Surface Growth in Deformable Solids using an Eulerian Formulation
Surface Growth in Deformable Solids using an Eulerian Formulation
复制标题
使用欧拉公式在可变形固体中进行表面生长
DOI：
10.1016/j.jmps.2021.104499
复制
发表时间：
2021
影响因子：
5.3
通讯作者：
Dayal, Kaushik
中科院分区：
文献类型：
--
作者：
Naghibzadeh, Kiana;Walkington, Noel;Dayal, Kaushik
生长发生在从生物组织到增材制造的广泛系统中。这项工作考虑了表面生长，其中质量从周围介质或从体内添加到连续体的边界。与内部的体生长相反，对表面生长的描述需要在体中加入新的连续体粒子。这对于用于具有固定量材料的情况的固体的标准连续体制剂是具有挑战性的。最近的方法来处理这个问题，例如，使用高维时间演变的参考configurations.In这项工作中，欧拉方法来解决这个问题，使侧步的问题，构建的参考配置。然而，这提出了确定固体的应力响应的补充挑战，这通常需要在欧拉公式中不能立即获得的变形梯度。为了解决这个问题，该方法引入了额外的运动学描述符，即松弛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学相容性。零应力变形和弹性变形被用来消除从配方中的变形梯度，与弹性变形的演变所示的输运方程。结果模型只有密度，速度和弹性变形作为欧拉设置中的变量。所提出的方法被应用到简化的例子，演示非正常的增长和增长与边界tractions.The松弛变形和弹性变形在此配方的介绍提供了一个描述的表面生长，从而添加的材料可以带来自己的运动学信息。不严格地说，添加的材料通过规定松弛变形和弹性变形“引入其自身的参考构型”。这种运动学描述使得，例如，使用标准的正常增长速度和一个简单的方法来规定边界条件的非正常增长建模。
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.
登录
查看更多内容
肌动蛋白网络的表面生长
DOI：
--
发表时间：
2010
期刊：
影响因子：
--
作者：
P. Papadopoulos;N. Hodge
通讯作者：
N. Hodge
影响因子：
2.7
作者：
Drozdov, AD
通讯作者：
Drozdov, AD
表面生长的力学和热力学被视为移动不连续性
影响因子：
2.4
作者：
J. Ganghoffer
通讯作者：
J. Ganghoffer
影响因子：
5.3
作者：
Agrawal, Vaibhav;Dayal, Kaushik
通讯作者：
Dayal, Kaushik
打印非欧几里得实体。
影响因子：
8.6
作者：
G. Zurlo;L. Truskinovsky
通讯作者：
L. Truskinovsky