The current paper establishes an axisymmetric model for an inductive heating process. Therein, the fully coupled MAXWELL equations, assuming a temperature dependent permeability, are combined with the non-linear heat conduction equation to yield a monolithic solution strategy. The latter is based on a consistent linearization together with a higher order finite element discretization using GALERKIN'S method in space. For the temporal discretization, the generalized Newmark-? methods, higher order RUNGE-KUTTA methods, and discontinuous and continuous GALERKIN methods are used. Furthermore, the residual error is introduced to open an alternative way to obtain a numerically efficient estimation of the time integration accuracy. Simulation results of the electric, magnetic and thermal fields are provided, together with parameter studies concerning spatial discretization, frequency dependence and penetration depth of the heating zone. Another topic analyzed is the residual error and its estimation quality regarding polynomial degree and time step size. A further aspect of this work is the investigation of the thermal fluid-structure interaction with respect to functionally graded materials. Different coupling strategies for the acceleration of the fixed-point iteration in each time step is in the foreground. Relaxation methods as well as extrapolation methods make it possible to significantly reduce the number of fixed point iterations. At the same time, an adaptive strategy with higher order RUNGE-KUTTA methods can provide a further advantage in combination with acceleration methods.

The present thesis investigates the usage of higher order accurate time integrators together with appropriate error estimators for small and finite dynamic (visco)plasticity. Therefore, a general (visco)plastic problem is defined which serves as a basis to create closed-form solution strategies. A classical access towards small and finite (visco)plasticity is integrated into this concept. This approach is based on the idea, that the balance of linear momentum is formulated in a weak sense and the material laws are included indirectly. Thus, separate time discretizations are implemented and an appropriate coupling between them is necessary. Limitations for the usage of time integrators are the consequence. In contrast, an alternative multifield formulation is derived, adapting the principle of Jourdain. The idea is to assume that the balance of energy - taking into account a pseudopotential representing dissipative effects – resembles a rate-type functional, whose stationarity condition leads to the equations describing small or finite dynamic (visco)plasticity. Accordingly, the material laws and the balance of linear momentum can be solved on the same level and only one single time discretization has to be performed. A greater freedom in the choice of time integrators is obtained and the application of higher order accurate schemes - such as Newmark’s method, fully implicit as well as diagonally implicit Runge-Kutta schemes, and continuous as well as discontinuous Galerkin methods - is facilitated. An analysis and a comparison of the classical and the multifield formulation is accomplished by means of distinct examples. In this context, a dynamic benchmark problem is developed, which allows to focus on the effect of different time integrators. For this investigation, a variety of time discretization error estimators are formulated, evaluated, and compared.

Special topic volume with invited peer-reviewed papers only

Selected peer-reviewed extended articles based on abstracts presented at the 7th International Conference on Recent Advances in Materials, Minerals and Environment (RAMM2022) Aggregated Book

Smart Materials in Additive Manufacturing, Volume 2 covers the mechanics, modeling, and applications of the technology and the materials produced by it. It approaches the topic from an engineering design perspective with cutting-edge modeling techniques and real-world applications and case studies highlighted throughout. The book demonstrates 4D printing techniques for electro-induced shape memory polymers, pneumatic soft actuators, textiles, and more. Modeling techniques with ABAQUS and machine learning are outlined, as are manufacturing techniques for highly elastic skin, tunable RF and wireless structures and modules, and 4D printed structures with tunable mechanical properties. Closed-loop control of 4D printed hydrogel soft robots, hierarchical motion of 4D printed structures using the temperature memory effect, multimaterials 4D printing using a grasshopper plugin, shape reversible 4D printing, and variable stiffness 4D printing are each discussed as well. Outlines cutting-edge techniques, structural design, modeling, simulation, and tools for application-based 4D printing Details design, modeling, simulation, and manufacturing considerations for various fields Includes case studies demonstrating real-world situations where the techniques and concepts discussed were successfully deployed Applications covered include textiles, soft robotics, auxetics and metamaterials, micromachines, sensors, bioprinting, and wireless devices Covers the mechanics, manufacturing processes and applications of 4D-printed smart materials and structures Discusses applications in civil, mechanical, aerospace, polymer and biomedical engineering Presents experimental, numerical and analytical studies in a simple and straightforward manner, providing tools that can be immediately implemented and adapted by readers to fit their work