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Nonconvex Model of Material Growth: Mathematical Theory

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Abstract

The model of volumetric material growth is introduced in the framework of finite elasticity. The new results obtained for the model are presented with complete proofs. The state variables include the deformations, temperature and the growth factor matrix function. The existence of global in time solutions for the quasistatic deformations boundary value problem coupled with the energy balance and the evolution of the growth factor is shown. The mathematical results can be applied to a wide class of growth models in mechanics and biology.

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Authors and Affiliations

  1. LEMTA, Nancy Universitè, 2, Avenue de la Forêt de Haye, BP 90161-54505, Vandoeuvre Cedex, France

    J. F. Ganghoffer

  2. Novosibirsk State University, Pirogova 2, 630090, Novosibirsk, Russia

    P. I. Plotnikov

  3. Lavrentyev Institute of Hydrodynamics SB RAS, Lavrentyev pr.15, 630090, Novisibirsk, Russia

    P. I. Plotnikov

  4. Institut Élie Cartan Nancy, UMR7502 (Université Lorraine, CNRS, INRIA), Laboratoire de Mathématiques, Université de Lorraine, B.P. 239, 54506, Vandoeuvre-lès-Nancy Cedex, France

    J. Sokolowski

  5. Systems Research Institute of the Polish Academy of Sciences, ul. Newelska 6, 01-447, Warsaw, Poland

    J. Sokolowski

Authors
  1. J. F. Ganghoffer
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  2. P. I. Plotnikov
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  3. J. Sokolowski
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Correspondence to P. I. Plotnikov.

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Communicated by G. Dal Maso

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Ganghoffer, J.F., Plotnikov, P.I. & Sokolowski, J. Nonconvex Model of Material Growth: Mathematical Theory. Arch Rational Mech Anal 230, 839–910 (2018). https://doi.org/10.1007/s00205-018-1259-8

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  • DOI: https://doi.org/10.1007/s00205-018-1259-8

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