Multiscale Biomechanics and Tribology of Inorganic and Organic Systems

This introductory chapter is dedicated to the life and work of Sergey Grigirievich Psakhie, his outstanding contributions to the development of science and education in Russia and especially in the Tomsk region as well as to his numerous international collaborations and research interests. It further includes personal notes from some of his closest collaborators: Georg-Peter Ostermeyer, Valentin L. Popov, Lev B. Zuev and Valery V. Ruzich. The Chapter is concluded by an overview of Sergey G. Psakhie’s most significant scientific publications.

Orthopaedic and dental implant treatments have allowed to enhance the quality of life of millions of patients. Total hip/knee arthroplasty is a surgical replacement of the hip/knee joint with an artificial prosthesis. The aim of joint replacement surgery is to relieve pain improve function, often for sufferers of osteoarthritis, which affects around a third of people aged over fifty. Nowadays, total hip and knee replacement (THR) surgeries are considered routine procedures with generally excellent outcomes. Given the increasing life expectancy of the world population, however, many patients will require revision or removal of the artificial joint during their lifetime. The most common cause of failure of hip and knee replacements is mechanical instability secondary to wear of the articulating components. Thus, tribological and biomechanical aspects of joint arthroplasty are of specific interest in addressing the needs of younger, more active patients. The most significant improvements in the longevity of artificial joints have been achieved through the introduction of more wear resistant bearing surfaces. These innovations, however, brought about new tribocorrosion phenomena, such as fretting corrosion at the modular junctions of hip implants. Stiffness mismatch between the prosthesis components, non-physiological stress transfer and uneven implant-bone stress distribution are all involved in premature failure of hip arthroplasty. The development of more durable hip and knee prostheses requires a comprehensive understanding of biomechanics and tribocorrosion of implant materials. Some of these insights can also be applied to the design and development of dental implants.

The authors outline the results of long-term interdisciplinary research aimed at identifying the possibility and the methods of controlling tangential displacements in seismically dangerous faults to reduce the seismic risk of potential earthquakes. The studies include full-scale physical and numerical modeling of P-T conditions in the earth’s crust contributing to the initiation of displacement in the stick-slip regime and associated seismic radiation. A cooperation of specialists in physical mesomechanics, seismogeology, geomechanics, and tribology made it possible to combine and generalize data on the mechanisms for the formation of the sources of dangerous earthquakes in the highly stressed segments of faults. We consider the prospect of man-caused actions on the deep horizons of fault zones using powerful shocks or vibrations in combination with injecting aqueous solutions through deep wells to manage the slip mode. We show that such actions contribute to a decrease in the coseismic slip velocity in the fault zone, and, therefore, cause a decrease in the amplitude and energy of seismic vibrations. In conclusion, we substantiate the efficiency of the use of combined impacts on potentially seismically hazardous segments of fault zones identified in the medium-term seismic prognosis. Finally, we discuss the importance of the full-scale validation of the proposed approach to managing the displacement regime in highly-stressed segments of fault zones. Validation should be based on large-scale tests involving advanced technologies for drilling deep multidirectional wells, injection of complex fluids, and localized vibrational or pulse impacts on deep horizons.

Methods of particles are now recognized as an effective tool for numerical modeling of dynamic mechanical and coupled processes in solids and liquids. This chapter is devoted to a brief review of recent advances in the development of the popular particle-based discrete element method (DEM). DEM is conventionally considered as a highly specialized technique for modeling the flow of granular media and the fracture of brittle materials at micro- and mesoscopic scales. However, in the last decade, great progress has been made in the development of the formalism of this method. It is largely associated with the works of the scientific group of Professor S. G. Psakhie. The most important achievement of this group is a generalized formulation of the method of homogeneously deformable discrete elements. In the chapter, we describe keystones of this implementation of DEM and a universal approach that allows one to apply various rheological models of materials (including coupled models of porous fluid-saturated solids) to a discrete element. The new formalism makes possible qualitative expansion of the scope of application of the particle-based discrete element technique to materials with various rheological properties and to the range of considered scales form microscopic to macroscopic. The capabilities of this method are especially in demand in the study of the features of contact interaction of materials. To demonstrate these capabilities, we briefly review two recent applications concerning (a) the effect of adhesive interaction on the regime of wear of surface asperities under tangential contact of bodies and (b) the nonmonotonic dependence of the stress concentration in the neck of the human femur on the dynamics of hip joint contact loading.

