A theory of growth is developed, utilizing the notion of a directional density function that captures the number and distribution of the material particles and their changes in time. A spatial (or Eulerian) description of kinematics is adopted, and the constitutive theory for a growing body is developed that relates the stress to the directional density function. The equation that governs the evolution of the directional density function is derived. An example of internal surface growth is presented.

中文翻译：

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增长的机械理论

利用定向密度函数的概念发展了生长理论，该函数捕获材料颗粒的数量和分布及其随时间的变化。采用运动学的空间（或欧拉）描述，并发展了生长体的本构理论，将应力与方向密度函数联系起来。导出了控制方向密度函数演化的方程。给出了内表面生长的示例。