Mechanistic constitutive law for plant cell wall growth

Develop a mechanistic constitutive law for growth within the proposed poromorphoelastic framework by specifying the rate-of-growth tensor L_G for plant cell walls in terms of explicit mechanical drivers and material parameters; determine which specific mechanical quantity (for example, Eshelby stress or strain measures) should serve as the driver of growth; and ascertain whether such a growth law can be derived from rational mechanics principles rather than phenomenological assumptions.

Background

The paper introduces a hydromechanical field theory for plant morphogenesis that couples tissue mechanics with water transport in a poromorphoelastic framework. While it presents a strain-based growth law to capture observed phenomenology, the authors emphasize that a foundational, mechanistically grounded growth law is needed to link macroscopic tissue behavior to underlying physical drivers.

They note that, despite the utility of strain-based approaches, it is not fully established which mechanical quantity should drive growth at the continuum level, nor whether such a law can be derived rigorously from rational mechanics. The resolution of this issue is central to building predictive, physically grounded models of plant morphogenesis.