Validity of Eshelby-stress-driven growth laws for plant tissues

Determine whether growth laws that adopt the Eshelby stress tensor as the driving force can reproduce the basic properties and growth phenomenology of plant living matter within morphoelastic continuum formulations.

Background

In deriving thermodynamic constraints, the authors show that the Eshelby stress naturally appears as a candidate driving force for growth via the Coleman–Noll procedure. While such stress-based laws are common in other biological contexts, the authors question their suitability for plant tissues, where wall yielding and remodeling are often modeled as passive, plastic-like processes with complex anisotropies and thresholds.

They explicitly state uncertainty about whether simple Eshelby-stress-based growth laws can capture basic plant mechanical behaviors, prompting a targeted open question on the validity of such laws in plant morphomechanics.

References

Whether simple growth laws based on the Eshelby stress can reproduce basic properties of plant matter remains unclear to us.

— Hydromechanical field theory of plant morphogenesis  (2409.02775 - Oliveri et al., 2024) in Subsubsection "Growth law", Section "Constitutive laws"

This work advances quantitative stability in a controlled isotropic, matched-modulus setting, while broader questions involving general eigenstrains, mismatch, anisotropy, interfaces, multiple inclusions, and larger finite departures remain open.

— Quantitative Eshelby stability: local and finite-shape theory through AI-assisted mechanics  (2610.13400 - Ni, 9 Oct 2026) in Discussion, Section 3.3, subsection “From one problem to a mechanics problem map”