A brief guide to synchrotron radiation-based microtomography in (structural) geology and rock mechanics

This contribution outlines Synchrotron-based X-ray micro-tomography and its potential use in structural geology and rock mechanics. The paper complements several recent reviews of X-ray microtomography. We summarize the general approach to data acquisition, post-processing as well as analysis and thereby aim to provide an entry point for the interested reader. The paper includes tables listing relevant beamlines, a list of all available imaging techniques, and available free and commercial software packages for data visualization and quantification. We highlight potential applications in a review of relevant literature including time-resolved experiments and digital rock physics. The paper concludes with a report on ongoing developments and upgrades at synchrotron facilities to frame the future possibilities for imaging sub-second processes in centimetre-sized samples.

Numerical estimation of 3D mechanical forces exerted by cells on non-linear materials

The exchange of physical forces in both cell-cell and cell-matrix interactions play a significant role in a variety of physiological and pathological processes, such as cell migration, cancer metastasis, inflammation and wound healing. Therefore, great interest exists in accurately quantifying the forces that cells exert on their substrate during migration. Traction Force Microscopy (TFM) is the most widely used method for measuring cell traction forces. Several mathematical techniques have been developed to estimate forces from TFM experiments. However, certain simplifications are commonly assumed, such as linear elasticity of the materials and/or free geometries, which in some cases may lead to inaccurate results. Here, cellular forces are numerically estimated by solving a minimization problem that combines multiple non-linear FEM solutions. Our simulations, free from constraints on the geometrical and the mechanical conditions, show that forces are predicted with higher accuracy than when using the standard approaches.

High-throughput indentational elasticity measurements of hydrogel extracellular matrix substrates

Much interest surrounds the effect of extracellular matrix (ECM) elasticity on cell behavior. Here we present a rapid method for measuring the elasticity of synthetic ECM substrates based on indentation of the substrate with a ferromagnetic sphere and optical tracking of the resulting deformation. We find that this method yields order-of-magnitude agreement with atomic force microscopy elasticity measurements, but that the degree of this agreement depends strongly on sphere density and gel elasticity. In its regime of greatest accuracy, we envision that this method may be used for high-throughput characterization of ECM substrates in cell biological studies.

Mechanics of microfilaments networks : a cross-scales study

The mechanical properties of microfilament networks are systematically summarized at different special scales in this paper. We have presented the mechanical models of single microfilaments and microfilament networks at microscale. By adopting a coarse-grained simulation strategy, the mechanical stability of microfilaments related cellular structures are analysed. Structural analysis is conducted to microfilament networks to understand the stress relaxation under compression. The nanoscale molecular mechanisms of the microfilaments deformation is also summarized from the viewpoint of molecular dynamics simulation. This paper provides the fundaments of multiscale modelling framework for the mechanical behaviours simulation of hierarchical microfilament networks.

A comparison of stability and bifurcation criteria for inflated spherical elastic shells

The nonlinear stability analysis introduced by Chen and Haughton [1] is employed to study the full nonlinear stability of the non-homogeneous spherically symmetric deformation of an elastic thick-walled sphere. The shell is composed of an arbitrary homogeneous, incompressible elastic material. The stability criterion ultimately requires the solution of a third-order nonlinear ordinary differential equation. Numerical calculations performed for a wide variety of well-known incompressible materials are then compared with existing bifurcation results and are found to be identical. Further analysis and comparison between stability and bifurcation are conducted for the case of thin shells and we prove by direct calculation that the two criteria are identical for all modes and all materials.

On extension and torsion of a compressible elastic circular cylinder

In this paper we examine the combined extension and torsion of a compressible isotropic elastic cylinder of finite extent. The equilibrium equations are formulated in terms of the principal stretches and then applied to the special case of pure torsion superimposed on a uniform extension (an isochoric deformation). Explicit necessary and sufficient conditions on the strain-energy function for the material to support this deformation with vanishing traction on the lateral surfaces of the cylinder are obtained. Some strain-energy functions satisfying these conditions are considered, existing results are recovered as special cases and new results are obtained. We also point out how the strain-energy functions generated from the considered isochoric deformation considered (of a compressible material) can be used to generate energy functions and corresponding solutions for the incompressible theory.

