Complexity in modeling of residual stresses and strains during polymerization of bone cement: Effects of conversion, constraint, heat transfer, and viscoelastic property changes

Aseptic loosening of cemented joint prostheses remains a significant concern in orthopedic biomaterials. One possible contributor to cement loosening is the development of porosity, residual stresses, and local fracture of the cement that may arise from the in-situ polymerization of the cement. In-situ polymerization of acrylic bone cement is a complex set of interacting processes that involve polymerization reactions, heat generation and transfer, full or partial mechanical constraint, evolution of conversion- and temperature- dependent viscoelastic material properties, and thermal and conversion-driven changes in the density of the cement. Interactions between heat transfer and polymerization can lead to polymerization fronts moving through the material. Density changes during polymerization can, in the presence of mechanical constraint, lead to the development of locally high residual strain energy and residual stresses. This study models the interactions during bone cement polymerization and determines how residual stresses develop in cement and incorporates temperature and conversion-dependent viscoelastic behavior. The results show that the presence of polymerization fronts in bone cement result in locally high residual strain energies. A novel heredity integral approach is presented to track residual stresses incorporating conversion and temperature dependent material properly changes. Finally, the relative contribution of thermal- and conversion-dependent strains to residual stresses is evaluated and it is found that the conversion-based strains are the major contributor to the overall behavior. This framework provides the basis for understanding the complex development of residual stresses and can be used as the basis for developing more complex models of cement behavior.