@article{58492,
  abstract     = {{A coupled finite plasticity ductile damage and failure model is proposed for the finite element simulation of clinch joining, which incorporates stress-state dependency and regularisation by gradient-enhancement of the damage variable. Ductile damage is determined based on a failure indicator governed by a failure surface in stress space. The latter is exemplary chosen as a combination of the Hosford–Coulomb and Cockcroft–Latham–Oh failure criteria for the high and low stress triaxiality range, respectively, to cover the wide stress range encountered in forming. Damage is coupled to elasto-plasticity to capture the damage-induced degradation of the stiffness and flow stress. This affects the material behaviour up to failure, thereby realistically altering the stress state. Consequently, especially for highly ductile materials, where substantial necking and localisation precede material fracture, the failure prediction is enhanced. The resulting stress softening is regularised by gradient-enhancement to obtain mesh-objective results. The analysis of a modified punch test experiment emphasises how the damage-induced softening effect can strongly alter the actual stress state towards failure. Moreover, the impact of successful regularisation is shown, and the applicability of the damage and failure model to clinch joining is proven.}},
  author       = {{Friedlein, Johannes and Mergheim, Julia and Steinmann, Paul}},
  issn         = {{0022-5096}},
  journal      = {{Journal of the Mechanics and Physics of Solids}},
  keywords     = {{Finite plasticity, Ductile damage, Gradient-enhancement, Stress-state dependency, Failure}},
  publisher    = {{Elsevier BV}},
  title        = {{{Modelling of stress-state-dependent ductile damage with gradient-enhancement exemplified for clinch joining}}},
  doi          = {{10.1016/j.jmps.2025.106026}},
  volume       = {{196}},
  year         = {{2025}},
}

@article{57472,
  abstract     = {{In this paper we introduce, in a Hilbert space setting, a second order dynamical system with asymptotically vanishing damping and vanishing Tikhonov regularization that approaches a multiobjective optimization problem with convex and differentiable components of the objective function. Trajectory solutions are shown to exist in finite dimensions. We prove fast convergence of the function values, quantified in terms of a merit function. Based on the regime considered, we establish both weak and, in some cases, strong convergence of trajectory solutions toward a weak Pareto optimal solution. To achieve this, we apply Tikhonov regularization individually to each component of the objective function. This work extends results from single objective convex optimization into the multiobjective setting.}},
  author       = {{Bot, Radu Ioan and Sonntag, Konstantin}},
  journal      = {{Journal of Mathematical Analysis and Applications}},
  keywords     = {{Pareto optimization, Lyapunov analysis, gradient-like dynamical systems, inertial dynamics, asymptotic vanishing damping, Tikhonov regularization, strong convergence}},
  title        = {{{Inertial dynamics with vanishing Tikhonov regularization for multobjective optimization}}},
  year         = {{2025}},
}

@article{32447,
  abstract     = {{We present a new gradient-like dynamical system related to unconstrained convex smooth multiobjective optimization which involves inertial effects and asymptotic vanishing damping. To the best of our knowledge, this system is the first inertial gradient-like system for multiobjective optimization problems including asymptotic vanishing damping, expanding the ideas previously laid out in [H. Attouch and G. Garrigos, Multiobjective Optimization: An Inertial Dynamical Approach to Pareto Optima, preprint, arXiv:1506.02823, 2015]. We prove existence of solutions to this system in finite dimensions and further prove that its bounded solutions converge weakly to weakly Pareto optimal points. In addition, we obtain a convergence rate of order \(\mathcal{O}(t^{-2})\) for the function values measured with a merit function. This approach presents a good basis for the development of fast gradient methods for multiobjective optimization.}},
  author       = {{Sonntag, Konstantin and Peitz, Sebastian}},
  issn         = {{1095-7189}},
  journal      = {{SIAM Journal on Optimization}},
  keywords     = {{multiobjective optimization, Pareto optimization, Lyapunov analysis, gradient-likedynamical systems, inertial dynamics, asymptotic vanishing damping, fast convergence}},
  number       = {{3}},
  pages        = {{2259 -- 2286}},
  publisher    = {{Society for Industrial and Applied Mathematics}},
  title        = {{{Fast Convergence of Inertial Multiobjective Gradient-Like Systems with Asymptotic Vanishing Damping}}},
  doi          = {{10.1137/23M1588512}},
  volume       = {{34}},
  year         = {{2024}},
}