The chapter presents recent advances in developing numerical models for multiscale simulation of the femur–endoprosthesis system for the case of hip resurfacing arthroplasty. The models are based on the movable cellular automaton method, which is a representative of the discrete element approach in solid mechanics and allows correctly simulating mechanical behavior of a variety of elastoplastic materials including fracture and mass mixing. At the lowest scale, the model describes sliding friction between two rough surfaces of TiN coatings, which correspond to different parts of the friction pair of hip resurfacing endoprosthesis. At this scale, such parameters of the contacting surfaces as the thickness, roughness, and mechanical properties are considered explicitly. The next scale of the model corresponds to a resurfacing cap for the femur head rotating in the artificial acetabulum insert. Here, sliding friction is explicitly computed based on the effective coefficient of friction obtained at the previous scale. At the macroscale, the proximal part of the femur with a resurfacing cap is simulated at different loads. The bone is considered as a composite consisting of outer cortical and inner cancellous tissues, which are simulated within two approaches: the first implies their linear elastic behavior, the second considers these tissues as Boit’s poroelastic bodies. The later allows revealing the role of the interstitial biological fluid in the mechanical behavior of the bone. Based on the analysis of the obtained results, the plan for future works is proposed.

In recent years, research has increasingly focused on the complex processes involved in friction contacts. Especially in tribological high-loaded contacts, characterized by the presence of contact modifying wear particles, macroscopic friction shows a surprisingly high dynamic complexity on many temporal and local scales. There are dominant effects on mesoscopic scales such as the geometric self-organization structures of the wear dust in the contact, which can significantly change the local contact surfaces. For the description and simulation of these phenomena, abstract methods have shown their effectiveness. One class of methods are cellular automata, both volume- and particle-based. The latter are in particular the Movable Cellular Automata developed by Sergey Psakhie. The scales of these discrete methods are freely selectable in wide ranges between the macro world and the atomic scale. Nevertheless, they provide reliable information on mesoscopic balances in the boundary layer and thus also on the macroscopic behavior of the tribocontact. The success of these methods is shown by the example of an automotive brake. The question of the relative insensitivity of the scales of these mesoscopic methods is examined in detail.

One of the principal methods of preventing large earthquakes is stimulation of a large series of small events. The result is a transfer of the rapid tectonic dynamics in a creep mode. In this chapter, we discuss possibilities for such a transfer in the framework of simplified models of a subduction zone. The proposed model describes well the basic characteristic features of geo-medium behavior, in particular, statistics of earthquakes (Gutenberg Richter and Omori laws). Its analysis shows that local relatively low-energy impacts can switch block dynamics from stick–slip to creep mode. Thus, it is possible to change the statistics of seismic energy release by means of a series of local, periodic, and relatively low energy impacts. This means a principal possibility of “suppressing” strong earthquakes. Additionally, a modified version of the Burridge-Knopoff model including a simple model for state dependent friction force is derived and studied. The friction model describes a velocity weakening of friction between moving blocks and an increase of static friction during stick periods. It provides a simplified but qualitatively correct stability diagram for the transition from smooth sliding to a stick–slip behavior as observed in various tribological systems. Attractor properties of the model dynamic equations were studied under a broad range of parameters for one- and two-dimensional systems.

Mechanical surface hardening processes have long been of interest to science and technology. Today, surface modification technologies have reached a new level. One of them is friction stir processing that refines the grain structure of the material to a submicrocrystalline state. Previously, the severe plastic deformation occurring during processing was mainly described from the standpoint of temperature and deformation, because the process is primarily thermomechanical. Modeling of friction stir welding and processing predicted well the heat generation in a quasi-liquid medium. However, the friction stir process takes place in the solid phase, and therefore the mass transfer issues remained unresolved. The present work develops the concept of adhesive-cohesive mass transfer during which the rotating tool entrains the material due to adhesion, builds up a transfer layer due to cohesion, and then leaves it behind. Thus, the transfer layer thickness is a clear criterion for the mass transfer effectiveness. Here we investigate the effect of the load on the transfer layer and analyze it from the viewpoint of the friction coefficient and heat generation. It is shown that the transfer layer thickness increases with increasing load, reaches a maximum, and then decreases. In so doing, the average moment on the tool and the temperature constantly grow, while the friction coefficient decreases. This means that the mass transfer cannot be fully described in terms of temperature and strain. The given load dependence of the transfer layer thickness is explained by an increase in the cohesion forces with increasing load, and then by a decrease in cohesion due to material overheating. The maximum transfer layer thickness is equal to the feed to rotation rate ratio and is observed at the axial load that causes a stress close to the yield point of the material. Additional plasticization of the material resulting from the acoustoplastic effect induced by ultrasonic treatment slightly reduces the transfer layer thickness, but has almost no effect on the moment, friction coefficient, and temperature. The surface roughness of the processed material is found to have a similar load dependence.

