  The mechanism by which cells measure the dimension of the organ in which they
are embedded, and slow down their growth when the final size is reached, is a
long-standing problem of developmental biology. The role of mechanics in this
feedback is considered important. Morphoelasticity is a standard continuum
framework for modeling growing elastic tissues. However, in this theory, in the
absence of additional variables, the feedback between growth and mechanical
stress leads to either a collapse or unbounded growth of the tissue, but
usually prohibits reaching a finite asymptotic size ('size control'). In this
article, we modify this classical setting to include an energetic cost
associated with growth, leading to the physical effect of size control. The
present model simultaneously provides a qualitatively correct residual stress
profile and has a naturally emerging necrotic core, all of which have
previously been experimentally established in multicellular spheroids. This is
achieved through a local feedback mechanism derived from a thermodynamical
framework. The model delivers testable predictions for experimental systems and
could be a step towards the understanding of the role of mechanics in the
multifaceted question of how growing organs attain their final size.
