The mechanics of configurational forces and material evolution

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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.