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The purpose of this paper is to present the freely available finite element simulation software Pyrit.

In a first step, the design principles and the objective of the software project are defined. Then, the software’s structure is established: The software is organized in packages for which an overview is given. The structure is based on the typical steps of a simulation workflow, i.e., problem definition, problem-solving and post-processing. State-of-the-art software engineering principles are applied to ensure a high code quality at all times. Finally, the modeling and simulation workflow of Pyrit is demonstrated by three examples.

Pyrit is a field simulation software based on the finite element method written in Python to solve coupled systems of partial differential equations. It is designed as a modular software that is easily modifiable and extendable. The framework can, therefore, be adapted to various activities, i.e., research, education and industry collaboration.

The focus of Pyrit are static and quasistatic electromagnetic problems as well as (coupled) heat conduction problems. It allows for both time domain and frequency domain simulations.

In research, problem-specific modifications and direct access to the source code of simulation tools are essential. With Pyrit, the authors present a computationally efficient and platform-independent simulation software for various electromagnetic and thermal field problems.

This paper aims to consider a multiscale electromagnetic wave problem for a housing with a ventilation grill. Using the standard finite element method to discretise the apertures leads to an unduly large number of unknowns. An efficient approach to simulate the multiple scales is introduced. The aim is to significantly reduce the computational costs.

A domain decomposition technique with upscaling is applied to cope with the different scales. The idea is to split the domain of computation into an exterior domain and multiple non-overlapping sub-domains. Each sub-domain represents a single aperture and uses the same finite element mesh. The identical mesh of the sub-domains is efficiently exploited by the hybrid discontinuous Galerkin method and a Schur complement which facilitates the transition from fine meshes in the sub-domains to a coarse mesh in the exterior domain. A coarse skeleton grid is used on the interface between the exterior domain and the individual sub-domains to avoid large dense blocks in the finite element discretisation matrix.

Applying a Schur complement to the identical discretisation of the sub-domains leads to a method that scales very well with respect to the number of apertures.

The error compared to the standard finite element method is negligible and the computational costs are significantly reduced.

Nonlinear solution approaches for inverse problems require fast simulation techniques for the underlying sensing problem. In this work, the authors investigate finite element (FE) based sensor simulations for the inverse problem of electrical capacitance tomography. Two known computational bottlenecks are the assembly of the FE equation system as well as the computation of the Jacobian. Here, existing computation techniques like adjoint field approaches require additional simulations. This paper aims to present fast numerical techniques for the sensor simulation and computations with the Jacobian matrix.

For the FE equation system, a solution strategy based on Green’s functions is derived. Its relation to the solution of a standard FE formulation is discussed. A fast stiffness matrix assembly based on an eigenvector decomposition is shown. Based on the properties of the Green’s functions, Jacobian operations are derived, which allow the computation of matrix vector products with the Jacobian for free, i.e. no additional solves are required. This is demonstrated by a Broyden–Fletcher–Goldfarb–Shanno-based image reconstruction algorithm.

MATLAB-based time measurements of the new methods show a significant acceleration for all calculation steps compared to reference implementations with standard methods. E.g. for the Jacobian operations, improvement factors of well over 100 could be found.

The paper shows new methods for solving known computational tasks for solving inverse problems. A particular advantage is the coherent derivation and elaboration of the results. The approaches can also be applicable to other inverse problems.

The “chiralisation” of Euclidean polygonal tessellations is a novel, recent method which has been used to design new auxetic metamaterials with complex topologies and improved geometric versatility over traditional chiral honeycombs. This paper aims to design and manufacture chiral honeycombs representative of four distinct classes of 2D Euclidean tessellations with hexagonal rotational symmetry using fused-deposition additive manufacturing and experimentally analysed the mechanical properties and failure modes of these metamaterials.

Finite Element simulations were also used to study the high-strain compressive performance of these systems under both periodic boundary conditions and realistic, finite conditions. Experimental uniaxial compressive loading tests were applied to additively manufactured prototypes and digital image correlation was used to measure the Poisson’s ratio and analyse the deformation behaviour of these systems.

The results obtained demonstrate that these systems have the ability to exhibit a wide range of Poisson’s ratios (positive, quasi-zero and negative values) and stiffnesses as well as unusual failure modes characterised by a sequential layer-by-layer collapse of specific, non-adjacent ligaments. These findings provide useful insights on the mechanical properties and deformation behaviours of this new class of metamaterials and indicate that these chiral honeycombs could potentially possess anomalous characteristics which are not commonly found in traditional chiral metamaterials based on regular monohedral tilings.

To the best of the authors’ knowledge, the authors have analysed for the first time the high strain behaviour and failure modes of chiral metamaterials based on Euclidean multi-polygonal tessellations.

Laser sintering of polyamide lattice-based lightweight fairing components for subsequent racetrack testing requires a high quality and a reliable design. Hence, the purpose of this study was to develop a design methodology for such additively manufactured prototypes, considering efficient generation and structural simulation of boundary conformal non-periodic lattices, optimization of production parameters as well as experimental validation.

Multi-curved, sandwich structure-based demonstrators were designed, simulated and experimentally tested with boundary conformal lattice cells. The demonstrator’s non-periodic lattice cells were simplified by forward homogenization processes. To represent the stiffness of the top and bottom face sheet, constant isotropic and mapped transversely isotropic simulation approaches were compared. The dimensional accuracy of lattice cells and demonstrators were measured with a gauge caliper and a three-dimensional scanning system. The optimized process parameters for lattice structures were transferred onto a large volume laser sintering system. The stiffness of each finite element analysis was verified by an experimental test setup including a digital image correlation system.

