Kinematics of surface growth
Kinematics of surface growth
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DOI：
10.1007/s002850050081
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发表时间：
1997-09
影响因子：
1.9
通讯作者：
R. Skalak;D. A. Farrow;A. Hoger
中科院分区：
文献类型：
--
作者：
R. Skalak;D. A. Farrow;A. Hoger
本文建立了描述固定生长面和移动生长面情况的一般数学框架。该公式具有Skalak（1981）提出的数学结构，但在本文中进行了扩展，包括对可能的奇点、不相容、残余应力和移动生长面的讨论。此外，还提出了从生长表面上的生长速度分布计算结构的最终形式所必需的一般理论方程，并在若干实例中加以应用。结果表明，虽然假设生长总是在与当前生长表面垂直的方向上生长通常是足够的，但在某些方面，与生长表面成一定角度的生长可能更充分地代表生物现实。从理论的观点来看，在某些情况下，为了避免在生长速度场中假定奇点，必须与生长面成一定角度生长。开发了在固定和移动表面上生长的例子，以模拟角、贝壳、鹿角、牙齿和类似生物结构的产生。
In this paper a general mathematical framework is developed to describe cases of fixed and moving growth surfaces. This formulation has the mathematical structure suggested by Skalak (1981), but is extended herein to include discussion of possible singularities, incompatibilities, residual stresses and moving growth surfaces. Further, the general theoretical equations necessary for the computation of the final form of a structure from the distribution of growth velocities on a growth surface are presented and applied in a number of examples. It is shown that although assuming growth is always in a direction normal to the current growth surface is generally sufficient, growth at an angle to the growth surface may represent the biological reality more fully in some respects. From a theoretical viewpoint, growth at an angle to a growth surface is necessary in some situations to avoid postulating singularities in the growth velocity field. Examples of growth on fixed and moving surfaces are developed to simulate the generation of horns, seashells, antlers, teeth and similar biological structures.