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Surface growth in deformable solids using an Eulerian formulation

机译：使用欧拉配方的可变形固体的表面生长

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摘要

Growth occurs in a wide range of systems ranging from biological tissue to additive manufacturing. This work considers surface growth, in which mass is added to the boundary of a continuum body from the ambient medium or from within the body. In contrast to bulk growth in the interior, the description of surface growth requires the addition of new continuum particles to the body. This is challenging for standard continuum formulations for solids that are meant for situations with a fixed amount of material. Recent approaches to handle this have used, for instance, higher-dimensional time-evolving reference configurations.In this work, an Eulerian approach to this problem is formulated, enabling the side-stepping of the issue of constructing the reference configuration. However, this raises the complementary challenge of determining the stress response of the solid, which typically requires the deformation gradient that is not immediately available in the Eulerian formulation. To resolve this, the approach introduces additional kinematic descriptors, namely the relaxed zero-stress deformation and the elastic deformation; in contrast to the deformation gradient, these have the important advantage that they are not required to satisfy kinematic compatibility. The zero-stress deformation and the elastic deformation are used to eliminate the deformation gradient from the formulation, with the evolution of the elastic deformation shown to be governed by a transport equation. The resulting model has only the density, velocity, and elastic deformation as variables in the Eulerian setting. The proposed method is applied to simplified examples that demonstrate non-normal growth and growth with boundary tractions.The introduction in this formulation of the relaxed deformation and the elastic deformation provides a description of surface growth whereby the added material can bring in its own kinematic information. Loosely, the added material "brings in its own reference configuration" through the specification of the relaxed deformation and the elastic deformation. This kinematic description enables, e.g., modeling of non-normal growth using a standard normal growth velocity and a simple approach to prescribing boundary conditions.
机译：生长发生在从生物组织到添加剂制造的各种系统中。该工作考虑表面生长，其中质量从环境介质或身体内部添加到连续体的边界中。与内部的散装生长相反，表面生长的描述需要向身体添加新的连续颗粒。这对标准连续体配方具有挑战，该固体配方适用于具有固定数量材料的情况。例如，处理此操作的最新方法已经使用了更高维度的时间不断发展的参考配置。在此工作中，制定了对此问题的eulerian方法，使得侧踩到构建参考配置的问题。然而，这提高了确定固体应激响应的互补挑战，这通常需要在欧拉配方中不可用的变形梯度。为了解决这一点，该方法引入了额外的运动描述符，即放松的零应力变形和弹性变形;与变形梯度相比，这些具有重要的优点，即它们不需要满足运动兼容性。零应力变形和弹性变形用于消除制剂的变形梯度，随着弹性变形的演变而被认为由传送方程管辖。由此产生的模型仅具有密度，速度和弹性变形，作为欧拉仪中的变量。该方法应用于简化的实施例，其表现出非正常生长和具有边界诉讼的生长。在这种放松变形和弹性变形的这种制剂中引入提供了表面生长的描述，其中添加的材料可以引入其自身的运动信息。松散地，通过宽松变形和弹性变形的规格，添加的材料“以自己的参考配置引入”。这种运动学描述使得例如使用标准正常生长速度和规定边界条件的简单方法建模非正常生长。

著录项

  • 来源
    《Journal of the Mechanics and Physics of Solids》 |2021年第9期|104499.1-104499.13|共13页
  • 作者

    S. Kiana Naghibzadeh; Noel Walkington; Kaushik Dayal;

  • 作者单位

    Department of Civil and Environmental Engineering Carnegie Mellon University United States of America;

    Center for Nonlinear Analysis Department of Mathematical Sciences Carnegie Mellon University United States of America;

    Department of Civil and Environmental Engineering Carnegie Mellon University United States of America Center for Nonlinear Analysis Department of Mathematical Sciences Carnegie Mellon University United States of America Department of Materials Science and Engineering Carnegie Mellon University United States of America;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
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