This work explores a continuum-mechanical model for a body simultaneously undergoing finite deformation and surface growth/resorption. This is accomplished by defining the kinematics as well as the set of material points that constitute the domain of a physical body at a given time in terms of an evolving reference configuration. The implications of spatial and temporal discretization are discussed, and an extension of the Arbitrary Lagrangian–Eulerian finite element method is proposed to enforce the resulting balance laws on the grown/resorbed body in two spatial dimensions. Representative numerical examples are presented to highlight the predictive capabilities of the model and the numerical properties of the proposed solution method.

这项工作探索了同时经历有限变形和表面生长/吸收的物体的连续介质力学模型。这是通过定义运动学以及根据不断变化的参考配置在给定时间构成物理体域的一组物质点来实现的。讨论了空间和时间离散化的影响，并提出了对任意拉格朗日-欧拉有限元方法的扩展，以在两个空间维度上对生长/吸收体执行由此产生的平衡定律。提供了具有代表性的数值示例，以突出模型的预测能力和所提出的求解方法的数值特性。