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Shape memory alloys (SMAs) are attracting materials in various science and engineering fields for the sake of interesting properties. These thermomechanical properties i.e. shape memory effect and pseudoelasticity are modelled here by macroscopic approach with the help of 5-th order polynomial dependence. A new prosthesis made of SMA is applied to connect ossicular chain in a middle ear. The middle ear is a small biomechanical system which consists of three ossicles: a malleus, an incus and a stapes. The ossicles form a conduction system to transmit sound from the external ear to the fluids of the inner ear. The middle ear reconstructed by means of shape memory prosthesis is modelled here as a nonlinear 2 degrees of freedom system because usually the incus is damaged and then the prosthesis connect the malleus with the stapes. In the medical practice a middle ear dysfunction happens very often. The ossicular chain can be partially destroyed by inflammatory diseases such as chronic otitis media or cholesteatoma. Then, an ossiculoplasty, that is reconstruction of the middle-ear ossicles is necessary to improve hearing.. Nowadays, a variety of middle ear prostheses are available but the choice of prosthesis type, its material and size is the main practical problem. Adjustment of a prosthesis to a specific anatomical condition in the middle ear is one of the main difficulties. Therefore, a new idea of shape memory prosthesis which can adjust its length is proposed and analyzed here.
Analytical solution of the proposed model is found with the help of the multiple times scales method. Next, a numerical study of biomechanical system is performed. The cubic nonlinearity is the most influential on the system dynamics in the first order approximation which is converged with numerical outcomes. Moreover, an impact phenomenon is analyzed numerically as a separate problem existing in the reconstructed middle ear. The results show different kind of solutions starting form regular ones, which are the most desirable, to chaotic ones.