A linearized and incompressible constitutive model for arteries

Area of Science:

• Biomechanics
• Materials Science
• Biomedical Engineering

Background:

• Blood vessels are often modeled as pseudoelastic, orthotropic, and incompressible materials in biomechanical studies.
• Describing arterial constitutive behavior requires a minimal set of elastic constants.

Purpose of the Study:

• To develop a constitutive model for pseudoelastic, incompressible, orthotropic arterial materials using a generalized Hooke's law and a novel logarithmic-exponential strain.
• To reduce the number of independent elastic constants required for modeling arterial tissue.
• To analyze and interpret model parameters under the incompressibility constraint.

Main Methods:

• Adoption of a generalized Hooke's law for co-rotational Cauchy stress.
• Utilization of a recently proposed logarithmic-exponential strain tensor that accounts for material nonlinearity and zero trace for volume-preserving deformations.
• Fitting the developed model to experimental data from porcine coronary arteries using inflation-stretch tests.

Main Results:

• The number of independent elastic constants for the orthotropic model was reduced from ten to seven.
• The logarithmic-exponential strain tensor simplifies the analysis of incompressibility constraints.
• Four parameters (material nonlinearity 'n', and Young's moduli E₁, E₂, E₃ in circumferential, axial, and radial directions, respectively) were sufficient to fit the experimental data.

Conclusions:

• The proposed constitutive model offers a simplified yet accurate representation of arterial biomechanics.
• The model effectively captures material nonlinearity and incompressibility in blood vessels.
• Further discussion on the model's advantages and limitations is provided.