Multiscale Biomechanics and Tribology of Inorganic and Organic Systems

This open access book gathers authoritative contributions concerning multiscale problems in biomechanics, geomechanics, materials science and tribology. It is written in memory of Sergey Grigorievich Psakhie to feature various aspects of his multifaceted research interests, ranging from theoretical physics, computer modeling of materials and material characterization at the atomic scale, to applications in space industry, medicine and geotectonics, and including organizational, psychological and philosophical aspects of scientific research and teaching as well. This book covers new advances relating to orthopedic implants, concerning the physiological, tribological and materials aspects of their behavior; medical and geological applications of permeable fluid-saturated materials; earthquake dynamics together with aspects relating to their managed and gentle release; lubrication, wear and material transfer in natural and artificial joints; material research in manufacturing processes; hard-soft matter interaction, including adhesive and capillary effects; using nanostructures for influencing living cells and for cancer treatment; manufacturing of surfaces with desired properties; self-organization of hierarchical structures during plastic deformation and thermal treatment; mechanics of composites and coatings; and many more. Covering established knowledge as well as new models and methods, this book provides readers with a comprehensive overview of the field, yet also with extensive details on each single topic

Predictive Modelling of Tribological Systems using Movable Cellular Automata

In the science of tribology, where there is an enormous degree of uncertainty, mathematical models that convey state-of-the-art scientific knowledge are invaluable tools for unveiling the underlying phenomena. A well-structured modelling framework that guarantees a connection between mathematical representations and experimental observations, can help in the systematic identification of the most realistic hypotheses among a pool of possibilities. This thesis is concerned with identifying the most appropriate computational model for the prediction of friction and wear in tribological applications, and the development of a predictive model and simulation tool based on the identified method. Accordingly, a thorough review of the literature has been conducted to find the most appropriate approach for predicting friction and wear using computer simulations, with the multi-scale approach in mind. It was concluded that the Movable Cellular Automata (MCA) method is the most suitable method for multi-scale modelling of tribological systems. It has been established from the state-of-the-art review in Chapter 2 of this thesis, that it is essential to be able to model continuous as well as discontinuous behaviour of materials on a range of scales from atomistic to micro scales to be able to simulate the first-bodies and third body simultaneously (also known as a multi-body) in a tribological system. This can only be done using a multi-scale particle-based method because continuum methods such as FEM are none-predictive and are not capable of describing the discontinuous nature of materials on the micro scale. The most important and well-known particle-based methods are molecular dynamics (MD) and the discrete element methods (DEM). Although MD has been widely used to simulate elastic and plastic deformation of materials, it is limited to the atomistic and nanoscales and cannot be used to simulate materials on the macro-scale. On the other hand, DEM is capable of simulating materials on the meso/micro scales and has been expanded since the algorithm was first proposed by Cundall and Strack, in 1979 and adopted by a number of scientific and engineering disciplines. However, it is limited to the simulation of granular materials and elastic brittle solid materials due to its contact configurations and laws. Even with the use of bond models to simulate cohesive and plastic materials, it shows major limitations with parametric estimations and validation against experimental results because its contact laws use parameters that cannot be directly obtained from the material properties or from experiments. The MCA method solves these problems using a hybrid technique, combining advantages of the classical cellular automata method and molecular dynamics and forming a model for simulating elasticity, plasticity and fracture in ductile consolidated materials. It covers both the meso and micro scales, and can even “theoretically” be used on the nano scale if the simulation tool is computationally powerful enough. A distinguishing feature of the MCA method is the description of interaction of forces between automata in terms of stress tensor components. This way a direct relationship between the MCA model parameters of particle interactions and tensor parameters of material constitutive law is established. This makes it possible to directly simulate materials and to implement different models and criteria of elasticity, plasticity and fracture, and describe elastic-plastic deformation using the theory of plastic flow. Hence, in MCA there is no need for parametric fitting because all model parameters can be directly obtained from the material mechanical properties. To model surfaces in contact and friction behaviour using MCA, the particle size can be chosen large enough to consider the contacting surface as a rough plane, which is the approach used in all MCA studies of contacting surfaces so far. The other approach is to specify a very small particle size so that it can directly simulate a real surface, which allows for the direct investigation of material behaviour and processes on all three scale levels (atomic, meso and macro) in an explicit form. This has still been proven difficult to do because it is too computationally extensive and only a small area of the contact can be simulated due to the high numbers of particles required to simulate a real solid. Furthermore, until now, no commercial software is available for MCA simulations, only a 2D MCA demo-version which was developed by the Laboratory of CAD of Materials at the Institute of Strength Physics and Materials Science in Tomsk, Russia, in 2005. The developers of the MCA method use their own in-house codes. This thesis presents the successful development of a 3D MCA open-source software for the scientific and tribology communities to use. This was done by implementing the MCA method within the framework of the open-source code LIGGGHTS. It follows the formulations of the 3D elastic-plastic model developed by the authors including Sergey G. Psakhie, Valentin L. Popov, Evgeny V. Shilko, and the external supervisor on this thesis Alexey Yu. Smolin, which has been successfully implemented in the open-source code LIGGGHTS. Details of the mathematical formulations can be found in [1]–[3], and section 3.5 of this thesis. The MCA model has been successfully implemented to simulate ductile consolidated materials. Specifically, new interaction laws were implemented, as well as features related to particle packing, particle interaction forces, bonding of particles, and others. The model has also been successfully verified, validated, and used in simulating indentation. The validation against experimental results showed that using the developed model, correct material mechanical response can be simulated using direct macroscopic mechanical material properties. The implemented code still shows limitations in terms of computational capacity because the parallelization of the code has not been completely implemented yet. Nevertheless, this thesis extends the capabilities of LIGGGHTS software to provide an open-source tool for using the MCA method to simulate solid material deformation behaviour. It also significantly increases the potential of using MCA in an HPC environment, producing results otherwise difficult to obtain

