low fractal dimension must be formed; slow slip events can exist only in a certain parametric domain called the “dome of slow events”. It is found that the probability of slow slip occurrence is higher on fault regions characterized by maximum fractal dimension values: fault tips, fault branching and fault intersection zones.

Here we provide a review of research on slow motions and strain waves in the Earth and propose a substantiated hypothesis that all stress-strain perturbations in the form of slow waves propagating in solids and geomedia, including plastic waves in metals and waves in faults of different scales, are of common physical nature. Loaded solids and geomedia are active hierarchically organized multiscale systems that display nonlinear dynamics and lose their stability when disturbed by any dynamic processes at block boundaries, e.g., displacements in fault zones. Such a medium cooperatively responds to parametric excitation by generating slow strain waves (autowaves) as a way of its self-organization. In support of the proposed concept, a consistent mathematical model is suggested for describing the evolution of stress-strain states and slow strain autowaves in an unstable elastoplastic medium, and examples of simulations are presented for strain autowaves in ductile materials under tension and quasi-brittle materials and geomedia with a fault zone under compression.

The paper proposes a system of second-order ordinary differential equations with solutions interpreted as trajectories of a turbulent vortex wake. The trajectories are modeled by complexes of geodesic lines in non-Euclidean geometries and are analyzed to select a proper geometry by choosing a particular gauge for modeling the whole class of turbulent vortex wake trajectories. Examples are given of geodesic and partially geodesic gauges to model a particular complex of linear vortex wake trajectories, and possible ways are suggested to apply the theory to turbulence mesodynamics in cosmic plasma.