Mapping forces in 3D elastic assembly of grains

Our understanding of the elasticity and rheology of disordered materials, such as granular piles, foams, emulsions or dense suspensions relies on improving experimental tools to characterize their behaviour at the particle scale. While 2D observations are now routinely carried out in laboratories, 3D measurements remain a challenge. In this paper, we use a simple model system, a packing of soft elastic spheres, to illustrate the capability of X-ray microtomography to characterise the internal structure and local behaviour of granular systems. Image analysis techniques can resolve grain positions, shapes and contact areas; this is used to investigate the material's microstructure and its evolution upon strain. In addition to morphological measurements, we develop a technique to quantify contact forces and estimate the internal stress tensor. As will be illustrated in this paper, this opens the door to a broad array of static and dynamical measurements in 3D disordered systems

Influence of a bow of finite width on bowed string motion: numerical modelling and experimental evidence

An enhanced physical model of the bowed string presented previously [1] is explored. It takes into account: the width of the bow, the angular motion of the string, bow-hair elasticity and string bending stiffness. The results of an analytical investigation of a model system - an infinite string sticking to a bow of finite width and driven on one side of the bow - are compared with experimental results published by Cremer [2] and reinterpreted here. Comparison shows that both the width of the bow and the bow-hair elasticity have a large impact on the reflection and transmission behaviour. In general, bending stiffness plays a minor role. Furthermore, a method of numerical simulation of the stiff string bowed with a bow of finite width is presented along with some preliminary results.

On the growth and form of the gut.

The developing vertebrate gut tube forms a reproducible looped pattern as it grows into the body cavity. Here we use developmental experiments to eliminate alternative models and show that gut looping morphogenesis is driven by the homogeneous and isotropic forces that arise from the relative growth between the gut tube and the anchoring dorsal mesenteric sheet, tissues that grow at different rates. A simple physical mimic, using a differentially strained composite of a pliable rubber tube and a soft latex sheet is consistent with this mechanism and produces similar patterns. We devise a mathematical theory and a computational model for the number, size and shape of intestinal loops based solely on the measurable geometry, elasticity and relative growth of the tissues. The predictions of our theory are quantitatively consistent with observations of intestinal loops at different stages of development in the chick embryo. Our model also accounts for the qualitative and quantitative variation in the distinct gut looping patterns seen in a variety of species including quail, finch and mouse, illuminating how the simple macroscopic mechanics of differential growth drives the morphology of the developing gut.

Improved models for drop-on-demand ink-jet shortening

A previous 1-D model for the shortening of an unbroken drop-on-demand ink-jet ligament has been extended to the case of an arbitrary attached tail mass, and can also include extensional viscosity (which has ∼ 2% effect) as well as linear elasticity in the fluid. Predictions from the improved model are shown to be very similar to results from 2-D axisymmetric numerical simulations of DoD ink-jet ligaments and also to the results of recent experiments on Newtonian fluids jetted without satellite formation.

Mapping forces in a 3D elastic assembly of grains

Our understanding of the elasticity and rheology of disordered materials, such as granular piles, foams, emulsions or dense suspensions relies on improving experimental tools to characterise their behaviour at the particle scale. While 2D observations are now routinely carried out in laboratories, 3D measurements remain a challenge. In this paper, we use a simple model system, a packing of soft elastic spheres, to illustrate the capability of X-ray microtomography to characterise the internal structure and local behaviour of granular systems. Image analysis techniques can resolve grain positions, shapes and contact areas; this is used to investigate the materials microstructure and its evolution upon strain. In addition to morphological measurements, we develop a technique to quantify contact forces and estimate the internal stress tensor. As will be illustrated in this paper, this opens the door to a broad array of static and dynamical measurements in 3D disordered systems. © 2011 Elsevier Ltd. All rights reserved.

Parallel implementation of Multilevel BDDC

In application of the Balancing Domain Decomposition by Constraints (BDDC) to a case with many substructures, solving the coarse problem exactly becomes the bottleneck which spoils scalability of the solver. However, it is straightforward for BDDC to substitute the exact solution of the coarse problem by another step of BDDC method with subdomains playing the role of elements. In this way, the algorithm of three-level BDDC method is obtained. If this approach is applied recursively, multilevel BDDC method is derived. We present a detailed description of a recently developed parallel implementation of this algorithm. The implementation is applied to an engineering problem of linear elasticity and a benchmark problem of Stokes flow in a cavity. Results by the multilevel approach are compared to those by the standard (two-level) BDDC method.

Ultra-structural defects cause low bone matrix stiffness despite high mineralization in osteogenesis imperfecta mice.

Bone is a complex material with a hierarchical multi-scale organization from the molecule to the organ scale. The genetic bone disease, osteogenesis imperfecta, is primarily caused by mutations in the collagen type I genes, resulting in bone fragility. Because the basis of the disease is molecular with ramifications at the whole bone level, it provides a platform for investigating the relationship between structure, composition, and mechanics throughout the hierarchy. Prior studies have individually shown that OI leads to: 1. increased bone mineralization, 2. decreased elastic modulus, and 3. smaller apatite crystal size. However, these have not been studied together and the mechanism for how mineral structure influences tissue mechanics has not been identified. This lack of understanding inhibits the development of more accurate models and therapies. To address this research gap, we used a mouse model of the disease (oim) to measure these outcomes together in order to propose an underlying mechanism for the changes in properties. Our main finding was that despite increased mineralization, oim bones have lower stiffness that may result from the poorly organized mineral matrix with significantly smaller, highly packed and disoriented apatite crystals. Using a composite framework, we interpret the lower oim bone matrix elasticity observed as the result of a change in the aspect ratio of apatite crystals and a disruption of the crystal connectivity.

Characterizing the mechanics of cultured cell monolayers.

One-cell-thick monolayers are the simplest tissues in multicellular organisms, yet they fulfill critical roles in development and normal physiology. In early development, embryonic morphogenesis results largely from monolayer rearrangement and deformation due to internally generated forces. Later, monolayers act as physical barriers separating the internal environment from the exterior and must withstand externally applied forces. Though resisting and generating mechanical forces is an essential part of monolayer function, simple experimental methods to characterize monolayer mechanical properties are lacking. Here, we describe a system for tensile testing of freely suspended cultured monolayers that enables the examination of their mechanical behavior at multi-, uni-, and subcellular scales. Using this system, we provide measurements of monolayer elasticity and show that this is two orders of magnitude larger than the elasticity of their isolated cellular components. Monolayers could withstand more than a doubling in length before failing through rupture of intercellular junctions. Measurement of stress at fracture enabled a first estimation of the average force needed to separate cells within truly mature monolayers, approximately ninefold larger than measured in pairs of isolated cells. As in single cells, monolayer mechanical properties were strongly dependent on the integrity of the actin cytoskeleton, myosin, and intercellular adhesions interfacing adjacent cells. High magnification imaging revealed that keratin filaments became progressively stretched during extension, suggesting they participate in monolayer mechanics. This multiscale study of monolayer response to deformation enabled by our device provides the first quantitative investigation of the link between monolayer biology and mechanics.