Defects such as vacancies, impurities, dislocations and grain boundaries have a profound effect on materials properties of solids even at dilute concentrations. This is because defects intimately couple quantum chemistry, atomistic physics and continuum mechanics. Thus a predictive understanding of the role of defects in determining macroscopic properties requires the resolution of quantum mechanics at macroscopic scales. This talk will describe the need for such modeling, the opportunities it offers, the challenges it poses, the state-of-the-art, and conclude with some new promising approaches.

Multi-scale methods are a new paradigm in many branches of engineering science. When resolving smaller and smaller scale evolving discontinuities become more important, as do non-mechanical effects like humidity and temperature. We will start by a concise classification of multi-scale computational mechanics, and we will concentrate on computational methods that allow for concurrent computing at multiple scales. Difficulties that relate to the efficient and accurate coupling between the various subdomains will be highlighted, with an emphasis on the coupling of domains that are modelled by dissimilar field equations. Next, we will focus on evolving discontinuities that arise at different scales and discuss various methods resolving them, including level sets, phase-field approaches, partition-of-unity methods, and isogeometric analysis. Finally, approaches will be outlined for multi-scale analyses that include coupling of evolving discontinuities with non-mechanical effects.

I will discuss our recent efforts to develop a first principles, theoretical description of the events leading to droplet splashing on a solid surface, by focusing on a peculiar singularity that occurs in the equation of motion before the droplet contacts the substrate. Experiments have long showed that the most violent splashes are preceded by the ejection of a very thin fluid sheet from the vicinity of the contact point, though the fluid mechanical origin of this sheet has been completely unclear. From simulations and a theoretical discussion beginning from the Navier Stokes equation, we demonstrate that the sheet originates before the droplet contacts the solid surface, and give detailed predictions for the characteristics of the sheet (thickness, speed, velocity). For a ~ 1mm droplet thrown at a surface at a few meters per second, the sheet ejects upwards at 100m/sec when the droplet is 10s of nanometers from the solid surface. Recent experiments probing these predictions will also be described.

Microsystems (or Micro Electro Mechanical Systems, MEMS) are devices, like e.g. micro accelerometers, micro gyroscopes and micro pumps, whose dimensions are in the range of fractions of micrometers to millimetres with sensing and actuating functions. The great versatility and the reduced unit cost have been the basic ingredients for the large diffusion of microsystems in various fields like the consumer and automotive markets, structural monitoring and biomedical devices. The purpose of this talk is to describe some aspects of the microsystems complexity from a mechanical perspective. The focus will be on specific issues studied during the last nine years in strict collaboration with a major industrial partner. Starting from real cases, the presentation will deal in particular with the dynamics of resonant devices, the study of dissipative and multi physics phenomena, the study of key reliability issues such as fracture, fatigue and spontaneous adhesion (or stiction).

Particle methods have recently emerged as engineering tools that can be widely used in many different disciplines. Due to their meshless nature, they are especially well suited for problems with either many discrete bodies which can move independently or in problems with changing boundaries and topologies. Traditional discrete element approaches (DEM) can deal with millions of particles using appropriate interaction forces and efficient neighborhood search. However, these simulations are often not based on continuum mechanics based approaches and require a lot of heuristics and experience. On the other hand, approaches like Smoothed Particle Hydrodynamics (SPH) directly discretize and solve partial differential equations and can be used for both, simulating solids and/or fluids and even mixtures of both. Interestingly, DEM and SPH can efficiently share the same program environment. In this talk, besides an introduction to the main components of particle simulations, also many application examples from solids and fluids will be shown.

Nature has shown us that some hearts do not require valves to achieve unidirectional flow. In its earliest stages, the vertebrate heart consists of a primitive tube that drives blood through a simple vascular network nourishing tissues and other developing organ systems. Traditional developmental dogma states that valveless, unidirectional pumping in biological systems occurs by peristalsis. However, our in vivo studies of embryonic Zebrafish heart (Nature 2003) where we mapped the movement of both the myocardial cells in the developing heart tube wall as well as the flow of blood through the tube contradicts the notion of peristalsis as a pumping mechanism in the valveless embryonic heart. Instead, we have discovered an intriguing wave reflection process based on impedance mismatches at the boundaries of the heart tube (Science 2006). From these observations we have developed a physio-mathematical model that proposes an elastic wave resonance mechanism (JFM 2006) of the heart tube as the more likely pumping mechanism. In this model fewer cells are required to actively contract in order to maintain the pumping action than are necessary in a peristaltic mechanism. Inspired by this design, we have succeeded in constructing a series of mechanical counterparts to this biological pump on a range of size scale including scales comparable to that of embryonic zebrafish heart (e.g. ~400 microns). This new generation of biologically-inspired pumps functions on both the micro- and macro-scale and do not possess valves or blades. These advantages offer exciting new potentials for use in applications where delicate transport of blood, drugs or other biological fluids are desired. Also, in this lecture, we will discuss some of our recent experimental observations that may teach us how to grow biological micro-pumps.

