morphoelasticity

Morphoelasticity is a continuum mechanics framework for modeling growth and remodeling in biological tissues and other materials that undergo large deformations. Central to the theory is the multiplicative decomposition of the deformation gradient F into a growth part F_g and an elastic part F_e, such that F = F_e F_g. The growth tensor F_g captures local, inelastic changes in size and shape due to processes like proliferation, accretion, or structural remodeling, while F_e accounts for the elastic response needed to maintain compatibility with external loads and boundary conditions. Growth is often driven by biological signals or chemical potentials, and F_g can be anisotropic, reflecting directional growth.

Because F_g generally does not produce a configuration compatible with the current stresses and constraints, residual stresses arise, which are captured by the elastic deformation F_e and the associated strain energy density W(F_e). The governing equations combine kinematics, balance laws, and constitutive relations for the elastic response, with constitutive laws often derived from hyperelastic models. Growth laws specify the evolution of F_g in time, typically as a function of local stresses, chemical transport, or morphogen concentrations.

The theory is widely used to study morphogenesis in plants and animals, arterial remodeling, tumor growth, wound healing, and soft tissue mechanics. Historically, the multiplicative decomposition approach was popularized in biomechanics by Rodriguez, Hoger, and McCulloch (1994) and has since been extended by many researchers to include remodeling, anisotropic growth, and changing material properties. Computational methods include finite element implementations that solve for F_g and F_e subject to given boundary conditions.