![]() III/3 (Springer,Berlin-Heidelberg-New York) 196 and Noll W., in The non-Linear Field Theories of Mechanics, Handbuch der Physik, edited by Flügge s., Vol. ![]() III/3 (Springer, Berlin-Heidelberg-New York) 1960. Handbuch der Physik, edited by Flügge S., Vol. and Toupin R., in The Classical Field Theories. I., A Course of Higher Mathematics: Integral Equations and Partial Differential Equations (Pergamon Press, Oxford, London) 1964. W., Non-linear Theory of Elasticity (Dover, New York) 1997. M., Theory of Elasticity (Pergamon Press, Oxford, London, Paris) 1960. ![]() A., Material Inhomogeneities in Elasticity (Chapman & Hall/CRC, CRC Press Company, London, New York) 1993. Liu I-Shih, Continuum Mechanics (Springer, Berlin-Heidelberg-New York) 2002. M., Mechanics (Pergamon Press, Oxford, London, Paris). Lanczos C., The Variational Principles of Mechanics, 4th edition (Dover Publications Inc., New York) 1970. C., Mechanics of Continua (John Wiley & Sons, Inc:, New York) 1980. R., Mathematical Foundations of Elasticity (Dover Publications Inc., New York) 1983.Įringen A. After determining field equations, exploiting the constitutive framework, and discussing possible alternatives to the constitutive framework adopted in this review, we tackle the interaction between growth and transport phenomena by proposing an asymptotic analysis of the upscaled field equations based on the existence of various characteristic time-scales and the introduction of the Green’s function formalism. To this end, we regard biological systems as porous media, and, through the adaptation of the theory of upscaling to our purposes, we try to formulate a macroscopic thermomechanic description of growth from pore scale considerations. On this basis, and with the aid of mixture theory, we extend our description of growth to multiphasic systems. For our purposes, we start with a brief overview of the general formalism of continuum physics for monophasic bodies, which is necessary for establishing a continuum thermomechanic treatment of growth, and we discuss a possible interpretation of growth in terms of symmetry breaking and their dynamical restoration. In particular, we shall focus on biological growth as a representative element of this class. Our main concern is framing the issue of transport of chemical substances in living systems, and studying their interaction with a class of phenomena that involve several scales of observation. We report on some peculiar aspects of transport phenomena in living systems, discuss the theoretical framework on which their mathematical treatment has been developed, and summarise some results that have been recently pointed out.
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