A Review of the Combination of Experimental Measurements and Fibril-Reinforced Modeling for Investigation of Articular Cartilage and Chondrocyte Response to Loading

Table 1

Development of fibril-reinforced biphasic biomechanical models of articular cartilage.

Material model	Total stress	Primary material parameters	References
Fibril-reinforced poroelastic	𝝈𝑡=𝝈𝑛𝑓+𝝈𝑓−𝑝𝐈	𝐸𝑓, 𝐸𝑛𝑓, 𝜈𝑛𝑓, 𝑘	[7, 119, 131]
Fibril-reinforced poroviscoelastic	𝝈𝑡=𝝈𝑛𝑓+𝝈𝑓−𝑝𝐈	𝐸^0𝑓, 𝐸^𝜀𝑓, 𝜂, 𝐸𝑛𝑓, 𝜈𝑛𝑓, 𝑘	[17, 18]
Fibril-reinforced poroviscoelastic swelling	𝝈𝑡=𝝈𝑛𝑓+𝝈𝑓−Δ𝜋𝐈−𝜇𝑓𝐈	𝐸^0𝑓, 𝐸^𝜀𝑓, 𝜂, 𝐸𝑛𝑓, 𝜈𝑛𝑓, 𝑘, 𝑐𝐹	[12]

𝝈_𝑡: total stress; 𝝈_𝑛𝑓: stress of the nonfibrillar matrix; 𝝈_𝑓: stress of the fibrillar matrix; 𝑝: fluid pressure; 𝐈: unit tensor; Δ𝜋: osmotic pressure gradient; 𝜇_𝑓: chemical potential of fluid.