Multi-phase, large-strain constitutive models of cartilage for finite element analyses in 3-D

Finite element (FE) modeling plays a well-established and increasingly significant role in analyses of articular cartilage at the organ, tissue, and cell scales: for example understanding the functional relationships among constituents, microstructure, and tissue function in diarthrodial joints. A constitutive model, the crux of an accurate FE model, formalizes the functional dependencies among physical variables (e.g., strain, stress, and energy), thereby providing the missing equations to close the system generated by the classical balance principals, while accounting for the specific behavior of cartilage. In the future, fully 3-D FE modeling of cartilage could provide clinical diagnostic tools for patient-specific analyses. Computational analyses of full, patient-specific knee joints under load, especially before and after surgical intervention, would facilitate: (1) investigating fundamental research questions, e.g., structure-function relationships, load support, and mechanobiological cellular stimuli; (2) assessing individual patients, e.g., assessing joint integrity, preventing damage, and prescribing therapies; and (3) advancing tissue engineering, i.e., building replacement materials for cartilage. Approaches to computational modeling generally aim to adopt the simplest possible formulation that can describe experimental data, yet the complexity of articular cartilage mechanics demands similarly complex models. This review discusses extant multi-phase, large-strain (i.e., finite-deformation) constitutive models for cartilage which have been implemented in 3-D nonlinear finite elements. These have paved the way toward 3-D patient-specific clinical tools and along with advances in the underlying continuum theories and computational methods provide the foundations of improved constitutive models for 3-D FE modeling of cartilage in the future.