A novel manoeuvering model based on low-aspect-ratio lift theory and Lagrangian mechanics

This paper proposes a physically motivated reappraisal of manoeuvring models for ships and presents a new model developed from first principles by application of low aspect-ratio aerodynamic theory and Lagrangian mechanics. The coefficients of the model are shown to be related to physical processes, and validation is presented using the results from a planar motion mechanism dataset.

Mechanics of Polyropylene-Seed-Coat-Fibres Composites AndPolyropylene –Wood Fibres Composites-A Comparative Study

Forestry by-products have potential applications as components of wood composites. Replacement of conventional pine radiata wood-fibres by the fibres from the seeds (SCF) of the by-products, require determining and optimizing the mechanical properties to producing highest quality products. Response to mechanical stress is an important aspect to consider towards partial or full replacement of the wood-fibres by SCFs. In the present study the critical strain energy release rate, and the fracture toughness are derived from the published data. The present work uses rules of mixture to derive the mechanical and the physical properties of the SCF and relates the performance of the composites of the wood-fibres and the SCF to chemical composition, dispersion, weight and Vf of the fibres. We have also derived the Gc, the critical strain energy release rate, KIC, the fracture toughness of the composites.

A strain-based failure criterion for pillar stability analysis

Strain-based failure criteria have several advantages over stress-based failure criteria: they can account for elastic and inelastic strains, they utilise direct, observables effects instead of inferred effects (strain gauges vs. stress estimates), and model complete stress-strain curves including pre-peak, non-linear elasticity and post-peak strain weakening. In this study, a strain-based failure criterion derived from thermodynamic first principles utilising the concepts of continuum damage mechanics is presented. Furthermore, implementation of this failure criterion into a finite-element simulation is demonstrated and applied to the stability of underground mining coal pillars. In numerical studies, pillar strength is usually expressed in terms of critical stresses or stress-based failure criteria where scaling with pillar width and height is common. Previous publications have employed the finite-element method for pillar stability analysis using stress-based failure criterion such as Mohr-Coulomb and Hoek-Brown or stress-based scalar damage models. A novel constitutive material model, which takes into consideration anisotropy as well as elastic strain and damage as state variables has been developed and is presented in this paper. The damage threshold and its evolution are strain-controlled, and coupling of the state variables is achieved through the damage-induced degradation of the elasticity tensor. This material model is implemented into the finite-element software ABAQUS and can be applied to 3D problems. Initial results show that this new material model is capable of describing the non-linear behaviour of geomaterials commonly observed before peak strength is reached as well as post-peak strain softening. Furthermore, it is demonstrated that the model can account for directional dependency of failure behaviour (i.e. anisotropy) and has the potential to be expanded to environmental controls like temperature or moisture.

Comprehensive contribution of filament thickness and crosslinker failure to the rheological property of F-actin cytoskeleton

Rheological property of F-actin cytoskeleton is significant to the restructuring of cytoskeleton under a variety of cell activities. This study numerically validates the rheological property of F-actin cytoskeleton is not only a result of kinetic energy dissipation of F-actin, but also greatly depends on the configuration remodeling of networks structure. Both filament geometry and crosslinker properties can affect the remodeling of F-actin cytoskeleton. The crosslinker unbinding is found to dissipate energy and induce prominent stress relaxation in the F-actin adjacent to cross-linkages. Coupled with F-actin elasticity, the energy dissipation and stress relaxation are more significant in bundled F-actin networks than in single F-actin networks.

Rules and mechanics

So far in this book, we have seen a large number of methods for generating content for existing games. So, if you have a game already, you could now generate many things for it: maps, levels, terrain, vegetation, weapons, dungeons, racing tracks. But what if you don’t already have a game, and want to generate the game itself? What would you generate, and how? At the heart of any game are its rules. This chapter will discuss representations for game rules of different kinds, along with methods to generate them, and evaluation functions and constraints that help us judge complete games rather than just isolated content artefacts. Our main focus here will be on methods for generating interesting, fun, and/or balanced game rules. However, an important perspective that will permeate the chapter is that game rule encodings and evaluation functions can encode game design expertise and style, and thus help us understand game design. By formalising aspects of the game rules, we define a space of possible rules more precisely than could be done through writing about rules in qualitative terms; and by choosing which aspects of the rules to formalise, we define what aspects of the game are interesting to explore and introduce variation in. In this way, each game generator can be thought of an executable micro-theory of game design, though often a simplified, and sometimes even a caricatured one

