AbstractSeveral types of tube-like fibre-reinforced tissue, including arteries and veins, different kinds of mu'/> On the preservation of fibre direction during axisymmetric hyperelastic mass-growth of a finite fibre-reinforced tube
  • 主题
高级搜索  >
历史搜索 清空历史
首页> 外文期刊>Journal of engineering mathematics >On the preservation of fibre direction during axisymmetric hyperelastic mass-growth of a finite fibre-reinforced tube
【24h】

On the preservation of fibre direction during axisymmetric hyperelastic mass-growth of a finite fibre-reinforced tube

机译：有限纤维增强轴对称超弹性质量增长过程中纤维方向的保持

获取原文
获取原文并翻译 | 示例
           
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

AbstractSeveral types of tube-like fibre-reinforced tissue, including arteries and veins, different kinds of muscles, biological tubes as well as plants and trees, grow in an axially symmetric manner that preserves their own shape as well as the direction and, hence, the shape of their embedded fibres. This study considers the general, three-dimensional, axisymmetric mass-growth pattern of a finite tube reinforced by a single family of fibres growing with and within the tube, and investigates the influence that the preservation of fibre direction exerts on relevant mathematical modelling, as well on the physical behaviour of the tube. Accordingly, complete sets of necessary conditions that enable such axisymmetric tube patterns to take place are initially developed, not only for fibres preserving a general direction, but also for all six particular cases in which fibres grow normal to either one or two of the cylindrical polar coordinate directions. The implied conditions are of kinematic character but independent of the constitutive behaviour of the growing tube material. Because they hold in addition to and simultaneously with standard kinematic relations and equilibrium equations, they describe growth by an overdetermined system of equations. In cases of hyperelastic mass-growth, the additional information they thus provide enables identification of specific classes of strain energy densities for growth that are admissible and, therefore, suitable for the implied type of axisymmetric tube mass-growth to take place. The presented analysis is applicable to many different particular cases of axisymmetric mass-growth of tube-like tissue, though admissible classes of relevant strain energy densities for growth are identified only for a few example applications. These consider and discuss cases of relevant hyperelastic mass-growth which (i) is of purely dilatational nature, (ii) combines dilatational and torsional deformation, (iii) enables preservation of shape and direction of helically growing fibres, as well as (iv) plane fibres growing on the cross section of an infinitely long fibre-reinforced tube. The analysis can be extended towards mass-growth modelling of tube-like tissue that contains two or more families of fibres. Potential combination of the outlined theoretical process with suitable data obtained from relevant experimental observations could lead to realistic forms of much sought strain energy functions for growth.
机译： Abstract 几种类型的管状纤维增强组织，包括动脉和静脉，不同种类的肌肉，生物管以及植物和树木以轴向对称的方式生长，从而保留了它们自己的形状以及其嵌入的纤维的方向和形状。这项研究考虑了由单个纤维家族随管子在管内生长而增强的有限管的一般，三维，轴对称质量增长模式，并研究了保持纤维方向对相关数学模型的影响，例如对管子的物理行为有很好的了解。因此，最初开发了使这种轴对称的管型发生的必要条件的整套集合，不仅对于保持总体方向的纤维，而且对于所有六种特定的情况（其中纤维垂直于一个或两个圆柱极增长）都已开发完成。协调方向。隐含条件具有运动学特性，但与生长的管材的本构行为无关。因为它们除了包含标准运动学关系和平衡方程式之外，还同时包含，因此它们通过超定方程组来描述增长。因此，在超弹性质量增长的情况下，它们提供的附加信息使得能够识别允许增长的特定类别的应变能密度，因此适合于隐含类型的轴对称管质量增长。提出的分析适用于管状组织轴对称质量增长的许多不同特殊情况，尽管仅在少数示例应用中确定了允许的相关应变能密度增长类别。这些考虑并讨论了相关的超弹性质量增长的情况，其中（i）具有纯粹的扩张性质，（ii）结合了扩张变形和扭转变形，（iii）能够保持螺旋状生长的纤维的形状和方向，以及（iv）平面纤维在无限长的纤维增强管的横截面上生长。该分析可以扩展到包含两个或多个纤维家族的管状组织的大量生长模型。概述的理论过程与从相关实验观察中获得的适当数据的潜在组合可能会导致许多形式的增长所需的应变能函数的现实形式。

著录项

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号