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Author

Goriely, Alain (7)

Moulton, Derek E. (2)Baker, Ruth E. (1)De Pascalis, Riccardo (1)Destrade, Michel (1)View MoreJournalJournal of Elasticity (3)Archive for Rational Mechanics and Analysis (1)Biomechanics and Modeling in Mechanobiology (1)Journal of Mathematical Biology (1)Zeitschrift für angewandte Mathematik und Physik (1)KAUST Grant NumberKUK-C1-013-04 (6)KUKC1-013-04 (1)Publisher
Springer Nature (7)

SubjectAnticavitation (1)Biological growth (1)Bleb (1)Cavitation (1)Cell mechanics (1)View MoreTypeArticle (7)Year (Issue Date)2013 (1)2012 (3)2011 (1)2010 (2)Item AvailabilityMetadata Only (7)

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Cellular blebs: pressure-driven, axisymmetric, membrane protrusions

Woolley, Thomas E.; Gaffney, Eamonn A.; Oliver, James M.; Baker, Ruth E.; Waters, Sarah L.; Goriely, Alain (Biomechanics and Modeling in Mechanobiology, Springer Nature, 2013-07-16) [Article]

Blebs are cellular protrusions that are used by cells for multiple purposes including locomotion. A mechanical model for the problem of pressure-driven blebs based on force and moment balances of an axisymmetric shell model is proposed. The formation of a bleb is initiated by weakening the shell over a small region, and the deformation of the cellular membrane from the cortex is obtained during inflation. However, simply weakening the shell leads to an area increase of more than 4 %, which is physically unrealistic. Thus, the model is extended to include a reconfiguration process that allows large blebs to form with small increases in area. It is observed that both geometric and biomechanical constraints are important in this process. In particular, it is shown that although blebs are driven by a pressure difference across the cellular membrane, it is not the limiting factor in determining bleb size. © 2013 Springer-Verlag Berlin Heidelberg.

Anticavitation and Differential Growth in Elastic Shells

Moulton, Derek E.; Goriely, Alain (Journal of Elasticity, Springer Nature, 2010-07-22) [Article]

Elastic anticavitation is the phenomenon of a void in an elastic solid collapsing on itself. Under the action of mechanical loading alone typical materials do not admit anticavitation. We study the possibility of anticavitation as a consequence of an imposed differential growth. Working in the geometry of a spherical shell, we seek radial growth functions which cause the shell to deform to a solid sphere. It is shown, surprisingly, that most material models do not admit full anticavitation, even when infinite growth or resorption is imposed at the inner surface of the shell. However, void collapse can occur in a limiting sense when radial and circumferential growth are properly balanced. Growth functions which diverge or vanish at a point arise naturally in a cumulative growth process. © 2010 Springer Science+Business Media B.V.

Nonlinear Correction to the Euler Buckling Formula for Compressed Cylinders with Guided-Guided End Conditions

De Pascalis, Riccardo; Destrade, Michel; Goriely, Alain (Journal of Elasticity, Springer Nature, 2010-07-22) [Article]

Euler's celebrated buckling formula gives the critical load N for the buckling of a slender cylindrical column with radius B and length L as N/(π3B2)=(E/4)(B/L)2 where E is Young's modulus. Its derivation relies on the assumptions that linear elasticity applies to this problem, and that the slenderness (B/L) is an infinitesimal quantity. Here we ask the following question: What is the first non-linear correction in the right hand-side of this equation when terms up to (B/L)4 are kept? To answer this question, we specialize the exact solution of incremental non-linear elasticity for the homogeneous compression of a thick compressible cylinder with lubricated ends to the theory of third-order elasticity. In particular, we highlight the way second- and third-order constants-including Poisson's ratio-all appear in the coefficient of (B/L)4. © 2010 Springer Science+Business Media B.V.

Stability Estimates for a Twisted Rod Under Terminal Loads: A Three-dimensional Study

Majumdar, Apala; Prior, Christopher; Goriely, Alain (Journal of Elasticity, Springer Nature, 2012-03-01) [Article]

The stability of an inextensible unshearable elastic rod with quadratic strain energy density subject to end loads is considered. We study the second variation of the corresponding rod-energy, making a distinction between in-plane and out-of-plane perturbations and isotropic and anisotropic cross-sections, respectively. In all cases, we demonstrate that the naturally straight state is a local energy minimizer in parameter regimes specified by material constants. These stability results are also accompanied by instability results in parameter regimes defined in terms of material constants. © 2012 Springer Science+Business Media B.V.

Self-diffusion in remodeling and growth

Epstein, Marcelo; Goriely, Alain (Zeitschrift für angewandte Mathematik und Physik, Springer Nature, 2011-07-16) [Article]

Self-diffusion, or the flux of mass of a single species within itself, is viewed as an independent phenomenon amenable to treatment by the introduction of an auxiliary field of diffusion velocities. The theory is shown to be heuristically derivable as a limiting case of that of an ordinary binary mixture. © 2011 Springer Basel AG.

Surface growth kinematics via local curve evolution

Moulton, Derek E.; Goriely, Alain (Journal of Mathematical Biology, Springer Nature, 2012-11-18) [Article]

A mathematical framework is developed to model the kinematics of surface growth for objects that can be generated by evolving a curve in space, such as seashells and horns. Growth is dictated by a growth velocity vector field defined at every point on a generating curve. A local orthonormal basis is attached to each point of the generating curve and the velocity field is given in terms of the local coordinate directions, leading to a fully local and elegant mathematical structure. Several examples of increasing complexity are provided, and we demonstrate how biologically relevant structures such as logarithmic shells and horns emerge as analytical solutions of the kinematics equations with a small number of parameters that can be linked to the underlying growth process. Direct access to cell tracks and local orientation enables for connections to be made to the underlying growth process. © 2012 Springer-Verlag Berlin Heidelberg.

Riemann–Cartan Geometry of Nonlinear Dislocation Mechanics

Yavari, Arash; Goriely, Alain (Archive for Rational Mechanics and Analysis, Springer Nature, 2012-03-09) [Article]

We present a geometric theory of nonlinear solids with distributed dislocations. In this theory the material manifold-where the body is stress free-is a Weitzenböck manifold, that is, a manifold with a flat affine connection with torsion but vanishing non-metricity. Torsion of the material manifold is identified with the dislocation density tensor of nonlinear dislocation mechanics. Using Cartan's moving frames we construct the material manifold for several examples of bodies with distributed dislocations. We also present non-trivial examples of zero-stress dislocation distributions. More importantly, in this geometric framework we are able to calculate the residual stress fields, assuming that the nonlinear elastic body is incompressible. We derive the governing equations of nonlinear dislocation mechanics covariantly using balance of energy and its covariance. © 2012 Springer-Verlag.

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