A formal derivation of a continuous model from an individual-based description of mechanical interactions between two contiguous cell populations with different proliferative and mechanical characteristics leads to a free-boundary problem for the cell densities. The well-posedness results and the construction of travelling-wave solutions for the one-dimensional free-boundary problem with nonlinear transmission conditions are presented, and numerical simulations illustrate the consistency between the individual-based model and the corresponding free-boundary formulation.
To model the stress-based growth of plant tissues at the cellular level, a multiplicative decomposition of the deformation gradient into elastic and growth components is employed, and homogenization techniques are applied to derive the associated macroscopic equations. Numerical solutions for the macroscopic model highlight the impact of microscopic structure and tissue heterogeneity on deformation and growth.