An a posteriori approach to the mechanics of volumetric growth

This work focuses on the study of volumetric growth, i.e., the branch of biomechanics that investigates the variation of mass of biological systems, modeled as continuous media. Our purpose is to analyze in detail a perspective of growth, taken from the literature, that follows the paradigm of analytical mechanics. The analysis unfolds through (i) the introduction of suitable structural kinematic descriptors associated with growth; (ii) the identification of generalized forces dual to the virtual variations of such descriptors; (iii) the formulation of the principle of virtual work; and (iv) the establishment of a constitutive framework capable of capturing the phenomenology of interest. Within this setting, we determine the growth law of the problem at hand as a consequence of the dynamics of its structural descriptors. Accordingly, we term the growth law obtained this way the “a posteriori growth law”, and we call the resulting overall approach the “a posteriori approach”.