laboratoire de physique statistique
 
 
laboratoire de physique statistique

Publications

Rechercher
2010 


Martine BEN AMAR 


4
P U B L I C A T I O N S



 
2010
Swelling instability of surface-attached gels as a model of soft tissue growth under geometric constraints - Ben Amar, Martine and Ciarletta, Pasquale
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 58935-954 (2010) 
LPS


Abstract : The purpose of this work is to provide a theoretical analysis of the mechanical behavior of the growth of soft materials under geometrical constraints. In particular, we focus on the swelling of a gel layer clamped to a substrate, which is still the subject of many experimental tests. Because the constrained swelling process induces compressive stresses, all these experiments exhibit surface instabilities, which ultimately lead to cusp formation. Our model is based on fixing a neo-Hookean constitutive energy together with the incompressibility requirement for a volumetric, homogeneous mass addition. Our approach is developed mostly, but not uniquely, in the plane strain configuration. We show how the standard equilibrium equations from continuum mechanics have a similarity with the two-dimensional Stokes flows, and we use a nonlinear stream function for the exact treatment of the incompressibility constraint. A free energy approach allows the extension both to arbitrary hyperelastic strain energies and to additional interactions, such as surface energies. We find that, at constant volumetric growth, the threshold for a wavy instability is completely governed by the amount of growth. Nevertheless, the determination of the wavelength at threshold, which scales with the initial thickness of the gel layer, requires the coupling with a surface effect. Our findings, which are valid in proximity of the threshold, are compared to experimental results. The proposed treatment can be extended to weakly nonlinearities within the aim of the theory of bifurcations. (C) 2010 Elsevier Ltd. All rights reserved.
Localized growth of layered tissues - Dervaux, Julien and Ben Amar, Martine
IMA JOURNAL OF APPLIED MATHEMATICS 75571-580 (2010) 
LPS


Abstract : Due to their structural heterogeneity, stratified media usually loose their initial symmetry when they grow. Mismatching expansions between distinct layers create elastic stresses that lead to the emergence of wavy patterns. In the context of morphogenesis, this process of constrained growth has been used to explain patterns in biological soft-layered tissues such as the fingerprints of the skin. Discovery of morphogens has however revealed that growth is not always a homogeneous process and can be highly localized. Spatially concentrated growth processes are thought to be responsible for the formation of various structures, from placodes in the chicken embryo to nevus and skin tumours. On a different ground, the processing of complex textured surfaces requires to understand the connection between the local variation of mass and the resulting surface profile. In this paper, we investigate a model of a locally growing thin sheet bound to a soft infinite substrate. We show that, in two dimensions, bending effects select the shape of the growing sheet, therefore preventing the fabrication of an arbitrary surface. In three dimensions, the high energetic cost of stretching sets a stronger constraint on the attainable patterns and provides a simple relation between the profile of the surface and the local properties of the growth process.
Self-Contact and Instabilities in the Anisotropic Growth of Elastic Membranes - Stoop, Norbert and Wittel, Falk K. and Ben Amar, Martine and Mueller, Martin Michael and Herrmann, Hans J.
PHYSICAL REVIEW LETTERS 105 (2010) 
LPS


Abstract : We investigate the morphology of thin discs and rings growing in the circumferential direction. Recent analytical results suggest that this growth produces symmetric excess cones ( e cones). We study the stability of such solutions considering self-contact and bending stress. We show that, contrary to what was assumed in previous analytical solutions, beyond a critical growth factor, no symmetric e cone solution is energetically minimal any more. Instead, we obtain skewed e cone solutions having lower energy, characterized by a skewness angle and repetitive spiral winding with increasing growth. These results are generalized to discs with varying thickness and rings with holes of different radii.
Instability patterns in ultrathin nematic films: Comparison between theory and experiment - Manyuhina, O. V. and Cazabat, A. -M. and Ben Amar, M.
EPL 92 (2010) 
LPS


Abstract : Motivated by recent experimental observations (Delabre U. et al., Langmuir, 24 (2008) 3998), we reconsider an instability of ultrathin nematic films, spread on liquid substrates. Within a continuum elastic theory of liquid crystals, in the harmonic approximation, we find an analytical expressions for the critical thickness as well as for the critical wave number, characterizing the onset of instability towards the stripe phase. Comparing theoretical predictions with experimental observations, we establish the utility of surface-like term such as an azimuthal anchoring. Copyright (C) EPLA, 2010