Multiscale biomechanics and tribology of inorganic and organic systems : In memory of Professor Sergey Psakhie

This open access book gathers authoritative contributions concerning multiscale problems in biomechanics, geomechanics, materials science and tribology. It is written in memory of Sergey Grigorievich Psakhie to feature various aspects of his multifaceted research interests, ranging from theoretical physics, computer modeling of materials and material characterization at the atomic scale, to applications in space industry, medicine and geotectonics, and including organizational, psychological and philosophical aspects of scientific research and teaching as well. This book covers new advances relating to orthopedic implants, concerning the physiological, tribological and materials aspects of their behavior; medical and geological applications of permeable fluid-saturated materials; earthquake dynamics together with aspects relating to their managed and gentle release; lubrication, wear and material transfer in natural and artificial joints; material research in manufacturing processes; hard-soft matter interaction, including adhesive and capillary effects; using nanostructures for influencing living cells and for cancer treatment; manufacturing of surfaces with desired properties; self-organization of hierarchical structures during plastic deformation and thermal treatment; mechanics of composites and coatings; and many more. Covering established knowledge as well as new models and methods, this book provides readers with a comprehensive overview of the field, yet also with extensive details on each single topic.TU Berlin, Open-Access-Mittel – 202

Modeling of Instabilities and Self-Organization at the Frictional Interface

The field of friction-induced self-organization and its practical importance remains unknown territory to many tribologists. Friction is usually thought of as irreversible dissipation of energy and deterioration; however, under certain conditions, friction can lead to the formation of new structures at the interface, including in-situ tribofilms and various patterns at the interface. This thesis studies self-organization and instabilities at the frictional interface, including the instability due to the temperature-dependency of the coefficient of friction, the transient process of frictional running-in, frictional Turing systems, the stick-and-slip phenomenon, and, finally, contact angle (CA) hysteresis as an example of solid-liquid friction and dissipation. All these problems are chosen to bridge the gap between fundamental interest in understanding the conditions leading to self-organization and practical motivation. We study the relationship between friction-induced instabilities and friction-induced self-organization. Friction is usually thought of as a stabilizing factor; however, sometimes it leads to the instability of sliding, in particular when friction is coupled with another process. Instabilities constitute the main mechanism for pattern formation. At first, a stationary structure loses its stability; after that, vibrations with increasing amplitude occur, leading to a limit cycle corresponding to a periodic pattern. The self-organization is usually beneficial for friction and wear reduction because the tribological systems tend to enter a state with the lowest energy dissipation. The introductory chapter starts with basic definitions related to self-organization, instabilities and friction, literature review, and objectives. We discuss fundamental concepts that provide a methodological tool to investigate, understand and enhance beneficial processes in tribosystems which might lead to self-organization. These processes could result in the ability of a frictional surface to exhibit self-protection and self-healing properties. Hence, this research is dealing with the fundamental concepts that allow the possibility of the development of a new generation of tribosystem and materials that reinforce such properties. In chapter 2, we investigate instabilities due to the temperature-dependency of the coefficient of friction. The temperature-dependency of the coefficient of friction can have a significant effect on the frictional sliding stability, by leading to the formation of hot and cold spots on the contacting surfaces. We formulate a stability criterion and perform a case study of a brake disk. We show that the mechanism of instability can contribute to poor reproducibility of aircraft disk brake tests reported in the literature. Furthermore, a method to increase the reproducibility by dividing the disk into several sectors with decreased thermal conductivity between the sectors