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Goriely, A. (20)

Moulton, D. E. (3)Moulton, D.E. (3)Tabor, M. (3)Yavari, A. (3)View MoreJournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences (6)Mathematics and Mechanics of Solids (4)IMA Journal of Applied Mathematics (2)Journal of the Mechanics and Physics of Solids (2)Applied Physics Letters (1)View MoreKAUST Grant NumberKUK-C1-013-04 (17)KUK C1-013-04 (3)PublisherThe Royal Society (6)SAGE Publications (4)Elsevier BV (3)Oxford University Press (OUP) (2)AIP Publishing (1)View MoreSubjectgrowth (3)residual stress (3)Elasticity (2)Geometric elasticity (2)Instability (2)View MoreTypeArticle (20)Year (Issue Date)2014 (2)2013 (6)2012 (4)2011 (5)2010 (3)Item AvailabilityMetadata Only (20)

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Morphoelastic rods. Part I: A single growing elastic rod

Moulton, D.E.; Lessinnes, T.; Goriely, A. (Journal of the Mechanics and Physics of Solids, Elsevier BV, 2013-02) [Article]

A theory for the dynamics and statics of growing elastic rods is presented. First, a single growing rod is considered and the formalism of three-dimensional multiplicative decomposition of morphoelasticity is used to describe the bulk growth of Kirchhoff elastic rods. Possible constitutive laws for growth are discussed and analysed. Second, a rod constrained or glued to a rigid substrate is considered, with the mismatch between the attachment site and the growing rod inducing stress. This stress can eventually lead to instability, bifurcation, and buckling. © 2012 Elsevier Ltd. All rights reserved.

Controlling coverage of solution cast materials with unfavourable surface interactions

Burlakov, V. M.; Eperon, G. E.; Snaith, H. J.; Chapman, S. J.; Goriely, A. (Applied Physics Letters, AIP Publishing, 2014-03-03) [Article]

Creating uniform coatings of a solution-cast material is of central importance to a broad range of applications. Here, a robust and generic theoretical framework for calculating surface coverage by a solid film of material de-wetting a substrate is presented. Using experimental data from semiconductor thin films as an example, we calculate surface coverage for a wide range of annealing temperatures and film thicknesses. The model generally predicts that for each value of the annealing temperature there is a range of film thicknesses leading to poor surface coverage. The model accurately reproduces solution-cast thin film coverage for organometal halide perovskites, key modern photovoltaic materials, and identifies processing windows for both high and low levels of surface coverage. © 2014 AIP Publishing LLC.

Circumferential buckling instability of a growing cylindrical tube

Moulton, D.E.; Goriely, A. (Journal of the Mechanics and Physics of Solids, Elsevier BV, 2011-03) [Article]

A cylindrical elastic tube under uniform radial external pressure will buckle circumferentially to a non-circular cross-section at a critical pressure. The buckling represents an instability of the inner or outer edge of the tube. This is a common phenomenon in biological tissues, where it is referred to as mucosal folding. Here, we investigate this buckling instability in a growing elastic tube. A change in thickness due to growth can have a dramatic impact on circumferential buckling, both in the critical pressure and the buckling pattern. We consider both single- and bi-layer tubes and multiple boundary conditions. We highlight the competition between geometric effects, i.e. the change in tube dimensions, and mechanical effects, i.e. the effect of residual stress, due to differential growth. This competition can lead to non-intuitive results, such as a tube growing to be thinner and yet buckle at a higher pressure. © 2011 Elsevier Ltd. All rights reserved.

Synaptic Bistability Due to Nucleation and Evaporation of Receptor Clusters

Burlakov, V. M.; Emptage, N.; Goriely, A.; Bressloff, P. C. (Physical Review Letters, American Physical Society (APS), 2012-01-10) [Article]

We introduce a bistability mechanism for long-term synaptic plasticity based on switching between two metastable states that contain significantly different numbers of synaptic receptors. One state is characterized by a two-dimensional gas of mobile interacting receptors and is stabilized against clustering by a high nucleation barrier. The other state contains a receptor gas in equilibrium with a large cluster of immobile receptors, which is stabilized by the turnover rate of receptors into and out of the synapse. Transitions between the two states can be initiated by either an increase (potentiation) or a decrease (depotentiation) of the net receptor flux into the synapse. This changes the saturation level of the receptor gas and triggers nucleation or evaporation of receptor clusters. © 2012 American Physical Society.

Mechanical growth and morphogenesis of seashells

Moulton, D.E.; Goriely, A.; Chirat, R. (Journal of Theoretical Biology, Elsevier BV, 2012-10) [Article]

Seashells grow through the local deposition of mass along the aperture. Many mathematical descriptions of the shapes of shells have been provided over the years, and the basic logarithmic coiling seen in mollusks can be simulated with few parameters. However, the developmental mechanisms underlying shell coiling are largely not understood and the ubiquitous presence of ornamentation such as ribs, tubercles, or spines presents yet another level of difficulty. Here we develop a general model for shell growth based entirely on the local geometry and mechanics of the aperture and mantle. This local description enables us to efficiently describe both arbitrary growth velocities and the evolution of the shell aperture itself. We demonstrate how most shells can be simulated within this framework. We then turn to the mechanics underlying the shell morphogenesis, and develop models for the evolution of the aperture. We demonstrate that the elastic response of the mantle during shell deposition provides a natural mechanism for the formation of three-dimensional ornamentation in shells. © 2012 Elsevier Ltd.

