Continuum Model of the Biological Tissue

Abstract

The connection between the geometrical and statical quantities studied in the previous chapters must be complemented by equations establishing relationships among the stresses and deformations, their rates, temperature and structural changes of constructive materials, e.g. the tissue that forms the wall of a biological shell. The complete theoretical formulation is best achieved with application of the principles of thermodynamics supported by extensive experimentation, including in-plane and complex loading testing. The advantage of such approach is that it employs generalized quantities like entropy, free energy, Gibb’s potential, as fundamental descriptors. Specific problems are encountered due to discrete morphological structure of the biological tissue and the continuum scale, which is typically ~1 μm. For example, because of existing anisotropy, multidimensional strain data from the uniaxial experiments are not enough to extrapolate to the fully three-dimensional constitutive equations. Further, small specimen sizes, tethering effects, heterogeneity of deformation, difficulty in maintaining constant force distribution along specimen edges, make experiments on soft tissues very difficult. Also being heterogeneous, anisotropic, non-linear, viscoelastic, incompressible composites, soft biomaterials defy simple material models. Accounting for these particulars in constitutive models and both experimental evaluations remains a great challenge.

Everything is theoretically impossible, until it is done.

Robert A. Heinlein