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 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

Application of Particle Dampers on a Scaled Wind Turbine Generator to Improve Low-Frequency Vibro-Acoustic Behavior

The purpose of this paper is to introduce a honeycomb damping plate (HCDP) concept based on the particle damping technique to reduce the low-frequency vibration response of wind turbine generators. The HCDP cells contain granular materials and are mounted at different positions on the generator to reduce the transmission of vibrations from stator ring to stator arm. To investigate the efficiency of the HCDP concept in the laboratory, a small-scale replica inspired by the original wind turbine generator is used as reference geometry. The efficiency of the vibration attenuation by using the HCDP concept is experimentally investigated with the help of a laser scanning vibrometer device. In this contribution, the influence of four different granular materials on the vibration attenuation is experimentally investigated. Furthermore, the influence of HCDP positioning on the transmission path damping is analyzed. Apart from this, the effect of single-unit (SU) and multi-unit (MU) HCDP on the frequency response of the generator is also studied. The experimental approach in this paper shows good damping properties of the HCDP concept for reducing the vibration amplitude

Revisiting Mindlin's theory with regard to a gradient extended phase‐field model for fracture

The application of generalized continuum mechanics is rapidly increasing in different fields of science and engineering. In the literature, there are several theories extending the classical first-order continuum mechanics formulation to include size-effects [1]. One approach is the strain gradient theory with the intrinsic features of regularizing singular stress fields occurring, e.g., near crack tips. It is crucial to realize that using this theory, the strain energy density is still localized around the crack tip, but does not exhibit any signs of a singularity. Therefore, these models seem to be appropriate choices for studying cracks in mechanical problems. Over the past several years, the phase-field method has gathered considerable popularity in the computational mechanics community, in particular in the field of fracture mechanics [2]. Recently, the authors have shown that integrating the strain gradient theory into the phase-field fracture framework is likely to improve the quality of the final results due to the inherent non-singular nature of this theory [3]. In the present work, we will focus on a general formulation of the first strain gradient theory. To this end, the homogenization approach introduced in Ref. [4] is employed. It is based on a series of systematic finite element simulations using different loading cases to determine the equivalent material coefficients on the macro-scale (i.e., for a strain gradient elastic material) by taking the underlying micro-structure into account