is proposed. In chapter 3, we study frictional running-in. Running-in is a transient period on the onset of the frictional sliding, in which friction and wear decrease to their stationary values. In this research, running-in is interpreted as friction-induced self-organization process. We introduce a theoretical model of running-in and investigate rough profile evolution assuming that its kinetics is driven by two opposite processes or events, i.e., smoothening which is typical for the deformation-driven friction and wear, and roughening which is typical for the adhesion-driven friction and wear. To validate our modeling results, we examine experimentally running-in in ultrahigh vacuum friction tests for WC pin versus Cu substrate. We propose to calculate the Shannon entropy of a rough profile and to use it as a simple test for self-organization. We observe, theoretically and experimentally, how Shannon entropy as a characteristic of a rough surface profile changes during running-in, and quantifies the degree of orderliness of the self-organized system. In chapter 4, we investigate the possibility of the so-called Turing-type pattern formation during friction. Turing or reaction-diffusion systems describe variations of spatial concentrations of chemical components with time due to local chemical reactions coupled with diffusion. During friction, the patterns can form at the sliding interface due to the mass transfer (diffusion), heat transfer, various tribochemical reactions, and wear. We present a mathematical model, and solve the governing equations by using a finite-difference method. The results demonstrate a possibility of such pattern-formation. We also discuss existing experimental data that suggest that tribofilms can form in-situ at the frictional interface due to a variety of friction-induced chemical reactions (oxidation, the selective transfer of Cu ions, etc.). In chapter 5, we investigate how interfacial patterns including propagating trains of stick and slip zones form due to dynamic sliding instabilities. These can be categorized as self-organized patterns. We treat stick and slip as two phases at the interface, and study the effects related to phase transitions. Our results show how interfacial patterns form, how the transition between stick and slip zones occurs, and which parameters affect them. In chapter 6, we use Cellular Potts Model to study contact angle (CA) hysteresis as a measure of solid-liquid energy dissipation. We simulate CA hysteresis for a droplet over the tilted patterned surface, and a bubble placed under the surface immersed in liquid. We discuss the dependency of CA hysteresis on the surface structure and other parameters. This analysis allows decoupling of the 1D (pinning of the triple line) and 2D effects (adhesion hysteresis in the contact area) and obtain new insights on the nature of CA hysteresis. To summarize, we examine different cases in frictional interface and observe similar trends. We investigate and discus how these trends could be beneficial in design, synthesis and characterization of different materials and tribosystems. Furthermore, we describe how to utilize fundamental concepts for specific engineering applications. Finally, the main theme of this research is to find new applications of concept of self-organization to tribology and the role played by different physical and chemical interactions in modifying and controlling friction and wear

Interdependence of friction, wear, and noise: a review

Phenomena of friction, wear and noise in mechanical contacts are particularly important in the field of tribomechanics but equally complex if one wants to represent their exact relationship with mathematical models. Efforts have been made to describe these phenomena with different approaches in past. These efforts have been compiled in different reviews but most of them treated friction, wear mechanics and acoustic noise separately. However, an in-depth review that provides a critically analysis on their interdependencies is still missing. In this review paper, the interdependencies of friction, wear and noise are analysed in the mechanical contacts at asperitical level. The origin of frictional noise, its dependencies on contact’s mechanical properties, and its performance under different wear conditions are critically reviewed. A discussion on the existing mathematical models of friction and wear is also provided in the last section that leads to uncover the gap in the existing literature. This review concludes that still a comprehensive analytical modelling approach is required to relate the interdependencies of friction, noise, and wear with mathematical expression

