40 Jahre Zeitschrift Technische Mechanik

40 Jahre Zeitschrift Technische Mechanik40th anniversary of the journal Technische Mechani

Interplay of Fracture and Martensite Transformation in Microstructures:A Coupled Problem

We are witnessing a tremendous transition towards a society powered by net-zero carbon emission energy, with a corresponding escalating reliance on functional materials (FM). In recent years, the application of FM in multiphysics environments has brought new challenges to the mechanics and materials research communities. The underlying mechanism in FM, which governs several fundamental characteristics, is known as martensitic phase transformation (MPT). When it comes to the application of FM in the multiphysics context, a thorough understanding of the interplay between MPT and fracture plays a crucial role in FM design and application. In the present work, a coupled problem of crack nucleation and propagation and multivariant stress-induced MPT in elastic materials is presented using a finite element method based on Khachaturyan’s microelasticity theory. The problem is established based on a phase-field (PF) approach, which includes the Ginzburg–Landau equations with advanced thermodynamic potential and the variational formulation of Griffith’s theory. Therefore, the model consists of a coupled system of the Ginzburg–Landau equations and the static elasticity equation, and it characterizes evolution of distributions of austenite and two martensitic variants as well as crack growth in terms of corresponding order parameters. The numerical results show that crack growth does not begin until MPT has grown almost completely through the microstructure. Subsequent to the initial formation of the martensite variants, the initial crack propagates in such a way that its path mainly depends on the feature of martensite variant formations, the orientation and direction upon which the martensite plates are aligned, and the stress concentration between martensite plates. In addition, crack propagation behavior and martensite variant evaluations for different lattice orientation angles are presented and discussed in-detail

A study on harmonic excitation based experimental characterization of damping materials for acoustic simulations

The presented study deals with the experimental characterization of damping materials for acoustic simulations with respect to the stiffness and damping in dependence of the excitation frequency, i.e.~frequency-dependent elasticity modulus.The test rigs under consideration utilize a shaker, acceleration sensors and a laser Doppler vibrometer (LDV) to measure oscillating behaviour at frequencies ranging from 20 to 2000 Hz.Suitable mounting properties of the test rigs are examined experimentally and by finite element analysis. The applicability of the gained results for acoustic simulations is investigated with results from a window test setup

An EigenValue Stabilization Technique for Immersed Boundary Finite Element Methods in Explicit Dynamics

The application of immersed boundary methods in static analyses is often impeded by poorly cut elements (small cut elements problem), leading to ill-conditioned linear systems of equations and stability problems. While these concerns may not be paramount in explicit dynamics, a substantial reduction in the critical time step size based on the smallest volume fraction $\chi$ of a cut element is observed. This reduction can be so drastic that it renders explicit time integration schemes impractical. To tackle this challenge, we propose the use of a dedicated eigenvalue stabilization (EVS) technique. The EVS-technique serves a dual purpose. Beyond merely improving the condition number of system matrices, it plays a pivotal role in extending the critical time increment, effectively broadening the stability region in explicit dynamics. As a result, our approach enables robust and efficient analyses of high-frequency transient problems using immersed boundary methods. A key advantage of the stabilization method lies in the fact that only element-level operations are required. This is accomplished by computing all eigenvalues of the element matrices and subsequently introducing a stabilization term that mitigates the adverse effects of cutting. Notably, the stabilization of the mass matrix $\mathbf{M}_\mathrm{c}$ of cut elements -- especially for high polynomial orders $p$ of the shape functions -- leads to a significant raise in the critical time step size $\Delta t_\mathrm{cr}$. To demonstrate the efficacy of our technique, we present two specifically selected dynamic benchmark examples related to wave propagation analysis, where an explicit time integration scheme must be employed to leverage the increase in the critical time step size.Comment: 45 pages, 25 figure

A phase field approach to study of transformation induced micro–cracking in a martensitic phase transformation

In this study, a coupled phase field (PF) method for the simulation of crack propagation and martensitic phase transformations is developed. In order to investigate the crack field and martensitic microstructure evolution the concept of the thermodynamic driving force, interfacial energy, the elastic energy, and the kinetic of phase field equations are introduced (time dependent Ginzburg Landau equation) [1]. The weak form and an algorithm for the solution of corresponding equations are implemented in the finite element program (FEAP). Since the phase transformation can form during the application of high amount of stresses, the influence of microcrack propagation on the formation of the martensitic phase has been studied. The crack tip produces high amount of concentrated stresses, which lead to a change in the distribution of the martensitic phases and it can also deviate the crack direction [2].Projekt DEAL 202

Code verification of non‐linear immersed boundary simulations using the method of manufactured solutions

Non‐standard finite element technologies, such as immersed boundary approaches, are typically based on novel algorithms and advanced methods, which require reliable testing of the implemented code. For this purpose, the method of manufactured solutions (MoMS) offers a great framework, enabling an easy and straightforward derivation of closed‐form reference solutions. In this contribution, the focus is kept on non‐linear analysis via the finite cell method (FCM), which is typically based on an unfitted geometry discretization and higher‐order shape functions. The code verification via MoMS generally requires the application of boundary conditions to all boundaries of the simulation domain, which need to be enforced in a weak sense on the immersed boundaries. To avoid this, we propose a novel way of deriving manufactured solutions, for which the necessary constraints on the embedded boundaries are directly fulfilled. Thus, weak boundary conditions can be eliminated from the FCM simulation, and the simulation complexity is reduced when testing other relevant features of the immersed code. In particular, we focus on finite strain analysis of 3D structures with a Neo‐Hookean material model, and show that the proposed technique enables a reliable code verification approach for all load steps throughout the deformation process

Autoregressive neural networks for predicting the behavior of viscoelastic materials

In the present work, the capabilities of neural networks to describe viscoelastic material behavior are investigated. Using real one-dimensional test data from a tensile test, autoregressive neural networks were trained. The best networks were then used to calculate the stress and the stiffness in displacement- and force-driven simulations. The results were compared with both experimental data and simulation results of a classical material model.The viscoelasticity discussed here plays a special role in the description of complex rubber materials, in addition to long-term effects, failure or heat-induced mechanisms. Classical material models simplify the real behavior, which is the reason for the occurrence of simulation errors. To overcome these limitations, this paper presents a different way of material modeling by describing the strain-stress correlation using a neural network. Previous stress states from the time history are used in the calculation to account for the path-dependent behavior of viscoelastic materials. Other effects, such as the influence of different temperatures, are not addressed in this work, but can be included with an appropriately large training data set

Enhanced Numerical Integration Scheme Based on Image Compression Techniques: Application to Rational Polygonal Interpolants

Polygonal finite elements offer an increased freedom in terms of mesh generation at the price of more complex, often rational, shape functions. Thus, the numerical integration of rational interpolants over polygonal domains is one of the challenges that needs to be solved. If, additionally, strong discontinuities are present in the integrand, e.g., when employing fictitious domain methods, special integration procedures must be developed. Therefore, we propose to extend the conventional quadtree-decomposition-based integration approach by image compression techniques. In this context, our focus is on unfitted polygonal elements using Wachspress shape functions. In order to assess the performance of the novel integration scheme, we investigate the integration error and the compression rate being related to the reduction in integration points. To this end, the area and the stiffness matrix of a single element are computed using different formulations of the shape functions, i.e., global and local, and partitioning schemes. Finally, the performance of the proposed integration scheme is evaluated by investigating two problems of linear elasticity.Projekt DEAL 202