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Modeling and simulation of nonlinear electro-thermo-mechanical continua with application to shape memory polymeric medical devices. (English) Zbl 1441.74077

Summary: Shape memory materials have gained considerable attention thanks to their ability to change physical properties when subjected to external stimuli such as temperature, pH, humidity, electromagnetic fields, etc. These materials are increasingly used for a large number of biomedical applications. For applications inside the human body, contactless control can be achieved by the addition of electric and/or magnetic particles that can react to electromagnetic fields, thus leading to a composite biomaterial. The difficulty of developing accurate numerical models for smart materials results from their multiscale nature and from the multiphysics coupling of involved phenomena. This coupling involves electromagnetic, thermal and mechanical problems. This paper contributes to the multiphysics modeling of a shape memory polymer material used as a medical stent. The stent is excited by electromagnetic fields produced by a coil which can be wrapped around a failing organ. In this paper we develop large deformation formulations for the coupled electro-thermo-mechanical problem using the electric potential to solve the electric problem. The formulations are then discretized and solved using the finite element method. Results are validated by comparison with results in the literature.

MSC:

74F15 Electromagnetic effects in solid mechanics
74S05 Finite element methods applied to problems in solid mechanics
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
74D10 Nonlinear constitutive equations for materials with memory

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References:

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