One of the most fundamental issues in biology is the nature of evolutionary transitions from single cell organisms to multicellular ones. Not surprisingly, for microscopic life in a fluid environment, many of the processes involved are related to transport and locomotion, for efficient exchange of chemical species with the environment is one of the most basic features of life. This is particularly so in the case of flagellated eukaryotes such as green algae, whose members serve as model organisms for the study of transitions to multicellularity. In this talk I will focus on studies of the stochastic nonlinear dynamics of these flagella, whose coordinated beating leads to graceful locomotion but also to fluid flows that can out-compete diffusion. A synthesis of high-speed imaging, micromanipulation, and three-dimensional tracking has quantified the stochastic dynamics of flagellar beating and allowed for tests of the hydrodynamic origins of flagellar synchronization.

Many technical and natural systems are characterized by presence of inherent or loading induced series of length scales. The fracture processes in such systems has many features. In particular, ordered systems of faults or cracks can be formed. Different scenarios of fracture process ordering will be analyzed (in particular, the possibilities of ordered multiscale crack systems formation accompanied by increasing or decreasing the scales of the sequentially formed cracks sub-systems will be illustrated). The problem of providing safety and reliability of the hierarchical technical systems will also be discussed accounting for the possibilities of energy redistribution between the scales of the system at fracture and probabilistic aspects of fracture processes in such systems. Examples of prevention of catastrophic failure in a hierarchical system will be given. The paper will be based on the studies performed by the author and his team as well as on the available publications of other specialists.

The next generation supercomputer of 10 Peta flops is now under construction as a national project in Japan. Not only the hardware development but also the software development is highly expected and the software development for the human body simulator is assigned as a grand challenge program for the effective use of this supercomputer. In this program, the multi-scale and multi-physics natures of the living matter are emphasized. Under this concept, we are developing the multi-scale simulator for a living human body. Basic strategy of the simulator is to utilize the medical image data taken by MRI, CT, or ultrasound for the prediction of disease and planning of therapy. For this purpose, we have developed full Eulerian fluid-structure-interaction solver without mesh generation procedure, which enables us to conduct the simulations directly from medical images. The method is based on the finite difference scheme with fractional step algorithm for incompressible flows and materials. The result has been validated through the deformable vesicle problem in the simple shear flow, and has been applied to a pressure-driven blood flow containing a large number of red blood cells and platelets. The mechanism of thrombus formation has been elucidated using this simulation and multi-scale modeling of platelets-vessel wall interaction.

Turbulent eddies near a wall are known to play essential role in the dynamics of turbulent boundary layers and are responsible for large contributions to the skin friction drag. The spatial dimensions of these structures scale with viscous units, and thus are small compared to physical flow dimensions.  The resolution of these structures in high fidelity numerical simulations is not practical, and one must resort to reduced order models to account for the effect of near wall turbulence on the outer flow structures. Based on recent direct numerical simulations, there is mounting evidence that the near wall structures are more robust and ordered than the outer layer structures independent of boundary and initial conditions, and thus are more amenable to reduced order modeling. We will show that there is a remarkable qualitative and quantitative similarity between the near wall structures in turbulent spots and in fully developed turbulence. Our work on the development and application of wall models for complex engineering calculations will be presented.
Prediction of the location of laminar/turbulence transition in boundary layers is a pacing item for numerical simulations.  We will demonstrate that the dynamic subgrid scale models used in large eddy simulations lead to negligible eddy viscosity in the laminar region, and therefore correctly predict the location of transition independent of the particular route to transition.

A challenging problem in solid mechanics is to understand the complex interaction between inertia effects and material properties that is taking place in the failure of ductile metals subjected to high loading rates. In this presentation, we investigate the dynamic signature that characterizes strain localization, ductile fracture and damage at high loading rates and we expose some perspectives.
The role of inertia in the development of viscoplastic flow instabilities such as multiple necking and multiple shear banding will be first discussed. Next, we analyze the evolution of strain localization towards fracture. The influence of material defects and of unloading waves in the selection of fracture sites will be reviewed in the light of numerical simulations, analytical approaches and experimental results.
At the micro-scale, elementary mechanisms of deformation can be significantly influenced by inertia. For instance, under dynamic conditions, the growth of micro-voids and the coalescence process are affected by local inertia effects that slow down the void expansion and modulate the way the voids interact together. A multiscale modeling is proposed that encompasses micro-inertia effects. This model is used to predict the internal damage by spalling observed in plate impact experiments and to get a new insight in the analysis of dynamic crack growth in fracture mechanics.

