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，相界运动）是一个新的和非常活跃的研究领域的主题，通常被称为摩擦力力学。我在这一领域的活动，总结在一个共同撰写的专著最近出版的Springer-Verlag，已导致认识到这种力量之间的相互联系和理论的材料不均匀性。在各种尺度（从纳米尺度到宇宙尺度）的材料随时间变化的本构行为的建模，这种关系的全部含义仍然是要很好地理解和利用重要的工程和生物医学应用。我打算继续我在材料生长和重塑领域的既定工作，更一般地说，是关于材料行为随时间演变的规律。此外，它建议扩展这些想法，将最近的研究结果开发正在进行的研究中进行的合作与同事和研究生，如我们最近的工作分形体的力学，一个完全成熟的数学公式的问题的增长，包括应变梯度效应和使用的化学反应混合物的理论。在接下来的几年里，我们建议：（i）进行这些公式的数值实现;（ii）与Walter Herzog教授合作（我们的运动机能学学院），在硬组织（骨）和软组织中进行原创实验（软骨，肌肉），以评估我们的模型的有效性和量化的增长变量; ㈢继续探索基于分形思想的物质模型的能力，使其不仅能够代表现有现象的几何形状（如血管分布），而且能够定量地表达基本的物理定律（如分形弹性）。这项研究提案的潜在结果的意义超出了所概述的直接应用。

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.