STRUCTURAL INTERFACES IN SOLID MECHANICS: A VIEW TO APPLICATIONS IN BIOLOGICAL SYSTEMS Davide Bigoni*, Alexander B. Movchan**, Massimiliano Gei* *Dipartimento di Ingegneria Meccanica e Strutturale, Università di Trento, via Mesiano 77, I-38050 Trento, Italy bigoni@ing.unitn.it, mgei@ing.unitn.it **Department of Mechanical Sciences, University of Liverpool, Liverpool L69 3BX, U.K. abm@maths.liv.ac.uk ABSTRACT The concept of structural interface is introduced focussing on potential applications in the field of bioengineering. In particular, some structural interfaces in biological systems are identified, with emphasis on the periodontal ligament in the tooth-bone system and the articular cartilage in diarthrodial joints. Speculations on possible applications in the modelling of receptor-ligand binding between proteins close the paper. INTRODUCTION The connexion between two solid bodies usually consist in a thin, deformable layer of peculiar mechanical characteristics. In particulate composite materials, for instance, a thin interphase often joints the inclusions to the matrix. In biological systems, the periodontal ligament and the articular cartilage represent examples of thin layers connecting bones. In contact mechanics, an interfacial layer separates the two bodies in contact. In all these cases, compared to the connected solids, the interfacial layer: • has small dimension, • suffers large strains, • is characterized by a strongly nonlinear behaviour. A trivial way to model the above systems is to treat the interface layer as a third body, characterized by nonlinear constitutive laws and subject to large strains. A numerical treatment of this problem is straightforward on one hand -in the sense that it can be pursued in principle with any commercial f.e. code- but highly unsatisfactory on the other. Several difficulties result in fact hidden in this approach. First, a fine, three dimensional mesh is required to model the interface layer, yielding an unnecessary dense mesh in the connected bodies. Second, a large strain formulation of all the system is required, even in the common case in which the solids connected are subject to small strains. Third, f.e. techniques are known to become inaccurate where stress concentrations may arise, and these may occur at the interface. A classical remedy to these inconveniences is represented by the concept of imperfect interface. Following this approach, the thickness of the interface layer is condensed to zero, but instead of the usual transmission conditions across the interface [[σ]] n = 0, u = 0, (1)