This chapter provides a brief review of computer simulation studies on the interaction of nanomaterials with biomembranes. The interest in this area is governed by the variety of possible biomedical applications of nanoparticles and nanomaterials as well as by the importance of understanding their possible cytotoxicity. Molecular dynamics is a flexible and versatile computer simulation tool, which allows us to research the molecular level mechanisms of nanomaterials interaction with cell or bacterial membrane, predicting in silico their behavior and estimating physicochemical properties. In particular, based on the molecular dynamics simulations, a bio-action mechanism of two-dimensional aluminum hydroxide nanostructures, termed aloohene, was discovered by the research team led by Professor S. G. Psakhie, accounting for its anticancer and antimicrobial properties. Here we review three groups of nanomaterials (NMs) based on their structure: nanoparticles (globular, non-elongated), (quasi)one-dimensional NMs (nanotube, nanofiber, nanorod) and two-dimensional NMs (nanosheet, nanolayer, nanocoated substrate). Analysis of the available in silico studies, thus can enable us a better understanding of how the geometry and surface properties of NMs govern the mechanisms of their interaction with cell or bacterial membranes.

The tumor microenvironment regulates tumor progression and the spread of cancer in the body. Applications of nanomaterials that can dysregulate tumor-microenvironment are emerging as a promising anti-cancer approaches, which can improve the efficacy of existing cancer treatments. We have reported that agglomerates of radially assembled Al hydroxide crumpled nanosheets with the disordered defective surface structure have a large positive charge and therefore can lead to ion imbalance at the cell perimembranous space through the selective adsorption of extracellular anionic species. This effect was demonstrated in vitro by reduced viability and proliferation of tumor cells, and further validated in a murine melanoma cancer model. Furthermore, crumpled Al hydroxide nanostructures showed a much stronger suppressive effect on tumor growth in combination with a minimally effective dose of doxorubicin. Taken together, the described approach of tumor microenvironment dysregulation through selective adsorption properties of folded crumpled nanostructures opened a new avenue for development of innovative anticancer therapy strategies.

The gauge dynamic theory of defects in a heterogeneous medium predicts the nonlinearity of plastic flow at low lattice curvature and structural turbulence with the formation of individual dynamic rotations at high curvature of the deformed medium. The present work is devoted to the experimental verification of the theoretical predictions. Experimentally studied are the influence of high-temperature radial shear rolling and subsequent cold rolling on the internal structure of metastable Fe–Cr–Mn austenitic stainless steel, formation of nonequilibrium ε- and α′-martensite phases, appearance of dynamic rotations on fracture surfaces, fatigue life in alternating bending, and wear resistance of the material. Scratch testing reveals a strong increase in the damping effect in the formed hierarchical mesosubstructure. The latter is responsible for a nanocrystalline grain structure in the material, hcp ε martensite and bcc α′ martensite in grains, a vortical filamentary substructure on the fracture surface as well as for improved high-cycle fatigue and wear resistance of the material. This is related to a high concentration of nanoscale mesoscopic structural states, which arise in lattice curvature zones during high-temperature radial shear rolling combined with smooth-roll cold rolling. These effects are explained by the self-consistent mechanical behavior of hcp ε-martensite laths in fcc austenite grains and bcc α′-martensite laths that form during cold rolling of the steel subjected to high-temperature radial shear rolling.

