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In this work, we have explored growth-induced mechanical instability in an isotropic circular hyperelastic plate. Consistent two-dimensional governing equations for a plate under a general finite strain are derived using a variational…

Pattern Formation and Solitons · Physics 2021-03-12 Sumit Mehta , Gangadharan Raju , Prashant Saxena

Liquid foams have been observed to behave like immersed granular materials in at least one respect: deformation tends to raise their liquid contents, a phenomenon called dilatancy. We present a geometrical interpretation thereof in foams…

Soft Condensed Matter · Physics 2009-09-29 Pierre Rognon , François Molino , Cyprien Gay

The flow of amorphous solids results from a combination of elastic deformation and local structural rearrangements, which induce non-local elastic deformations. These elements are incorporated into a mechanically-consistent mesoscopic model…

Soft Condensed Matter · Physics 2015-06-12 Alexandre Nicolas , Jean-Louis Barrat

Characterizing the softness of deformable materials having partial elastic and partial viscous behaviour via soft lubrication experiments has emerged as a versatile and robust methodology in recent times. However, a straightforward…

Soft Condensed Matter · Physics 2021-07-22 Pratyaksh Karan , Jeevanjyoti Chakraborty , Suman Chakraborty

Lattice defects in crystalline materials create long-range elastic fields which can be modelled on the atomistic scale using an infinite system of discrete nonlinear force balance equations. Starting with these equations, this work…

Analysis of PDEs · Mathematics 2022-08-10 Julian Braun , Thomas Hudson , Christoph Ortner

We study a theoretical model of mud cracks, that is, the fracture patterns resulting from the contraction with drying in a thin layer of a mixture of granules and water. In this model, we consider the slip on the bottom of this layer and…

patt-sol · Physics 2009-10-31 S. Kitsunezaki

Using three-dimensional numerical simulations, we demonstrate the growth saturation of an unstable thin liquid film on micropatterned hydrophilic-hydrophobic substrates. We consider different transverse-striped micropatterns, characterized…

Soft Condensed Matter · Physics 2011-10-26 Rodrigo Ledesma-Aguilar , Aurora Hernandez-Machado , Ignacio Pagonabarraga

A 2D lattice approach to describe hydraulic fracturing is presented. The interaction of fluid pressure and mechanical response is described by Biot's theory. The lattice model is applied to the analysis of a thick-walled cylinder, for which…

Materials Science · Physics 2014-12-03 Peter Grassl , Caroline Fahy , Domenico Gallipoli , Simon J. Wheeler

We introduce a model of fracture which includes the out-of-plane degrees of freedom necessary to describe buckling in a thin-sheet material. The model is a regular square lattice of elastic beams, rigidly connected at the nodes so as to…

Soft Condensed Matter · Physics 2007-05-23 Bjorn Skjetne , Torbjorn Helle , Alex Hansen

The injection of a fluid into another of larger viscosity in a Hele-Shaw cell usually results in the formation of highly branched patterns. Despite the richness of these structures, in many practical situations such convoluted shapes are…

Soft Condensed Matter · Physics 2010-12-14 Eduardo O. Dias , Fernando Parisio , Jose A. Miranda

In this paper, we study the dynamics of a two-dimensional viscous fluid evolving through a porous medium or a Hele-Shaw cell, driven by gravity and surface tension. A key feature of this study is that the fluid is confined within a vessel…

Analysis of PDEs · Mathematics 2026-04-09 Edoardo Bocchi , Ángel Castro , Francisco Gancedo

Tip-driven growth processes underlie the development of many plants. To date, tip-driven growth processes have been modelled as an elongating path or series of segments without taking into account lateral expansion during elongation.…

Biological Physics · Physics 2014-01-24 Alexander Bucksch , Greg Turk , Joshua S. Weitz

We consider a family of linearly elastic shells with thickness $2\varepsilon$ (where $\varepsilon$ is a small parameter). The shells are clamped along a portion of their lateral face, all having the same middle surface $S$, and may enter in…

Mathematical Physics · Physics 2016-11-23 Á. Rodríguez-Arós

The permeability anisotropy that results from a shear displacement 'u' between the complementary self-affine walls of a rough fracture is investigated. Experiments in which a dyed fluid displaces a transparent one as it is radially injected…

Soft Condensed Matter · Physics 2007-05-23 H. Auradou , G. Drazer , J. P. Hulin , J. Koplik

Fluid-induced slip of fractures is characterized by strong multiphysics couplings. Three physical processes are considered: Flow, rock deformation and fracture deformation. The fractures are represented as lower-dimensional objects embedded…

Geophysics · Physics 2017-12-19 Runar L. Berge , Inga Berre , Eirik Keilegavlen

Models of tumor growth, now commonly used, present several levels of complexity, both in terms of the biomedical ingredients and the mathematical description. The simplest ones contain competition for space using purely fluid mechanical…

Analysis of PDEs · Mathematics 2015-06-12 Benoît Perthame , Fernando Quirós , Juan Luis Vázquez

In this paper, we derive an effective model for transport processes in periodically perforated elastic media, taking into account, e.g., cyclic elastic deformations as they occur in lung tissue due to respiratory movement. The underlying…

Analysis of PDEs · Mathematics 2022-06-15 Jonas Knoch , Markus Gahn , Maria Neuss-Radu , Nicolas Neuß

The Saffman-Taylor instability occurs when a less viscous fluid is displacing a more viscous one in a rectangular Hele-Shaw cell. A surface tension on the interface between the two fluids is improving the stability. The multi-layer Hele -…

Fluid Dynamics · Physics 2019-03-06 Gelu Paşa

When a viscous fluid partially fills a Hele--Shaw channel, and is pushed by a pressure difference, the fluid interface is unstable due to the Saffman--Taylor instability. We consider the evolution of a fluid region of finite extent, bounded…

Fluid Dynamics · Physics 2024-05-20 Michael C Dallaston , Michael J W Jackson , Liam C Morrow , Scott W McCue

The paper deals with a problem of interaction between hydrodynamics and mechanics of nonlinear elastic bodies. The existence question for two-dimensional symmetric steady waves travelling on the surface of a deep ocean beneath a heavy…

Analysis of PDEs · Mathematics 2008-12-02 Pietro Baldi , John F Toland