The basis of cohesive surface modeling is to consider a continuum as consisting of both volumes and surfaces and provide a constitutive relation for each. Because the volumetric mechanical constitutive relation involves stresses and strains and the surface relation involves tractions and displacement jumps, a length scale is introduced. The basic ideas of a cohesive surface formulation can be traced back to the pioneering contributions of Barenblatt, Dugdale and Hillerborg for crack mechanics. These ideas have been generalized so that an initial crack is not required and a variety of cohesive constitutive relations can be considered. In this lecture an overview of cohesive surface modeling and its applications will be presented. Applications to a variety of problems will be discussed along with advantages and disadvantages of the cohesive framework.

Liquid helium has superfluid properties at low temperatures. For 4He the transition temperature is 2.17 K; for 3He, it is about 0.0025 K. Superfluids flow without friction and possess other extraordinary properties. One of them is the formation of line vortices whose diameters are atomic in scale. Quantum mechanics constrains their circulation to be discrete. These quantum vortices interact with each other, reconnect and form complex topological structures—among them a random tangle. Certain properties of this random tangle are similar to those of classical turbulence. For this reason, the random tangle is called quantum turbulence. We shall explore several fascinating properties of superfluid helium, present recent experimental, theoretical and computational results on quantum turbulence, and discuss their implications on our understanding of classical turbulence.

Virtually every solid material contains features that are different at different length scales. The challenge is to comprehend relationships between models at different length scales. This has led to a well-developed theory of “homogenization” mostly concentrating on the prediction of the effective response of heterogeneous materials. However emerging characterization methods in Experimental Mechanics, giving access to local fields at smaller and smaller scales, pose another challenge to modelers to devise efficient formulations that permit interpretation of the massive amount of data generated by these novel methods. Significant progress has been made in the last twenty years to model nonlinear heterogeneous materials which are made either from purely elastic or purely dissipative constituents. Emphasis is put here on the coupling between elastic and plastic effects. Incremental variational principles are exploited to propose approximate mean-field methods to predict accurately the overall response of heterogeneous materials as well as some of the statistics of the local fields.

Marine ice sheets, such as those in Western Antarctica comprise a grounded ice sheet coupled to a floating ice shelf. The position of the grounding line, where the sheet detaches from the bedrock to form the shelf, is determined dynamically by the forces acting on either side. On long, glacial timescales the sheet and shelf can be modelled using viscous fluid mechanics: the sheet is a shear-dominated viscous gravity current; the shelf is characterized by extensional flow with weak shear. On short timescales, including typical transit times for ice to pass through the grounding-line zone, the marine ice sheet behaves more elastically. I will present recent laboratory experiments and mathematical studies aimed at elucidating fundamental mechanisms controlling the evolution and stability of marine ice sheets and their grounding lines. Many aspects of the flow can be modelled using Newtonian fluids but interesting phenomena relate to Non-Newtonian rheology of large-scale ice flows.

Nanomechanics understandings for nanostructures are critical not only for their integrity concerns but also for their utilization. Attention here is focused on two types of low-dimensional materials, graphenes and nanocrystals, with characteristic lengths in nanometers or even angstrom scales. In nanocrystals, the dislocation mechanism is suppressed, and their plasticity is dictated by diffusive atomistic flow along the grain boundaries. Micromechanics models are developed for the plastic flow and fracture in nanocrystals. Simulations based on micro-structural evolution demonstrate the capability in predicting the brittle versus ductile transition of nanocrystal. To put this mechanism into atomistic images, in-situ tests of nano-crystalline gold were performed under HRTEM. We observe atoms flow along certain atomistic planes of the crack faces to advance the crack. This diffusion assisted mode, along with GB cavitation and cleavage, give a complete spectrum of defect evolutions in nanocrystals.
Beside the danger of to degrade the nanostructures, defects may also serve to enrich the functions of nanostructures. The functioning of prestine graphenes is rather difficult. Doping of graphenes, however, can be achieved along their edges. We collaborated with a group in KAUST to study the defect creation and evolution in graphenes. The HRTEM there can operate at low voltage but with 1.1 angstrom resolution. We devise a two-step method for atomic doping of graphene: the first step consists of creating holes and vacancies in graphene by bombardment of Au atoms, while the second step consists of doping atoms of various kinds to the edges of the hole and into the atomic vacancies. These doping atoms serve to functionalize the edges and to create catalysts in the form of single atom arrays. The mechanics of graphene is also explored by observing the atom-resolved mode-III fracture process in graphenes, and by elucidating the failure mechanisms of graphene nano-ribbon.

I will present the numerical issues, the successes and the perspective of direct numerical simulations using the volume of fluid method. The volume of fluid method has the capability of dealing with very complex interfacial and multiphase flow problems, such as bubble columns, high speed atomizing jets or breaking surface waves. Investigating these problems requires both a good numerical technique and physical insight, that allows progress to be made in conjunction with experimental investigations.