The notions of plastic flow localization are reviewed here. It have been shown that each type of localized plasticity pattern corresponds to a given stage of deformation hardening. In the course of plastic flow development a changeover in the types of localization patterns occurs. The types of localization patterns are limited to a total of four pattern types. A correspondence has been set up between the emergent localization pattern and the respective flow stage. It is found that the localization patterns are manifestations of the autowave nature of plastic flow localization process, with each pattern type corresponding to a definite type of autowave. Propagation velocity, dispersion and grain size dependence of wavelength have been determined experimentally for the phase autowave. An elastic-plastic strain invariant has also been introduced to relate the elastic and plastic properties of the deforming medium. It is found that the autowave’s characteristics follow directly from the latter invariant. A hypothetic quasi-particle has been introduced which correlates with the localized plasticity autowave; the probable properties of the quasi-particle have been estimated. Taking the quasi-particle approach, the characteristics of the plastic flow localization process are considered herein.

The aim of this work was to design and optimize compositions of three-component composites based on polyetheretherketone (PEEK) with enhanced tribological and mechanical properties. Initially, two-component PEEK-based composites loaded with molybdenum disulfide (MoS₂) and polytetrafluoroethylene (PTFE) were investigated. It was shown that an increase in dry friction mode tribological characteristics in metal-polymer and ceramic-polymer tribological contacts was attained by loading with lubricant fluoroplastic particles. In addition, molybdenum disulfide homogenized permolecular structure and improved matrix strength properties. After that, a methodology for identifying composition of multicomponent PEEK-based composites having prescribed properties which based on a limited amount of experimental data was proposed and implemented. It was shown that wear rate of the “PEEK + 10% PTFE + 0.5% MoS₂” composite decreased by 39 times when tested on the metal counterpart, and 15 times on the ceramic one compared with neat PEEK. However, in absolute terms, wear rate of the three-component composite on the metal counterpart was 1.5 times higher than on the ceramic one. A three-fold increase in wear resistance during friction on both the metal and ceramic counterparts was achieved for the “PEEK + 10% PTFE + 0.5% MoS₂” three-component composite compared with the “PEEK + 10% PTFE”. Simultaneous loading with two types of fillers slightly deteriorated the polymer composite structure compared with neat PEEK. However, wear rate was many times reduced due to facilitation of transfer film formation. For this reason, there was no microabrasive wear on both metal and ceramic counterpart surfaces.

The chapter is devoted to the analysis of the features of local structural rearrangements in nanostructured materials under shear loading and nanoindentation. The study was carried out using molecular dynamics-based computer simulation. In particular, we investigated the features of symmetric tilt grain boundary migration in bcc and fcc metals under shear loading. The main emphasis was on identifying atomic mechanisms responsible for the migration of symmetric tilt grain boundaries. We revealed that grain boundaries of this type can move with abnormally high velocities up to several hundred meters per second. The grain boundary velocity depends on the shear rate and grain boundary structure. It is important to note that the migration of grain boundary does not lead to the formation of structural defects. We showed that grain boundary moves in a pronounced jump-like manner as a result of a certain sequence of self-consistent displacements of grain boundary atomic planes and adjacent planes. The number of atomic planes involved in the migration process depends on the structure of the grain boundary. In the case of bcc vanadium, five planes participate in the migration of the Σ5(210)[001] grain boundary, and three planes determine the Σ5(310)[001] grain boundary motion. The Σ5(310)[001] grain boundary in fcc nickel moves as a result of rearrangements of six atomic planes. The stacking order of atomic planes participating in the grain boundary migration can change. A jump-like manner of grain boundary motion may be divided into two stages. The first stage is a long time interval of stress increase during shear loading. The grain boundary is motionless during this period and accumulates elastic strain energy. This is followed by the stage of jump-like grain boundary motion, which results in rapid stress drop. The related study was focused on understanding the atomic rearrangements responsible for the nucleation of plasticity near different crystallographic surfaces of fcc and bcc metals under nanoindentation. We showed that a wedge-shaped region, which consists of atoms with a changed symmetry of the nearest environment, is formed under the indentation of the (001) surface of the copper crystallite. Stacking faults arise in the (111) atomic planes of the contact zone under the indentation of the (011) surface. Their escape on the side free surface leads to a step formation. Indentation of the (111) surface is accompanied by nucleation of partial dislocations in the contact zone subsequent formation of nanotwins. The results of the nanoindentation of bcc iron bicrystal show that the grain boundary prevents the propagation of structural defects nucleated in the contact zone into the neighboring grain.

