Understanding Shape and Residual Stress Dynamics in Rod-Like Plant Organs

Residual stresses are common in rod-like plant organs such as roots and shoots, arising from mechanical incompatibilities between tissues with differing intrinsic lengths. Although mechanical regulation of cell wall growth is well established, the role of internally generated stresses in organ-scale morphogenesis remains poorly understood. Here, we introduce a tractable theoretical framework that couples structural residual stresses to growth-driven shape dynamics. We represent rod-like organs as bundles of morphoelastic rods connected in parallel, each corresponding to a distinct concentric tissue layer. Assuming elastic strain-driven growth and rod-like symmetry, the resulting mechanical constraints yield transparent analytical relationships linking tissue heterogeneity to macroscopic observables such as axial strain rates, bending dynamics, and residual stress distributions. Using a minimal two-layer model representing the epidermis and inner tissues, we show how tissue incompatibilities can generate phenomena including effective autotropism, mechanical memory, and discontinuous growth dynamics following cell division. Overall, our framework demonstrates how residual stresses may contribute to plant morphogenesis and provides a foundation for future investigations of mechano-chemical growth control in plants.