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

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

A strain gradient enhanced model for the phase‐field approach to fracture

Phase-field modelling has been shown to be a powerful tool for simulating fracture processes and predicting the crack path under complex loading conditions. Note that the total energy of fracture in the classical phase-field formulations includes the strain energy density from the linear elasticity theory resulting in singular stresses at the crack tip. Recently, we have demonstrated that integrating the strain gradient elasticity into the conventional phase-field fracture formulations may improve the final results by alleviating the effects of a singular stress field around the crack tip [1]. The current contribution focuses on a more general formulation of strain gradient elasticity