A brief summary of fundamental results obtained in the IDG RAS on the mechanics of sliding along faults and fractures is presented. Conditions of emergence of different sliding regimes, and regularities of their evolution were investigated in the laboratory, as well as in numerical and field experiments. All possible sliding regimes were realized in the laboratory, from creep to dynamic failure. Experiments on triggering the contact zone have demonstrated that even a weak external disturbance can cause failure of a “prepared” contact. It was experimentally proven that even small variations of the percentage of materials exhibiting velocity strengthening and velocity weakening in the fault principal slip zone may result in a significant variation of the share of seismic energy radiated during a fault slip event. The obtained results lead to the conclusion that the radiation efficiency of an earthquake and the fault slip mode are governed by the ratio of two parameters—the rate of decrease of resistance to shear along the fault and the shear stiffness of the enclosing massif. The ideas developed were used to determine the principal possibility to artificially transform the slidding regime of a section of a fault into a slow deformation mode with a low share of seismic wave radiation.

A first integral approach, derived in an analogous fashion to Maxwell’s use of potential fields, is employed to investigate the flow characteristics, with a view to minimising friction, of shear-driven fluid motion between rigid surfaces in parallel alignment as a model for a lubricated joint, whether naturally occurring or engineered replacement. For a viscous bilayer arrangement comprised of immiscible liquids, it is shown how the flow and the shear stress along the separating interface is influenced by the mean thickness of the layers and the ratio of their respective viscosities. Considered in addition, is how the method can be extended for application to the more challenging problem of when one, or both, of the layers is a viscoelastic material.

A multiscale analysis is performed to investigate deformation and fracture in the aluminum-alumina composite and steel with a boride coating as an example. Model microstructure of the composite materials with irregular geometry of the matrix-particle and substrate-coating interfaces correspondent to the experimentally observed microstructure is taken into account explicitly as initial conditions of the boundary value problem that allows introducing multiple spatial scales. The problem in a plane strain formulation is solved numerically by the finite-difference method. Physically-based constitutive models are developed to describe isotropic strain hardening, strain rate and temperature effects, Luders band propagation and jerky flow, and fracture. Local regions experiencing bulk tension are found to occur during compression that control cracking of composites. Interrelated plastic strain localization in the steel substrate and aluminum matrix and crack origination and growth in the ceramic coating and particles are shown to depend on the strain rate, particle size and arrangement, as well as on the loading direction: tension or compression.

The efficiency and service life of products made from metal-ceramic tool alloys and used as cutting tools and friction units are determined by a combination of physical and strength properties of their surface layers with a thickness of up to 200 μm. Therefore, much attention is paid to their improvement at the present time. An effective way to increase the operational properties of the metal-ceramic alloy products is to modify the structure and the phase composition of the surface layers by forming multi-scale internal structures with a high proportion of low-dimensional (submicro and nano) components. For this purpose, surfaces are treated with concentrated energy fluxes. Pulse electron-beam irradiation (PEBI) in an inert gas plasma is one of the most effective methods. This chapter presents results of theoretical and experimental studies of this process. An example is the nanostructured hardened surface layer on the TiC-(Ni-Cr) metal-ceramic alloy (ratio of components 50:50) formed by PEBI in the plasma of argon, krypton, and xenon. Its multi-level structure, phase composition, as well as tribological and strength properties are shown.

We consider an adhesive contact between a thin soft layer on a rigid substrate and a rigid cylindrical indenter (“line contact”) taking the surface tension of the layer into account. First, it is shown that the boundary condition for the surface outside the contact area is given by the constant contact angle—as in the case of fluids in contact with solid surfaces. In the approximation of thin layer and under usual assumptions of small indentation and small inclination angles of the surface, the problem is solved analytically. In the case of a non-adhesive contact, surface tension makes the contact stiffer (at the given indentation depth, the contact half-width becomes smaller and the indentation force larger). In the case of adhesive contact, the influence of surface tension seems to be more complicated: For a flat-ended punch, it increases with increasing the surface tension, while for a wedge, it decreases. Thus, the influence of the surface tension on the adhesion force seems to be dependent on the particular geometry of the contacting bodies.

