Mathematical Models in Mechanical and Biomedical Tribology with Computational Simulations/Optimization Methods

Surface damage, wear, corrosion, and erosion-corrosion in bioengineering artificial implants, interior, exterior, or partlially-interior/exterior biomedical devices causes significant operational bioengineering/biomechanical difficulties—the same phenomena that occurs classically in a large number of mechanical systems/machinery. Additionally, this kind of deterioration could also involve prostheses, temporary prostheses or orthopaedic supplies, surgical permanent devices, and even surgery theatre tools, causing a series of important associated functional difficulties. This usually happens during surgery and the post-operation stage. The consequences of this industrial-biomedical design complexity are extent, from re-operation, failure of medical devices, or post-surgical discomfort/pain to complete malfunction of the device or prostheses. In addition to all these hurdles, there are economic loss and waste of operation-surgical time, re-operations and manoeuvres carried out in modifications or repair. The wear is caused mainly by solid surfaces in contact, with important participation of the lubrication physiological/artificial conditions. Corrosion of protective coatings also constitute a number of significant mechanical and bioengineering difficulties. Mathematical modelling through optimization methods, initially mostly developed for industrial mechanical systems, overcome these engineering/bioengineering complications/difficulties, and reduce the experimental/tribotesting period in the rather expensive manufacturing process. In this contribution we provide a brief review of the current classified wear, erosion and/or corrosion mathematical models in developed for general mechanics, and based on our recent modelling international publications in tribology, as a introductory research. Subsequently the aim focus on specific tribology for biomedical applications and, additionally, a brief of optimization methods for precise modelling of given appliances with computational series, programming presentation, and numerical-software practical recipes. Results comprise an initial review of tribological/wear/erosion/corrosion models with further simulations, computational nonlinear optimization programming and graphical data/examples both in mechanical and biomechanical engineering. 3D computational imaging series are sharply shown with extent explanations.