Understanding classroom trouble through regulative gravity and instructional elasticity

This paper aims to develop a more nuanced analytic vocabulary to typify how and where classroom trouble can manifest in pedagogic discourse. It draws on classroom ethnographies conducted in non-academic secondary school pathways and alternative programs in Australian communities with high youth unemployment, where the policy of ‘earning or learning’ till age 17 has effectively extended compulsory schooling. Three concepts are developed and exemplified: ‘regulative flares’, being moments when teachers resort to explicitly reasserting the lesson’s social order; ‘moral gravity’ to describe the degree to which the moral order underpinning the regulative discourse is tied to the immediate context or beyond; and ‘instructional elasticity’ to account for trouble originating in the instructional register.

Significant deterioration in nanomechanical quality occurs through incomplete extrafibrillar mineralization in rachitic bone: Evidence from in-situ synchrotron X-ray scattering and backscattered electron imaging

Bone diseases such as rickets and osteoporosis cause significant reduction in bone quantity and quality, which leads to mechanical abnormalities. However, the precise ultrastructural mechanism by which altered bone quality affects mechanical properties is not clearly understood. Here we demonstrate the functional link between altered bone quality (reduced mineralization) and abnormal fibrillar-level mechanics using a novel, real-time synchrotron X-ray nanomechanical imaging method to study a mouse model with rickets due to reduced extrafibrillar mineralization. A previously unreported N-ethyl-N-nitrosourea (ENU) mouse model for hypophosphatemic rickets (Hpr), as a result of missense Trp314Arg mutation of the phosphate regulating gene with homologies to endopeptidase on the X chromosome (Phex) and with features consistent with X-linked hypophosphatemic rickets (XLHR) in man, was investigated using in situ synchrotron small angle X-ray scattering to measure real-time changes in axial periodicity of the nanoscale mineralized fibrils in bone during tensile loading. These determine nanomechanical parameters including fibril elastic modulus and maximum fibril strain. Mineral content was estimated using backscattered electron imaging. A significant reduction of effective fibril modulus and enhancement of maximum fibril strain was found in Hpr mice. Effective fibril modulus and maximum fibril strain in the elastic region increased consistently with age in Hpr and wild-type mice. However, the mean mineral content was ∼21% lower in Hpr mice and was more heterogeneous in its distribution. Our results are consistent with a nanostructural mechanism in which incompletely mineralized fibrils show greater extensibility and lower stiffness, leading to macroscopic outcomes such as greater bone flexibility. Our study demonstrates the value of in situ X-ray nanomechanical imaging in linking the alterations in bone nanostructure to nanoscale mechanical deterioration in a metabolic bone disease. Copyright

The critical role of water in spider silk and its consequence for protein mechanics

Due to its remarkable mechanical and biological properties, there is considerable interest in understanding, and replicating, spider silk's stress-processing mechanisms and structure-function relationships. Here, we investigate the role of water in the nanoscale mechanics of the different regions in the spider silk fibre, and their relative contributions to stress processing. We propose that the inner core region, rich in spidroin II, retains water due to its inherent disorder, thereby providing a mechanism to dissipate energy as it breaks a sacrificial amide-water bond and gains order under strain, forming a stronger amide-amide bond. The spidroin I-rich outer core is more ordered under ambient conditions and is inherently stiffer and stronger, yet does not on its own provide high toughness. The markedly different interactions of the two proteins with water, and their distribution across the fibre, produce a stiffness differential and provide a balance between stiffness, strength and toughness under ambient conditions. Under wet conditions, this balance is destroyed as the stiff outer core material reverts to the behaviour of the inner core.

Size-dependent elasticity of nanocrystalline titania

Synchrotron-based high-pressure x-ray diffraction measurements indicate that compressibility, a fundamental materials property, can have a size-specific minimum value. The bulk modulus of nanocrystalline titania has a maximum at particle size of 15 nm. This can be explained by dislocation behavior because very high dislocation contents can be achieved when shear stress induced within nanoparticles counters the repulsion between dislocations. As particle size decreases, compression increasingly generates dislocation networks hardened by overlap of strain fields that shield intervening regions from external pressure. However, when particles become too small to sustain high dislocation concentrations, elastic stiffening declines. The compressibility has a minimum at intermediate sizes.