Modeling and simulation of nonlinear electro-thermo-mechanical continua with application to shape memory polymeric medical devices

Abstract

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.The increase of life expectancy creates a need to maintain the functions of 2 aging organs to allow greater independence for the elderly. Biomaterial implants 3 have the potential to fulfill some of these functions. The total number of im-4 plants in the world exceeds four hundred million per year and grows every year 5 [1]. Biomaterials are also increasingly used for a large number of biomedical ap-6 plications such as the prevention and cure of coronary heart disease and stroke, 7 as well as ophthalmological applications, biosensors and drug delivery systems 8 [2, 3]. They have the potential to contribute to the reduction of the cost of 9 health and the improvment of the life conditions. 10 Among biomaterials, shape memory materials have gained considerable at-11 tention in the biomedical community thanks to their ability to change physical 12 properties (morphing, structural rigidity, refractive index, etc.) when subjected 13to external stimuli such as temperature, pH, humidity, electromagnetic fields, 14 etc. This special behavior results from the the shape memory effect observed 15 in shape memory materials [4]. They are used in minimally invasive surgery as 16 embolic devices to treat aneurysm [5, 6] and as vascular stents [7, 8, 9]. Fig-17 ure 1 illustrate the deployment of a stent in a blood vessel. They can also be 18 used as portable sensors to monitor heart and respiratory rates and in con-19 trolled drug delivery systems thus allowing to reduce the side effects of drugs 20 [11, 12]. For these different uses, biomaterials must possess a number of prop-21 erties. They must be biocompatible to avoid toxicity in contact with biological 22 tissues. Biodegradability is a desirable property for temporary implants, and 23 for minimally invasiv...

Constitutive Modeling of multi-stimuli-responsive shape memory polymers with multi-functional capabilities

“…Here, by adopting the Neo-Hookean model for the purely mechanical hyperelastic property of the material, and based on the research works done in [28,48,50,53,54], a version of the nominal Helmholtz free energy density function for transversely isotropic electro-magneto-hyperelastic materials by ignoring the matric-fiber interaction is considered as: (23) in which 𝐶 1 , 𝐶 3 , 𝐶 4 , 𝐶 6 and 𝐶 7 are materials constants. q is a positive non-dimensional parameter that measures the rapidly increasing stiffness of the fibers with increasing stretch [55], and 𝐸 ̅ is a positive material modulus that measures the degree of anisotropy.…”

“…Considering the open literature, there are a lot of constitutive models for thermally-induced SMPs under small and large strains [22]. For other types of SMPs (e.g., electro-magneto-responsive SMPs), however, there is only one model for electro-responsive SMPs [23]. Thermally-induced SMPs have some disadvantages.…”

“…In the field of electro-or magneto-responsive SMPs, there are some numerical and experimental research works which are briefly introduced here. For the first time, recently, a constitutive model for electro-responsive SMPs under large deformation was developed by Niyonzima et al [23]. They developed a 3D model employing a multiphysics coupling of thermal, electric, and mechanical phenomena and eventually discretized and solved it using a finite element approach, and finally implemented it for the application of stents.…”

Micro-Structure Modelling and Electrical Properties Analysis of PZT Matrix Ferroelectric Composites

“…Relying upon the destructive data acquisition methods cannot furbish simulations of the physical response that can be compared against experiments since the specific sample was destroyed during data acquisition on the microstructure itself. In recent years, the introduction of computational simulation techniques has reduced the computational cost and time of the procedure [10][11][12][13][14]. Differing from a physical experiment, the method provides simulation using random numbers to conduct many virtual experiments on a computer and then analyzes the results of these experiments on a statistical basis to draw conclusions.…”

Influence of elastic-viscoplastic behaviour on the filling efficiency of amorphous thermoplastic polymer during the micro hot embossing process

“…The proposed model better describes the anisotropic effects due to molecular ordering during plastic yielding for large strains and a wide temperature range. Niyonzima et al[21] developed a thermos-mechanical constitutive model coupled with an electromagnetic field to describe the large deformation of the shape memory polymers. The numerical simulation of the deployment of the polymer stent in a vein of an arm was successfully achieved with the finite element method.…”