@article{58491,
  abstract     = {{<jats:p>Similar to bulk metal forming, clinch joining is characterised by large plastic deformations and a variety of different 3D stress states, including severe compression. However, inherent to plastic forming is the nucleation and growth of defects, whose detrimental effects on the material behaviour can be described by continuum damage models and eventually lead to material failure. As the damage evolution strongly depends on the stress state, a stress-state-dependent model is utilised to correctly track the accumulation. To formulate and parameterise this model, besides classical experiments, so-called modified punch tests are also integrated herein to enhance the calibration of the failure model by capturing a larger range of stress states and metal-forming-specific loading conditions. Moreover, when highly ductile materials are considered, such as the dual-phase steel HCT590X and the aluminium alloy EN AW-6014 T4 investigated here, strong necking and localisation might occur prior to fracture. This can alter the stress state and affect the actual strain at failure. This influence is captured by coupling plasticity and damage to incorporate the damage-induced softening effect. Its relative importance is shown by conducting inverse parameter identifications to determine damage and failure parameters for both mentioned ductile metals based on up to 12 different experiments.</jats:p>}},
  author       = {{Friedlein, Johannes and Böhnke, Max and Schlichter, Malte and Bobbert, Mathias and Meschut, Gerson and Mergheim, Julia and Steinmann, Paul}},
  issn         = {{2504-4494}},
  journal      = {{Journal of Manufacturing and Materials Processing}},
  keywords     = {{ductile damage, stress-state dependency, failure, parameter identification, punch test, clinching}},
  number       = {{4}},
  publisher    = {{MDPI AG}},
  title        = {{{Material Parameter Identification for a Stress-State-Dependent Ductile Damage and Failure Model Applied to Clinch Joining}}},
  doi          = {{10.3390/jmmp8040157}},
  volume       = {{8}},
  year         = {{2024}},
}

@article{56097,
  abstract     = {{We contrast different gradient-enhancements for plasticity-damage material models in the logarithmic strain space and compare them to reference models based on multiplicative plasticity. The models being compared include plasticity - gradient-damage, where the gradient-enhancement is applied on the local damage variable, and gradient-plasticity - damage with a gradient-enhanced plastic hardening variable. Thereby, gradient-plasticity proved to be able to simultaneously regularise plastic and ductile (plasticity-driven) damage localisation as confirmed by numerical localisation analyses. This appears to be especially advantageous for logarithmic strain space plasticity-damage, because of the observed plastic localisation even for the case of plasticity with hardening. Even though gradient-plasticity appears to be numerically more demanding, two numerical examples indicate a good robustness and mesh objectivity in the softening regime. Moreover, the internal length for plasticity is able to adjust the damage zone width, similarly to gradient-damage, however ensuring a priori that damage takes place exclusively inside the plastic zone.}},
  author       = {{Friedlein, Johannes and Mergheim, Julia and Steinmann, Paul}},
  issn         = {{0997-7538}},
  journal      = {{European Journal of Mechanics - A/Solids}},
  keywords     = {{Finite plasticity, Logarithmic strain space, Ductile damage, Gradient-enhancement, Gradient-plasticity, Gradient-damage, Loss of ellipticity}},
  publisher    = {{Elsevier BV}},
  title        = {{{Efficient gradient enhancements for plasticity with ductile damage in the logarithmic strain space}}},
  doi          = {{10.1016/j.euromechsol.2023.104946}},
  volume       = {{99}},
  year         = {{2023}},
}

@article{27186,
  abstract     = {{The presented paper aims to characterize the damage and fracture behavior of HX340LAD Micro-Alloyed steels using small punch test. Variations with respect to punch geometries and cutting clearance are made to describe the damage behavior of the material under different loading conditions. Experimental investigations are conducted to identify the crack initiation in the specimens. Furthermore, the numerical FEM simulations are performed to identify the stress state at crack initiation. It is shown that different stress states from shear to biaxial tension can be achieved by changing the geometries of punch and varying the cutting clearance. Moreover, it is presented how changing the configurations can influence the stress state variables: Triaxiality and lode angle parameter.}},
  author       = {{Otroshi, Mortaza and Meschut, Gerson}},
  issn         = {{1350-6307}},
  journal      = {{Engineering Failure Analysis}},
  keywords     = {{Ductile damage, stress state, small punch test, triaxiality, lode angle parameter}},
  number       = {{c}},
  publisher    = {{Elsevier}},
  title        = {{{Influence of cutting clearance and punch geometry on the stress state in small punch test }}},
  doi          = {{10.1016/j.engfailanal.2022.106183}},
  volume       = {{136}},
  year         = {{2022}},
}