Elastic cavitation, tube hollowing, and differential growth in plants and biological tissues

Goriely, A.; Moulton, D. E.; Vandiver, R. (EPL (Europhysics Letters), IOP Publishing, 2010-07-19) [Article]

Elastic cavitation is a well-known physical process by which elastic materials under stress can open cavities. Usually, cavitation is induced by applied loads on the elastic body. However, growing materials may generate stresses in the absence of applied loads and could induce cavity opening. Here, we demonstrate the possibility of spontaneous growth-induced cavitation in elastic materials and consider the implications of this phenomenon to biological tissues and in particular to the problem of schizogenous aerenchyma formation. Copyright © EPLA, 2010.

Three mechanical models for blebbing and multi-blebbing

Woolley, T. E.; Gaffney, E. A.; Waters, S. L.; Oliver, J. M.; Baker, R. E.; Goriely, A. (IMA Journal of Applied Mathematics, Oxford University Press (OUP), 2014-06-17) [Article]

Membrane protrusions known as blebs play important roles in many cellular phenomena. Here we present three mathematical models of the bleb formation, which use biological insights to produce phenotypically accurate pressure-driven expansions. First, we introduce a recently suggested solid mechanics framework that is able to create blebs through stretching the membrane. This framework is then extended to include reference state reconfigurations, which models membrane growth. Finally, the stretching and reconfiguring mechanical models are compared with a much simpler geometrically constrained solution. This allows us to demonstrate that simpler systems are able to capture much of the biological complexity despite more restrictive assumptions. Moreover, the simplicity of the spherical model allows us to consider multiple blebs in a tractable framework. © 2014 The authors 2014. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Weyl geometry and the nonlinear mechanics of distributed point defects

Yavari, A.; Goriely, A. (Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, The Royal Society, 2012-09-05) [Article]

The residual stress field of a nonlinear elastic solid with a spherically symmetric distribution of point defects is obtained explicitly using methods from differential geometry. The material manifold of a solid with distributed point defects-where the body is stress-free-is a flat Weyl manifold, i.e. a manifold with an affine connection that has non-metricity with vanishing traceless part, but both its torsion and curvature tensors vanish. Given a spherically symmetric point defect distribution, we construct its Weyl material manifold using the method of Cartan's moving frames. Having the material manifold, the anelasticity problem is transformed to a nonlinear elasticity problem and reduces the problem of computing the residual stresses to finding an embedding into the Euclidean ambient space. In the case of incompressible neo-Hookean solids, we calculate explicitly this residual stress field. We consider the example of a finite ball and a point defect distribution uniform in a smaller ball and vanishing elsewhere. We show that the residual stress field inside the smaller ball is uniform and hydrostatic. We also prove a nonlinear analogue of Eshelby's celebrated inclusion problem for a spherical inclusion in an isotropic incompressible nonlinear solid. © 2012 The Royal Society.

Riemann-Cartan geometry of nonlinear disclination mechanics

Yavari, A.; Goriely, A. (Mathematics and Mechanics of Solids, SAGE Publications, 2012-03-23) [Article]

In the continuous theory of defects in nonlinear elastic solids, it is known that a distribution of disclinations leads, in general, to a non-trivial residual stress field. To study this problem, we consider the particular case of determining the residual stress field of a cylindrically symmetric distribution of parallel wedge disclinations. We first use the tools of differential geometry to construct a Riemannian material manifold in which the body is stress-free. This manifold is metric compatible, has zero torsion, but has non-vanishing curvature. The problem then reduces to embedding this manifold in Euclidean 3-space following the procedure of a classical nonlinear elastic problem. We show that this embedding can be elegantly accomplished by using Cartan's method of moving frames and compute explicitly the residual stress field for various distributions in the case of a neo-Hookean material. © 2012 The Author(s).

Scalar evolution equations for shear waves in incompressible solids: a simple derivation of the Z, ZK, KZK and KP equations

Destrade, M.; Goriely, A.; Saccomandi, G. (Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, The Royal Society, 2010-12-08) [Article]

We study the propagation of two-dimensional finite-amplitude shear waves in a nonlinear pre-strained incompressible solid, and derive several asymptotic amplitude equations in a simple, consistent and rigorous manner. The scalar Zabolotskaya (Z) equation is shown to be the asymptotic limit of the equations of motion for all elastic generalized neo-Hookean solids (with strain energy depending only on the first principal invariant of Cauchy-Green strain). However, we show that the Z equation cannot be a scalar equation for the propagation of two-dimensional shear waves in general elastic materials (with strain energy depending on the first and second principal invariants of strain). Then, we introduce dispersive and dissipative terms to deduce the scalar Kadomtsev-Petviashvili (KP), Zabolotskaya-Khokhlov (ZK) and Khokhlov- Zabolotskaya-Kuznetsov (KZK) equations of incompressible solid mechanics. © 2010 The Royal Society.

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