Nonlinear elasticity of cross-linked networks

Area of Science:

• Biophysics
• Materials Science
• Cell Biology

Background:

• Cross-linked semiflexible polymer networks are crucial in cellular structures, e.g., actin networks for cell motility and spectrin networks for erythrocyte integrity.
• Understanding the mechanical properties of these networks is essential for comprehending cellular functions.

Purpose of the Study:

• To introduce a mechanical network model for semiflexible polymers at the mesh size scale.
• To derive a continuous constitutive law for stress-deformation relationships.
• To analyze the nonlinear mechanical properties and behavior of these networks.

Main Methods:

• Development of a simple mechanical network model at the mesh size scale.
• Derivation of a continuous constitutive law relating stress to deformation.
• Comparison of model predictions with experimental data for semiflexible polymer networks.

Main Results:

• The derived constitutive law is generically nonlinear, even for linear microscopic laws.
• Nonlinear bulk properties, including stiffening and negative normal stress under shear, match experimental data.
• Observed strain localization under uniaxial compression and a hierarchy of constitutive laws based on nonlinearity.

Conclusions:

• The model accurately describes the nonlinear mechanical behavior of semiflexible polymer networks.
• Provides a theoretical framework for continuum descriptions of networks like actin and spectrin in complex geometries.
• Facilitates coupling with growth problems, relevant for modeling cellular processes like actin-driven motility.