Morphogenesis of growing soft tissues.

Area of Science:

• Solid Mechanics
• Biophysics
• Materials Science

Background:

• Soft tissues exhibit growth, a complex phenomenon studied across biology, chemistry, and physics.
• Existing models attempt to capture tissue growth behavior.
• Finite elasticity provides a theoretical framework for understanding large deformations.

Purpose of the Study:

• To derive and analyze equations for thin elastic objects undergoing finite growth.
• To explore the consequences of Rodriguez's hypothesis on multiplicative decomposition of deformation.
• To investigate the application of the proposed growth model to hyperelastic materials.

Main Methods:

• Utilized the theory of finite elasticity.
• Postulated a multiplicative decomposition of the geometric deformation gradient into growth and elastic parts.
• Derived equations for thin elastic objects under finite growth, leading to a Föppl-von Kármán type model under specific scaling assumptions.

Main Results:

• Developed a theoretical framework for modeling finite growth in elastic bodies.
• Showed that under specific growth rate assumptions, the model aligns with the Föppl-von Kármán equations.
• Illustrated the model's application by analyzing the circumferential growth of a free hyperelastic disk.

Conclusions:

• The multiplicative decomposition of deformation provides a viable approach to modeling soft tissue growth.
• The derived Föppl-von Kármán type model offers insights into the mechanics of growing thin elastic structures.
• The study successfully demonstrates the model's utility in analyzing specific growth scenarios, such as in hyperelastic disks.