Mathematical models of cell migration and self-organization in embryogenesis

In this thesis we deal with mathematical models and numerical simulations for cell migration and self-organization in embryogenesis. The part of biology which studies the formation and development of the embryo from fertilization until birth is called embryology. Morphogenesis is then the part of embryology which is concerned with the development of patterns and forms. It is well known that although morphogenesis processes are controlled at the genetic scale, genes themselves cannot create the pattern. In general a series of biological mechanisms of self-organization intervene during the early development and the formation of particular biological structures can not be anticipated solely by genetic information. This needs to be taken into account in the choice of a suitable mathematical formulation of such phenomena. Two main main topics will be investigated: we will analyze and mathematically model the self-organizing cell migration in the morphogenesis of the lateral line in the zebrafish (Danio rerio); in a second part, starting from this model, we will propose, and will study both from the analytical and the numerical point of view, a mathematical model of collective motion under only alignment and chemotaxis effects. The present thesis is organized in four chapters. In Chapter 1 we will introduce biological elements about the morphogenetic process occurring in the development of the lateral line in a zebrafish. After a first discussion on the lateral line system and on its fundamental relevance in the current scientific research, we will focus on the main mechanisms of chemical signaling and collective cell migration that will be taken into account later in our mathematical formulation of the phenomenon. In Chapter 2 we will provide a mathematical-modelling background that, starting from the morphogenesis on the chemical scale, will gradually lead us to discuss the existing mathematical models, proposed in the last years to describe collective motion in living system and in particular in the biological field. Example of numerical simulations, and their comparison with experimental evidences will be briefly shown, taken from the recent modelling literature. In Chapter 3 we will introduce a mathematical model describing the self-organizing cell migration in the zebrafish lateral line primordium. We will discuss the derivation of the model, justifying our modelling choices and comparing them with the existing literature. The proposed model will adopt a hybrid “discrete in continuous” description, where cells are treated as discrete entities moving in a continuous space, and chemical signals at molecular level are described by continuous variables. On the chemical scale we will employ diffusion and chemotaxis equations, while on the cellular scale a Newtonian second order equation for each cell will take into account typical effects arising from collective dynamics models. Cell dimension will be recovered introducing suitable detection radii and nonlocal effects. Particular steady states, corresponding to emerging structures, said neuromasts, will then be investigated and their stability will be numerically assessed. Moreover, after a description of the designed numerical approximation scheme, some dynamical simulations will be proposed to show the powerful and the limit of our approach. Finally, we will discuss the estimate of the parameters of the model, derived in part by the biological and the modelling literature, in part by the stationary model or by a numerical data fitting. In Chapter 4 we will propose a Cucker and Smale-like mathematical model of collective motion. Our hybrid model will describe a system of interacting particles under an alignment and chemotaxis effect. From an analytical point of view local and global existence and uniqueness of the solution will be proved. Furthermore, the asymptotic behaviour of the model will be investigated on a linearized form of the system. From a numerical point of view, through an approximation scheme based on finite differences, the full nonlinear system will be simulated and some significant dynamical tests will be shown. Numerical results will be compared with those analytical, and new perspectives will be proposed

