The mechanics of configurational forces and material evolution

识别和严格分析驱动材料演化过程的力(塑性、生物生长、老化、重塑、位错和空位的运动、裂纹扩展、相界的运动)是一个新的、非常活跃的研究领域的主题，通常被称为构造力力学。我在这一领域的活动总结在最近由Springer-Verlag出版的一本合著的专著中，导致人们认识到这些力与材料不均匀理论之间的相互联系。这一关系对于在不同尺度(从纳米尺度到宇宙学)模拟材料随时间变化的本构行为的全部影响仍有待于在重要的工程和生物医学应用中得到很好的理解和开发。我建议继续我在物质生长和重塑领域的既定工作，以及更广泛地说，管理物质行为的时间演变的定律。此外，建议通过纳入与同事和研究生合作进行的正在进行的研究中发展的最新结果来扩展这些想法，例如我们最近在分形体力学方面的工作、关于生长问题的全面热力学公式、应变梯度效应的包含以及对化学反应混合物理论的使用。在接下来的几年里，我们建议：(I)对这些公式进行数值实现；(Ii)与Walter Herzog教授(我们运动学学院)合作，在硬组织(骨)和软组织(软骨、肌肉)中进行原创实验，以评估我们模型的有效性并量化生长变量；(Iii)继续探索基于分形思想的材料模型的能力，不仅表示手头现象的几何形状(如血管)，而且定量表达潜在的物理规律(如分形弹性)。这项研究提案的潜在结果的意义超出了概述的直接应用范围。

The identification and rigorous analysis of the forces that drive processes of material evolution (plasticity, biological growth, aging, remodeling, motion of dislocations and vacancies, crack propagation, motion of phase boundaries) is the topic of a new and very active area of research generally known as the Mechanics of Configurational Forces. My activities in this field, summarized in a co-authored monograph recently published by Springer-Verlag, have led to the recognition of the interconnection between such forces and the theory of material inhomogeneity. The full implications of this relationship for the modeling of the time-dependent constitutive behaviour of materials at various scales (from the nano scale to the cosmological) are still to be well understood and exploited in important engineering and biomedical applications. I propose to continue my established work in the field of material growth and remodeling and, more generally, of the laws that govern the time-evolution of material behaviour. Moreover, it is proposed to extend these ideas by incorporating recent findings developed in ongoing research carried out in collaboration with colleagues and graduate students, such as our recent work on the Mechanics of Fractal Bodies, a fully fledged thermodynamical formulation of the problem of growth, inclusion of strain-gradient effects and the use of the theory of chemically reacting mixtures. During the next few years, we propose to: (i) carry out a numerical implementation of these formulations; (ii) in collaboration with Professor Walter Herzog (of our Faculty of Kinesiology), perform original experiments in both hard tissue (bone) and soft tissue (cartilage, muscle) to assess the validity of our models and to quantify the growth variables; (iii) continue exploring the ability of material models based on fractal ideas not only to represent the geometry of the phenomena at hand (such as vascularity), but to quantitatively express the underlying physical laws (such as fractal elasticity). The significance of the potential results of this research proposal extends beyond the immediate applications outlined.