On a new model for inhomogeneous volume growth of elastic bodies.
On a new model for inhomogeneous volume growth of elastic bodies.
复制标题
弹性体非均匀体积增长的新模型
DOI：
10.1016/j.jmbbm.2013.01.027
复制
发表时间：
2014
影响因子：
3.9
通讯作者：
Bolea Albero A.
中科院分区：
文献类型：
--
作者：
Böl M;Bolea Albero A.
一般来说，生长的特点是材料的尺寸随着质量的增加而增加。在依赖于主要边界条件的情况下，生长以不同的、往往是复杂的方式发生。然而，在本文中，我们的目标是开发一种模型，用于生物系统以非均匀方式生长，从而即使在生长速率和材料特性均匀时也会产生残余应力。因此，一个描述性的例子可以是一个具有均匀的、各向同性的材料特性的物体，它生长在一个屏障上。当它与障壁接触时，发生不均匀生长。如果在这种情况下，屏障被移除，某些类型的身体保持新的形状主要是固定的。作为提出的现象学方法的一个关键思想，我们努力将有限塑性理论应用于基尔霍夫应力张量的等时程部分，以及允许新生长材料塑性变化的附加条件。这使我们能够描述具有流体样生长特性的弹性体。突出的例子是肿瘤，其特有的宏观机械生长行为可以根据细胞的论点来解释。最后，所提出的框架被嵌入到有限元环境中，这使我们能够用代表性的数值例子来结束这项研究。
In general, growth characterises the process by which a material increases in size by the addition of mass. In dependence on the prevailing boundary conditions growth occurs in different, often complex ways. However, in this paper we aim to develop a model for biological systems growing in an inhomogeneous manner thereby generating residual stresses even when growth rates and material properties are homogeneous. Consequently, a descriptive example could be a body featuring homogeneous, isotropic material characteristics that grows against a barrier. At the moment when it contacts the barrier inhomogeneous growth takes place. If thereupon the barrier is removed, some types of bodies keep the new shape mainly fixed. As a key idea of the proposed phenomenological approach, we effort the theory of finite plasticity applied to the isochoric part of the Kirchhoff stress tensor as well as an additional condition allowing for plastic changes in the new grown material, only. This allows us to describeelastic bodies with a fluid-like growth characteristic. Prominent examples are tumours where the characteristic macro mechanical growth behaviour can be explained based on cellular arguments. Finally, the proposed framework is embedded into the finite element context which allows us to close this study with representative numerical examples.