Discrete element method to study biofilm deformation in fluid flow

Ph. D. Thesis.Biofilms are the assemblage of one or more types of microorganisms, which are usually found attached and grew on surfaces, embedded in their extracellular polymeric substances (EPS). They could form diverse morphologies to adapt to different environments, especially in a flow system such as water filtration. Hydrodynamic conditions have a significant impact on the deformation and detachment of biofilm, which has been primarily investigated by the experiments. However, relevant modelling research is lacking. Therefore, the individual based model (IbM) is adopted to study the biofilm-fluid interaction in present work. In the first part of this work, the discrete element method was utilized to simulate the biofilm growth, deformation and detachment, where the fluid was mimicked by applying a simple shear force. Due to the fact that the biofilms would also affect the flow pattern in return, the simply one-way approach was then extended to a two-way coupled computational fluid dynamic – discrete element method (CFD-DEM) model. Biofilm deformation and detachment was investigated at varied inlet flow velocity. We have also studied the effect of the EPS content on the deformation and detachment of biofilms. Furthermore, the strain-stress curves during biofilm deformation have been captured by loading and unloading the fluid shear stress. Biofilm streamer (filamentous structure of biofilm) motion under different flow conditions is important for a wide range of industries as well. The flow-induced oscillations and cohesive failure of single and multiple biofilm streamers have been investigated based on the CFD-DEM model. In this section, we have studied the effect of streamer length on the oscillation at varied flow rates. The predicted single biofilm streamer oscillations in various flow rates agreed well with experimental measurements. We have also investigated the effect of the spatial arrangement of streamers on interactions between two oscillating streamers in parallel and tandem arrangements. Besides, cohesive failure of streamers was studied in an accelerating fluid flow, which is important for slowing down biofilm induced cloggingEPSRC, BBSR

Mathematical models of cell migration and self-organization in embryogenesis

In this thesis we deal with mathematical models and numerical simulations for cell migration and self-organization in embryogenesis. The part of biology which studies the formation and development of the embryo from fertilization until birth is called embryology. Morphogenesis is then the part of embryology which is concerned with the development of patterns and forms. It is well known that although morphogenesis processes are controlled at the genetic scale, genes themselves cannot create the pattern. In general a series of biological mechanisms of self-organization intervene during the early development and the formation of particular biological structures can not be anticipated solely by genetic information. This needs to be taken into account in the choice of a suitable mathematical formulation of such phenomena. Two main main topics will be investigated: we will analyze and mathematically model the self-organizing cell migration in the morphogenesis of the lateral line in the zebrafish (Danio rerio); in a second part, starting from this model, we will propose, and will study both from the analytical and the numerical point of view, a mathematical model of collective motion under only alignment and chemotaxis effects. The present thesis is organized in four chapters. In Chapter 1 we will introduce biological elements about the morphogenetic process occurring in the development of the lateral line in a zebrafish. After a first discussion on the lateral line system and on its fundamental relevance in the current scientific research, we will focus on the main mechanisms of chemical signaling and collective cell migration that will be taken into account later in our mathematical formulation of the phenomenon. In Chapter 2 we will provide a mathematical-modelling background that, starting from the morphogenesis on the chemical scale, will gradually lead us to discuss the existing mathematical models, proposed in the last years to describe collective motion in living system and in particular in the biological field. Example of numerical simulations, and their comparison with experimental evidences will be briefly shown, taken from the recent modelling literature. In Chapter 3 we will introduce a mathematical model describing the self-organizing cell migration in the zebrafish lateral line primordium. We will discuss the derivation of the model, justifying our modelling choices and comparing them with the existing literature. The proposed model will adopt a hybrid “discrete in continuous” description, where cells are treated as discrete entities moving in a continuous space, and chemical signals at molecular level are described by continuous variables. On the chemical scale we will employ diffusion and chemotaxis equations, while on the cellular scale a Newtonian second order equation for each cell will take into account typical effects arising from collective dynamics models. Cell dimension will be recovered introducing suitable detection radii and nonlocal effects. Particular steady states, corresponding to emerging structures, said neuromasts, will then be investigated and their stability will be numerically assessed. Moreover, after a description of the designed numerical approximation scheme, some dynamical simulations will be proposed to show the powerful and the limit of our approach. Finally, we will discuss the estimate of the parameters of the model, derived in part by the biological and the modelling literature, in part by the stationary model or by a numerical data fitting. In Chapter 4 we will propose a Cucker and Smale-like mathematical model of collective motion. Our hybrid model will describe a system of interacting particles under an alignment and chemotaxis effect. From an analytical point of view local and global existence and uniqueness of the solution will be proved. Furthermore, the asymptotic behaviour of the model will be investigated on a linearized form of the system. From a numerical point of view, through an approximation scheme based on finite differences, the full nonlinear system will be simulated and some significant dynamical tests will be shown. Numerical results will be compared with those analytical, and new perspectives will be proposed