A Coupled Multi-physics Analysis Model for Integrating Transient Electro-Magnetics and Structural Dynamic Fields with Damage
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The development of advanced material processing and the appearance of novel materials introduce a broad and promising area of multi-functional structures. The improvements of these structures over the traditional ones are the various capabilities to perform multiple tasks. Multi-physics phenomena, such as mechanical (ME) and electromagnetic (EM) coupling, are fundamental to study such structures. Some examples of these structures may be components of small unmanned airborne vehicles (UAVs), active skins of aircraft, or meta-materials for optical and communication systems. There is a need for a robust, coupled multi-physics computational model and codes supporting meaningful design of multi-functional structures and devices. In this dissertation, a generalized framework is developed for coupling EM and dynamic ME fields under finite deformation. To achieve a versatile and robust coupling scheme between fields, the problems are solved in a staggered way using a time-domain finite element (FE) method by a high performance parallel program. The deformation information from solved ME field is used to obtain the EM field in the same configuration. To account for finite deformation and its effects on the EM fields, a Lagrangian description is invoked for both ME field and EM field. Unlike traditional scheme to simulate EM field, the coupling scheme maps Maxwell’s equations from spatial to material coordinates in the reference configuration. For a efficient solution, a scalar potential and vector potentials are chosen as independent solution variables in lieu of EM field variables to reduce the degree of freedom. Non-uniqueness in the solution of the reduced set of equations is overcome through the introduction of a gauge condition in the FE formulations. The boundary conditions are appropriately represented in terms of the potentials that do not represent physical variables. A high performance, parallel code in FE method is developed to solve the multi- physics problems. The computational domain is decomposed and distributed to multiple processors using the ParMETIS library. Subsequently, the Portable, Extensible Toolkit for Scientific Computation or PETSc library, which is a Message Passing Interface (MPI) based library, is employed to accomplish the parallelization of the code for assembling and solving both the ME and the EM problems. Selected features of the code are validated using existing solutions in the literature, as well as comparison with results of simulations with commercial software. Convergence and accuracy of the code are examined. In view of functionality of different devices, two sets of multi-physics phenomena are studied thoroughly using the framework. The load-bearing antenna application requires the coupling between transient EM and dynamic ME fields. The simulations predict the evolution of electrical and magnetic fields and their fluxes in a vibrating substrate undergoing finite deformation. In this application, the Lorentz force generated in the coupling is negligible compared with the external applied mechanical load. Thus, the coupling is only one-way from the ME field to the EM fields. The effects of mechanical load frequency, amplitudes and direction on EM fields are investigated. Furthermore, a novel self-sensing piezoelectric sensor is introduced by implementing a three-dimensional isotropic damage model with piezoelectric material. In the contrast to the load-bearing antenna application, two-way coupling of electric field and ME field is necessary through piezoelectricity. The piezoelectric coupling is achieved in the reference configuration to accommodate the coupling under finite deformation. The damage criterion is established from the maximum deviatoric strain energy throughout the mechanical loading history. The degradation impacts on both mechanical stiffness and piezoelectric coupling constant. The damage developed in the structure can be predicted by the electric field generated from piezoelectricity. The difference of the electric field between damaged and undamaged structure is employed to correlate with the damage parameter and its time derivative. A rigorous functional form is proposed for the correlation function. The model is calibrated and validated by different simulation cases.