Normal stress anisotropy and marginal stability in athermal elastic networks

Area of Science:

• Biophysics
• Materials Science
• Polymer Physics

Background:

• Hydrogels made of semiflexible biopolymers like collagen exhibit axial contraction under shear, deviating from typical elastic material behavior (axial dilation).
• This unique behavior is attributed to the porous, two-component nature of hydrogels, leading to time-dependent compressibility.
• The measured normal stress in rheometry depends on timescale, reflecting axial stress (σzz) at long times and the first normal stress difference (N1) at short times.

Purpose of the Study:

• To numerically investigate the normal stresses generated under shear in subisostatic, athermal semiflexible polymer networks.
• To understand deviations from affine deformation behavior in these anisotropic biopolymer networks.
• To identify the factors controlling anomalies in normal stress behavior.

Main Methods:

• Numerical simulations of subisostatic, athermal semiflexible polymer networks.
• Analysis of normal stress generation under shear deformation.
• Investigation of nonaffine deformation and its relation to network rigidity.

Main Results:

• Subisostatic semiflexible polymer networks exhibit significant deviations from affine deformation under shear.
• These anomalies in normal stress behavior are controlled by a rigidity transition.
• The study quantifies the relationship between strain and network rigidity in determining stress responses.

Conclusions:

• The complex normal stress behavior in biopolymer hydrogels under shear is not fully captured by models for isotropic viscoelastic materials.
• Nonaffine deformation and network rigidity play crucial roles in the observed axial contraction and stress anomalies.
• Understanding these strain-dependent transitions is key to predicting and controlling the mechanical properties of biopolymer networks.