Modelling of residually stressed materials with application to AAA.

Area of Science:

• Biomechanics
• Computational mechanics
• Materials science

Background:

• Residual stresses arise from growth and adaptation in living tissues, influencing their mechanical properties.
• Accurate modeling of tissue mechanics requires incorporating residual stresses into constitutive equations.
• Understanding residual stress is crucial for analyzing the behavior of biological structures like blood vessels.

Purpose of the Study:

• To present a general elastic constitutive formulation that accounts for residual stress.
• To define the necessary tensors for a nonlinear, three-dimensional finite element implementation.
• To apply the developed theory and implementation to assess wall stress distribution in abdominal aortic aneurysms (AAAs).

Main Methods:

• Development of a general constitutive elastic formulation including residual stress.
• Specification of tensors for 3D nonlinear finite element analysis.
• Application to patient-specific abdominal aortic aneurysm geometry and anisotropic material properties (collagen fiber orientation).

Main Results:

• A validated framework for incorporating residual stresses into tissue mechanics modeling.
• Evaluation of wall stress distribution in an abdominal aortic aneurysm using patient-specific data.
• Demonstration of the anisotropic nature of aortic tissue influencing stress distribution.

Conclusions:

• The presented general elastic constitutive formulation and finite element implementation effectively model residually stressed biological tissues.
• The method provides a robust tool for analyzing stress distributions in patient-specific abdominal aortic aneurysms.
• This approach is adaptable for investigating other residually stressed biological systems by defining appropriate energy functions.