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”.
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