The stiffness prediction of the mapped was superior to the constant approach and underestimated the test results with −6.5%. Using a full scale fairing the applicability of the development process was successfully demonstrated.

The design approach elaborated in this research covers aspects from efficient geometry generation over structural simulation to experimental testing of produced parts. This methodology is not only relevant in the context of motor sports but is transferrable for all additively manufactured large scale components featuring a complex lattice sub-structure and is, therefore, relevant across industries.

Cables are ubiquitous in electronic-based systems. Electromagnetic emission of cables and crosstalk between wires is an important issue in electromagnetic compatibility and is to be minimized in the design phase. To facilitate the design, models of different complexity and accuracy, for instance, circuit models or finite element (FE) simulations, are used. The purpose of this study is to compare transmission line parameters obtained by measurements and simulations.

Transmission line parameters were determined by means of measurements in the frequency and time domain and by FE simulations in the frequency domain and compared. Finally, a Spice simulation with lumped elements was performed.

The determination of the effective permittivity of insulated wires seems to be a key issue in comparing measurements and simulations.

A space decomposition technique for a guided wave on an infinite configuration with constant cross-section has been introduced, where an analytic representation in the direction of propagation is used, and the transversal fields are approximated by FEs.

The purpose of this study concerns numerical studies and experimental validation of the mechanical behavior of hybrid specimens. These kinds of composite specimens are made up of thin carbon and glass substrates on which some Macro Fiber Composite^® (MFC) piezoelectric patches are glued. A proper design and manufacturing of the hybrid specimens as well as testing activities have been performed. The research activity has been carried out under the FutureWings project, funded by the European Commission within the 7th Framework.

The paper describes the basic assumptions made to define specimen geometries and to carry out experimental tests. Finite element (FE) results and experimental data (laser technique measurements) have been compared: it shows very good agreement for the displacements’ distribution along the specimens.

Within the objectives of the project, the study of passive and active deformation characteristics of the hybrid composite material has provided reference technical data and has allowed for the correct adaptation of the FE models. More in particular, using the hybrid specimens, both the bending deformations and the torsion deformations have been studied.

The deformation capability of the hybrid specimens will be used in the development of prototypical three-dimensional structures, that, through the electrical control of the MFC patches, will be able to change the curvature of their cross section or will be able to change the angle of torsion along their longitudinal axis.

The design of nonstandard specimens and the tests executed represent a novelty in the field of structures using piezoelectric actuators. The numerical and experimental data of the present research constitute a small step forward in the field of smart materials technology.

The purpose of this paper is to describe the approach for the design of cowlings for a new fast helicopter from the perspective of airworthiness requirements regarding high-speed impact resistance.

Validated numerical simulation was applied to flat and simple curved test panels. High-speed camera measurement and non-destructive testing (NDT) results were used for verification of the numerical models. The final design was optimized and verified by validated numerical simulation.

The comparison between numerical simulation based on static material properties with experimental results of high-speed load shows no significant influence of strain rate effect in composite material.

Owing to the sensitivity of the composite material on technology production, the results are limited by the material used and the production technology.

The application of flat and simple curved test panels for the verification and calibration of numerical models allows the optimized final design of the cowling and reduces the risk of structural non-compliance during verification tests.

Numerical models were verified for simulation of the real composite structure based on high-speed camera results and NDT inspection after impact. The proposed numerical model was simplified for application in a complex design and reduced calculation time.

In this study, the authors propose a novel digital twinning approach specifically designed for controlling transient thermal systems. The purpose of this study is to harness the combined power of deep learning (DL) and physics-based methods (PBM) to create an active virtual replica of the physical system.

To achieve this goal, we introduce a deep neural network (DNN) as the digital twin and a Finite Element (FE) model as the physical system. This integrated approach is used to address the challenges of controlling an unsteady heat transfer problem with an integrated feedback loop.

The results of our study demonstrate the effectiveness of the proposed digital twinning approach in regulating the maximum temperature within the system under varying and unsteady heat flux conditions. The DNN, trained on stationary data, plays a crucial role in determining the heat transfer coefficients necessary to maintain temperatures below a defined threshold value, such as the material’s melting point. The system is successfully controlled in 1D, 2D and 3D case studies. However, careful evaluations should be conducted if such a training approach, based on steady-state data, is applied to completely different transient heat transfer problems.

The present work represents one of the first examples of a comprehensive digital twinning approach to transient thermal systems, driven by data. One of the noteworthy features of this approach is its robustness. Adopting a training based on dimensionless data, the approach can seamlessly accommodate changes in thermal capacity and thermal conductivity without the need for retraining.

Performing accurate numerical simulations of electrical drives, the precise knowledge of the local magnetic material properties is of utmost importance. Due to the various manufacturing steps, e.g. heat treatment or cutting techniques, the magnetic material properties can strongly vary locally, and the assumption of homogenized global material parameters is no longer feasible. This paper aims to present the general methodology and two different solution strategies for determining the local magnetic material properties using reference and simulation data.

The general methodology combines methods based on measurement, numerical simulation and solving an inverse problem. Therefore, a sensor-actuator system is used to characterize electrical steel sheets locally. Based on the measurement data and results from the finite element simulation, the inverse problem is solved with two different solution strategies. The first one is a quasi Newton method (QNM) using Broyden's update formula to approximate the Jacobian and the second is an adjoint method. For comparison of both methods regarding convergence and efficiency, an artificial example with a linear material model is considered.

The QNM and the adjoint method show similar convergence behavior for two different cutting-edge effects. Furthermore, considering a priori information improved the convergence rate. However, no impact on the stability and the remaining error is observed.

The presented methodology enables a fast and simple determination of the local magnetic material properties of electrical steel sheets without the need for a large number of samples or special preparation procedures.