Simulation of the cytoskeletal response of cells on grooved or patterned substrates.

We analyse the response of osteoblasts on grooved substrates via a model that accounts for the cooperative feedback between intracellular signalling, focal adhesion development and stress fibre contractility. The grooved substrate is modelled as a pattern of alternating strips on which the cell can adhere and strips on which adhesion is inhibited. The coupled modelling scheme is shown to capture some key experimental observations including (i) the observation that osteoblasts orient themselves randomly on substrates with groove pitches less than about 150 nm but they align themselves with the direction of the grooves on substrates with larger pitches and (ii) actin fibres bridge over the grooves on substrates with groove pitches less than about 150 nm but form a network of fibres aligned with the ridges, with nearly no fibres across the grooves, for substrates with groove pitches greater than about 300 nm. Using the model, we demonstrate that the degree of bridging of the stress fibres across the grooves, and consequently the cell orientation, is governed by the diffusion of signalling proteins activated at the focal adhesion sites on the ridges. For large groove pitches, the signalling proteins are dephosphorylated before they can reach the regions of the cell above the grooves and hence stress fibres cannot form in those parts of the cell. On the other hand, the stress fibre activation signal diffuses to a reasonably spatially homogeneous level on substrates with small groove pitches and hence stable stress fibres develop across the grooves in these cases. The model thus rationalizes the responsiveness of osteoblasts to the topography of substrates based on the complex feedback involving focal adhesion formation on the ridges, the triggering of signalling pathways by these adhesions and the activation of stress fibre networks by these signals.A.V. and V.S.D. acknowledge the Royal Society for supporting A.V. through a Newton International Fellowship.This is the accepted manuscript of a paper published in the Journal of the Royal Society Interface (Vigliotti A, McMeeking RM, Deshpande VS, J. R. Soc. Interface 2015, 12, 20141320, doi:10.1098/rsif.2014.1320). The final version is available at http://dx.doi.org/10.1098/rsif.2014.1320

Growth rate of lithium filaments in ceramic electrolytes

© 2020 Lithium-ion batteries with single ion-conductor ceramic electrolytes short-circuit when subjected to charging currents above a critical current density. Here, we analyse the rate at which a lithium (Li) filament (sometimes referred to as a dendrite) will grow from the cathode towards the anode during charging of such batteries. The filament is modelled as a climbing edge dislocation with its growth occurring by Li+ flux from the electrolyte into the filament tip at constant chemical potential. The growth rate is set by a balance between the reduction of free-energy at the filament tip and energy dissipation associated with the resistance to the flux of Li+ through the filament tip. For charging currents above the critical current density, the filament growth rate increases with decreasing filament tip resistance. Imperfections, such as voids in the Li cathode along the electrolyte/cathode interface, decrease the critical current density but filament growth rates are also lower in these cases as filament growth rates scale with the charging currents. The predictions of the model are in excellent quantitative agreement with measurements and confirm that above the critical current density a filament can traverse the electrolyte in minutes or less. This suggests that initiation of filament growth is the critical step to prevent short-circuiting of the battery

Cooperative contractility: the role of stress fibres in the regulation of cell-cell junctions.

We present simulations of cell-cell adhesion as reported in a recent study [Liu et al., 2010, PNAS, 107(22), 9944-9] for two cells seeded on an array of micro-posts. The micro-post array allows for the measurement of forces exerted by the cell and these show that the cell-cell tugging stress is a constant and independent of the cell-cell junction area. In the current study, we demonstrate that a material model which includes the underlying cellular processes of stress fibre contractility and adhesion formation can capture these results. The simulations explain the experimentally observed phenomena whereby the cell-cell junction forces increase with junction size but the tractions exerted by the cell on the micro-post array are independent of the junction size. Further simulations on different types of micro-post arrays and cell phenotypes are presented as a guide to future experiments.WR and PMcG acknowledge Science Foundation Ireland grant 10/RFP/ENM2960 and Short Term Travel Fellowship (STTF 11).This is the accepted manuscript. The final version is available from Elsevier at http://www.sciencedirect.com/science/article/pii/S0021929014006137

Discrete dislocation plasticity analysis of the high-temperature cyclic response of composites

Discrete dislocation plasticity (DDP) analysis of the high-temperature cyclic deformation of two- phase composites comprising a plastic matrix and elastic precipitates is presented. Deformation of the matrix is by climb-assisted glide of dislocations while the precipitates deform by a combination of bulk elasticity and stress-driven interfacial diffusion. The DDP calculations predict a cyclically softening response due to the formation of dislocation cell structures within the matrix. The dislocation cell sizes decrease with decreasing size of the unit cell (or equivalently matrix channels) and this results in an increased cyclic softening rate in composites with smaller unit cells. Interfacial diffusion also enhances the formation of dislocation cell structures and thereby promotes cyclic softening. These results are consistent with predictions of the creep behaviour that indicate that the increase in the creep rate (i.e. tertiary creep) is also associated with the formation of dislocation cell structures within the matrix

