A membrane model from implicit elasticity theory: application to visceral pleura

Area of Science:

• Biomechanics
• Materials Science
• Solid Mechanics

Background:

• Membranous materials exhibit complex mechanical responses.
• Existing models may not fully capture nonlinear and anisotropic behaviors.
• Thermodynamic principles offer a robust framework for material modeling.

Purpose of the Study:

• To derive a new constitutive model, the Fungean solid, for membranous materials.
• To incorporate thermodynamic internal energy functions into the material model.
• To validate the model against experimental data from biological membranes.

Main Methods:

• Developed a Fungean solid model based on isotropic response functions and thermodynamic internal energy.
• Utilized Biot's definitions for stress and strain, adapted by Fung's law.
• Parameterized the model using biaxial experimental data from porcine pleural membrane.

Main Results:

• The Fungean membrane model supports a hypothesized isotropic/deviatoric split in stress and strain-rate.
• Experimental data confirmed highly nonlinear but mechanically isotropic material response.
• The four-parameter model reasonably described the observed mechanical behavior.

Conclusions:

• The derived Fungean solid model provides a simplified yet effective framework for describing membranous material mechanics.
• The model's ability to capture nonlinear and isotropic characteristics is supported by experimental validation.
• This approach offers potential for improved modeling of soft biological tissues.