Evaluation of the parallel coupling constitutive model for biomaterials using a fully coupled network-matrix model

Area of Science:

• Composite Materials
• Biomechanics
• Materials Science

Background:

• Biological materials often consist of fiber networks in elastic matrices.
• The parallel coupling model is widely used to predict composite material properties.
• This model neglects interactions between network and matrix components.

Purpose of the Study:

• To evaluate the accuracy of the parallel coupling model for fiber-matrix composites.
• To assess the model's performance in both linear and non-linear deformation regimes.
• To propose corrections for improving the model's predictive accuracy.

Main Methods:

• Utilized explicit, fully coupled models to simulate composite behavior.
• Analyzed both linear (small strain) and non-linear (large deformation) responses.
• Investigated the influence of component stiffness ratios and matrix properties (e.g., Poisson ratio, auxeticity).

Main Results:

• The parallel model exhibits errors in the linear regime when stiffness ratios are between 0.1-10, particularly as the matrix approaches incompressibility.
• In the non-linear regime, the model underestimates stiffening, predicting a softer response than observed.
• A proposed correction improves accuracy in both linear and non-linear regimes, especially when the matrix is not near incompressible (Poisson ratio ≠ 0.5).

Conclusions:

• The parallel coupling model requires correction for accurate prediction of composite effective properties, particularly for biological materials.
• The proposed correction enhances accuracy across linear and non-linear deformation ranges.
• Auxetic matrix properties can lead to composites with a broad range of linear elastic response.