Cohesive detachment of an elastic pillar from a dissimilar substrate

The adhesion of micron-scale surfaces due to intermolecular interactions is a subject of intense interest spanning electronics, biomechanics and the application of soft materials to engineering devices. The degree of adhesion is sensitive to the diameter of micro-pillars in addition to the degree of elastic mismatch between pillar and substrate. Adhesion-strength-controlled detachment of an elastic circular cylinder from a dissimilar substrate is predicted using a Dugdale-type of analysis, with a cohesive zone of uniform tensile strength emanating from the interface corner. Detachment initiates when the opening of the cohesive zone attains a critical value, giving way to crack formation. When the cohesive zone size at crack initiation is small compared to the pillar diameter, the initiation of detachment can be expressed in terms of a critical value H c of the corner stress intensity. The estimated pull-off force is somewhat sensitive to the choice of stick/slip boundary condition used on the cohesive zone, especially when the substrate material is much stiffer than the pillar material. The analysis can be used to predict the sensitivity of detachment force to the size of pillar and to the degree of elastic mismatch between pillar and substrate.NAF is grateful for financial support in the form of an ERC MULTILAT Grant 669764, and to the US ONR (N62909-14-1-N232, project manager, Dr. Dave Shifler). NAF and RMcM acknowledge support from the Alexander von Humboldt Foundation in the form of their Forschungspreise, which enabled them to undertake research at INM-Leibniz Institute for New Materials, Saarbrücken. EA acknowledges funding from the European Research Council under the European Union's Seventh Framework Programme (FP/2007-2013)/ERC Grant agreement no. 340929

Response of cells on a dense array of micro-posts

AbstractWe have analysed the response of cells on a bed of micro-posts idealized as a Winkler foundation using a homeostatic mechanics framework. The framework enables quantitative estimates of the stochastic response of cells along with the coupled analysis of cell spreading, contractility and mechano-sensitivity. In particular the model is shown to accurately predict that: (i) the extent of cell spreading, actin polymerisation as well as the traction forces that cells exert increase with increasing stiffness of the foundation; (ii) the traction forces that cells exert are primarily concentrated along the cell periphery; and (iii) while the total tractions increase with increasing cell area the average tractions are reasonably independent of cell area, i.e. for a given substrate stiffness, the average tractions that are normalized by cell area do not vary strongly with cell size. These results thus suggest that the increased foundation stiffness causes both the cell area and the average tractions that the cells exert to increase through higher levels of stress-fibre polymerization rather than the enhanced total tractions being directly linked through causation to the larger cell areas. A defining feature of the model is that its predictions are statistical in the form of probability distributions of observables such as the traction forces and cell area. In contrast, most existing models present solutions to specific boundary value problems where the cell morphology is imposed a priori. In particular, in line with observations we predict that the diversity of cell shapes, sizes and measured traction forces increase with increasing foundation stiffness. The homeostatic mechanics framework thus suggests that the diversity of observations in in vitro experiments is inherent to the homeostatic equilibrium of cells rather than being a result of experimental errors.</jats:p

Transformation Pathways of Silica under High Pressure

Concurrent molecular dynamics simulations and ab initio calculations show that densification of silica under pressure follows a ubiquitous two-stage mechanism. First, anions form a close-packed sub-lattice, governed by the strong repulsion between them. Next, cations redistribute onto the interstices. In cristobalite silica, the first stage is manifest by the formation of a metastable phase, which was observed experimentally a decade ago, but never indexed due to ambiguous diffraction patterns. Our simulations conclusively reveal its structure and its role in the densification of silica.Comment: 14 pages, 4 figure

Undrained expansion of a cylindrical cavity in clays with fabric anisotropy: theoretical solution

This paper presents a novel, exact, semi-analytical solution for the quasi-static undrained expansion of a cylindrical cavity in soft soils with fabric anisotropy. This is the first theoretical solution of the undrained expansion of a cylindrical cavity under plane strain conditions for soft soils with anisotropic behaviour of plastic nature. The solution is rigorously developed in detail, introducing a new stress invariant to deal with the soil fabric. The semianalytical solution requires numerical evaluation of a system of six first-order ordinary differential equations. The results agree with finite element analyses and show the influence of anisotropic plastic behaviour. The effective stresses at critical state are constant, and they may be analytically related to the undrained shear strength. The initial vertical cross-anisotropy caused by soil deposition changes towards a radial cross-anisotropy after cavity expansion. The analysis of the stress paths shows that proper modelling of anisotropic plastic behaviour involves modelling not only the initial fabric anisotropy but also its evolution with plastic straining.The research was initiated as part of GEO-INSTALL (Modelling Installation Effects in Geotechnical Engineering, PIAP-GA-2009-230638) and CREEP (Creep of Geomaterials, PIAP-GA-2011-286397) projects supported by the European Community through the programme Marie Curie Industry-Academia Partnerships and Pathways (IAPP) under the 7th Framework Programme