Growth-induced compatible strains

We studied the time evolution problem driven by growth for a non-Euclidean ball which at its initial state is equipped with a non-compatible distortion field. The problem is set within the framework of non-linear elasticity with large growing distortions. No bulk accretive forces are considered, and growth is only driven by the stress state. We showed that, when stress-driven growth is considered, distortions can evolve along different trajectories which share a common attracting manifold; moreover, they eventually attain a steady and compatible form, to which there corresponds a stress-free state of the ball.

[1]  L A Taber,et al.  Theoretical study of stress-modulated growth in the aorta. , 1996, Journal of theoretical biology.

[2]  Luciano Teresi,et al.  Strain induced shape formation in fibred cylindrical tubes , 2012 .

[3]  John M. Lee.  Riemannian Manifolds: An Introduction to Curvature , 1997 .

[4]  P. Nardinocchi,et al.  Electromechanical modeling of anisotropic cardiac tissues , 2013 .

[5]  Ray W. Ogden,et al.  Nearly isochoric elastic deformations: Application to rubberlike solids , 1978 .

[6]  P. Podio-Guidugli.  A Primer in Elasticity , 2000 .

[7]  R. Kupferman,et al.  Elastic theory of unconstrained non-Euclidean plates , 2008, 0810.2411.

[8]  Jay D Humphrey,et al.  Growth and remodeling in a thick-walled artery model: effects of spatial variations in wall constituents , 2008, Biomechanics and modeling in mechanobiology.

[9]  A. McCulloch,et al.  Stress-dependent finite growth in soft elastic tissues. , 1994, Journal of biomechanics.

[10]  Marcelo Epstein,et al.  Thermomechanics of volumetric growth in uniform bodies , 2000 .

[11]  E. Sharon,et al.  The mechanics of non-Euclidean plates , 2010 .

[12]  Antonio DiCarlo,et al.  Growth and balance , 2002 .

[13]  Pasquale Ciarletta,et al.  Morphogenesis of thin hyperelastic plates: A constitutive theory of biological growth in the Föppl-von Kármán limit , 2009 .

[14]  Anders Klarbring,et al.  Residual stresses in soft tissue as a consequence of growth and remodeling: application to an arterial geometry , 2008 .

[15]  Luciano Teresi,et al.  The elastic metric: A review of elasticity with large distortions , 2013 .

[16]  P. G. Ciarlet,et al.  An Introduction to Differential Geometry with Applications to Elasticity , 2006 .

[17]  C. Davini.  Some remarks on the continuum theory of defects in solids , 2001 .

[18]  Peter Fratzl,et al.  Tensile and compressive stresses in tracheids are induced by swelling based on geometrical constraints of the wood cell , 2007, Planta.

[19]  D. Steigmann,et al.  On the Evolution of Plasticity and Incompatibility , 2007 .

[20]  L A Taber,et al.  Biomechanical growth laws for muscle tissue. , 1998, Journal of theoretical biology.