According the JKR theory of adhesive contact, changes of the contact configuration after formation of the adhesive neck and before detaching are completely reversible. This means, that after formation of the initial contact, the force-distance dependencies should coincide, independently of the direction of the process (indentation or pull-off). In the majority of real systems, this invariance is not observed. The reasons for this may be either plastic deformation in the contacting bodies or surface roughness. One further mechanism of irreversibility (and corresponding energy dissipation) may be chemical heterogeneity of the contact interface leading to the spatial dependence of the specific work of adhesion. In the present paper, this “chemical” mechanism is analyzed on a simple example of an axisymmetric contact (with axisymmetric heterogeneity). It is shown that in the asymptotic case of a “microscopic heterogeneity”, the system follows, during both indentation and pull-off, JKR curves, however, corresponding to different specific surface energies. After the turning point of the movement, the contact area first does not change and the transition from one JKR curve to the other occurs via a linear dependency of the force on indentation depth. The macroscopic behavior is not sensitive to the absolute and relative widths of the regions with different surface energy but depends mainly on the values of the specific surface energy.

We give a brief description of the results obtained by Prof. Sergey G. Psakhie and his colleagues in the field of theoretical studies of mechanical response, including fracture, of permeable fluid-saturated materials. Such materials represent complex systems of interacting solid and liquid phases. Mechanical response of such a medium is determined by processes taking place in each phase as well as their interaction. This raised a need of developing a new theoretical approach of simulation of such media—the method of hybrid cellular automaton that allowed describing stress-strain fields in solid skeleton, transfer of a fluid in crack-pore volume and influence of fluid pressure on the stress state of the solid phase. The new method allowed theoretical estimation of strength of liquid-filled permeable geomaterials under complex loading conditions. Governing parameters controlling strength of samples under uniaxial loading and shear in confined conditions were identified.

The treatise proposes a model of biological fluid transfer in a dedicated macropore with microporous walls. The distribution of concentrations and velocity studies in the capillary wall for two flow regimes—convective and diffusive. The largest impact on the redistribution of concentration between the capillary volume and its porous wall is made by Darcy number and correlation of diffusion coefficients and concentration expansion. The velocity in the interface vicinity increases with rising pressure in the capillary volume or under decreasing porosity or without consideration of the concentration expansion.

A multi-scale computational approach was used for the investigation of a high strain rate deformation and fracture of magnesium and titanium alloys with a bimodal distribution of grain sizes under dynamic loading. The processes of inelastic deformation and damage of titanium alloys were investigated at the mesoscale level by the numerical simulation method. It was shown that localization of plastic deformation under tension at high strain rates depends on grain size distribution. The critical fracture stress of alloys depends on relative volumes of coarse grains in representative volume. Microcracks nucleation at quasi-static and dynamic loading is associated with strain localization in ultra-fine grained partial volumes. Microcracks arise in the vicinity of coarse and ultrafine grains boundaries. It is revealed that the occurrence of a bimodal grain size distributions causes increased ductility, but decreased tensile strength of UFG alloys. The increase in fine precipitation concentration results not only strengthening but also an increase in ductility of UFG alloys with bimodal grain size distribution.

In the author’s opinion, many global problems that face humanity—in the fields of education, medicine, management etc. can be tackled more effectively if the cyclic nature of self-reproducing systems—including living beings—is taken into account. Summarizing the main physiological findings of the last decades on “adaptation reactions”, one can very roughly say that the way of action which is effective in the sense of productive activity of people happens at the same time to be healthy, and it gives the participants of the process the feeling of happiness. The present paper represents a very short overview of the contemporary concepts of the adaptation reactions based on the fundamental understanding of their cyclic nature due to general properties of self-reproducing systems. One interesting feature of self-reproduction cycles is its first “phase of orientation” which was not discussed in detail in the past but plays a key role in the whole cycle.

In the present paper, we considered the phenomena of understanding and discoveries (as a sort of “social understanding”) and found that the empirical properties of these phenomena (the critical character and emerging of a new property) have much in common with first-order phase transitions. From this point of view, we discuss both the process of understanding and discoveries and the reasons impeding “seeing what lies in front of our eyes”. In our opinion, these ideas can be further studied on the same phenomenological basis, without detailed understanding of the underlying neuronal mechanisms.