Inelastic surface growth

Inelastic surface growth associated with continuous creation of incompatibility on the boundary of an evolving body is behind a variety of natural and technological processes, including embryonic development and 3D printing. In this paper we extend the recently proposed stress-space-centered theory of surface growth (PRL 119, 048001, 2017) by shifting the focus towards growth induced strains. To illustrate the new development we present several analytically tractable examples.

[1]  Xavier Letartre,et al.  Spherical curves design for micro-origami using intrinsic stress relaxation , 2013 .

[2]  L. V. Nikitin,et al.  Finite strains of viscoelastic muscle tissue , 1987 .

[3]  Vyacheslav E. Naumov,et al.  Mechanics of Growing Deformable Solids: A Review , 1994 .

[4]  Panayiotis Papadopoulos,et al.  A continuum theory of surface growth , 2010, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[5]  Gerard A Ateshian,et al.  On the theory of reactive mixtures for modeling biological growth , 2007, Biomechanics and modeling in mechanobiology.

[6]  Giuseppe Tomassetti,et al.  Steady accretion of an elastic body on a hard spherical surface and the notion of a four-dimensional reference space , 2016, 1603.03648.

[7]  Xanthippi Markenscoff,et al.  Configurational balance laws for incompatibility in stress space , 2007, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[8]  E. Kuhl,et al.  A continuum model for remodeling in living structures , 2007 .

[9]  Davide Carlo Ambrosi,et al.  Stress-Modulated Growth , 2007 .

[10]  R Skalak,et al.  Kinematics of surface growth , 1997, Journal of mathematical biology.

[11]  A. Goriely.  The Mathematics and Mechanics of Biological Growth , 2017 .

[12]  Andrea Bacigalupo,et al.  Effects of Layered Accretion on the Mechanics of Masonry Structures , 2012 .

[13]  Gérard A. Maugin,et al.  Configurational Forces: Thermomechanics, Physics, Mathematics, and Numerics , 2010 .

[14]  Arash Yavari,et al.  A Geometric Theory of Growth Mechanics , 2009, J. Nonlinear Sci..

[15]  Alain Goriely,et al.  Growth and instability in elastic tissues , 2005 .

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

[17]  Arash Yavari,et al.  Nonlinear mechanics of surface growth for cylindrical and spherical elastic bodies , 2017 .

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

[19]  Basile Audoly,et al.  Elastic rods with incompatible strain: Macroscopic versus microscopic buckling , 2017 .

[20]  Giuseppe Zurlo,et al.  Printing Non-Euclidean Solids. , 2017, Physical review letters.

[21]  Luigi Preziosi,et al.  Mechanobiology of interfacial growth , 2013 .

[22]  S. Jonathan Chapman,et al.  Modeling Growth in Biological Materials , 2012, SIAM Rev..