Cyclic loading of a heterogeneous non-linear poroelastic material

Area of Science:

• Poroelasticity
• Soft Matter Physics
• Biomaterials Science

Background:

• Cyclic loading is prevalent in poroelastic systems.
• Material response is complex, influenced by boundary conditions, pore structure, and mechanical properties.
• Heterogeneity in poroelastic materials, common in biological tissues like tendons, complicates their behavior.

Purpose of the Study:

• To analyze the impact of continuous heterogeneity in stiffness or permeability on the cyclic loading response of soft porous materials.
• To develop a framework applicable to various poroelastic structures, motivated by diseased tendon properties.
• To differentiate the material's response to cyclic stress versus cyclic displacement when heterogeneity is present.

Main Methods:

• Development of a one-dimensional non-linear poroelastic model.
• Assumption of Darcy flow and neo-Hookean elasticity for the solid skeleton.
• Application of uniaxial cyclic stress or displacement at one boundary, with heterogeneity introduced via a Gaussian bump function.

Main Results:

• The response to applied stress differs qualitatively from the response to applied displacement.
• Local stiffness decrease (damage) increases strain under stress and perturbs flux under displacement.
• Proximity of damage to the loaded boundary increases sensitivity to heterogeneity.

Conclusions:

• Heterogeneity critically influences poroelastic response to cyclic loading.
• Distinguishing between stress- and displacement-driven loading is essential.
• The developed model provides a foundation for understanding heterogeneity effects in complex poroelastic systems.