@inbook{34209,
  abstract     = {{Predicting the durability of components subjected to mechanical load under environmental conditions leading to corrosion is one of the most challenging tasks in mechanical engineering. The demand for precise predictions increases with the desire of lightweight design in transportation due to environmental protection. Corrosion with its manifold of mechanisms often occurs together with the production of hydrogen by electrochemical reactions. Hydrogen embrittlement is one of the most feared damage mechanisms for metal constructions often leading to early and unexpected failure. Until now, predictions are mostly based on costly experiments. Hence, a rational predictive model based on the fundamentals of electrochemistry and damage mechanics has to be developed in order to reduce the costs. In this work, a first model approach based on classical continuum damage mechanics is presented to couple both, the damage induced by the mechanical stress and the hydrogen embrittlement. An elaborated two-scale model based on the selfconsistent theory is applied to describe the mechanical damage due to fatigue. The electrochemical kinetics are elucidated through the Langmuir adsorption isotherm and the diffusion equation to consider the impact of hydrogen embrittlement on the fatigue. The modeling of the mechanism of hydrogen embrittlement defines the progress of damage accumulation due to the electrochemistry. The durability results like the S-N diagram show the influence of hydrogen embrittlement by varying, e.g. the fatigue frequency or the stress ratio.}},
  author       = {{Shi, Yuhao and Harzheim, Sven and Hofmann, Martin and Wallmersperger, Thomas}},
  booktitle    = {{Material Modeling and Structural Mechanics}},
  isbn         = {{9783030976743}},
  issn         = {{1869-8433}},
  keywords     = {{Hydrogen embrittlement, Fatigue, Continuum damage mechanics, Numerical simulation, Multi-field problem}},
  publisher    = {{Springer International Publishing}},
  title        = {{{A Damage Model for Corrosion Fatigue Due to Hydrogen Embrittlement}}},
  doi          = {{10.1007/978-3-030-97675-0_9}},
  year         = {{2022}},
}

@article{25476,
  abstract     = {{This study deals with the damage behavior of metallic materials by the application of different manufacturing processes and using different optical measurement methods to identify the crack initiation in the damage specimen. The study is intended to highlight the importance of considering manufacturing processes and optical measurement methods in a numerical simulation when analyzing the damage behavior of metallic materials. To describe the damage behavior of the material in the process chain simulations, it is important to calibrate the parameters of damage model more accurately. These parameters are determined using experimental investigation of desired damage specimens. In this regard, a selected damage specimen manufactured by different cutting processes is first experimentally and then numerically investigated. It is shown that the manufacturing process and the optical measurement methods influence the stress state analyzed in the numerical simulation.}},
  author       = {{Otroshi, Mortaza and Meschut, Gerson and Nesakumar, Aathavan}},
  journal      = {{Journal of Manufacturing Engineering}},
  keywords     = {{Damage behaviour, Stress triaxiality, Manufacturing process and Optical measurement}},
  number       = {{3}},
  pages        = {{70--76}},
  title        = {{{The influence of manufacturing processes and optical measurement methods on the damage behavior of HX340LAD micro-alloyed steels}}},
  doi          = {{https://doi.org/10.37255/jme.v16i3pp070-076}},
  volume       = {{16}},
  year         = {{2021}},
}

@article{20143,
  author       = {{Otroshi, Mortaza and Rossel, Moritz and Meschut, Gerson}},
  journal      = {{Journal of Advanced Joining Processes}},
  keywords     = {{Self-pierce riveting, Ductile fracture, Damage modeling, GISSMO damage model}},
  publisher    = {{Elsevier}},
  title        = {{{Stress state dependent damage modeling of self-pierce riveting process simulation using GISSMO damage model}}},
  doi          = {{10.1016/j.jajp.2020.100015}},
  volume       = {{1}},
  year         = {{2020}},
}

@article{11927,
  abstract     = {{Maximizing the output signal-to-noise ratio (SNR) of a sensor array in the presence of spatially colored noise leads to a generalized eigenvalue problem. While this approach has extensively been employed in narrowband (antenna) array beamforming, it is typically not used for broadband (microphone) array beamforming due to the uncontrolled amount of speech distortion introduced by a narrowband SNR criterion. In this paper, we show how the distortion of the desired signal can be controlled by a single-channel post-filter, resulting in a performance comparable to the generalized minimum variance distortionless response beamformer, where arbitrary transfer functions relate the source and the microphones. Results are given both for directional and diffuse noise. A novel gradient ascent adaptation algorithm is presented, and its good convergence properties are experimentally revealed by comparison with alternatives from the literature. A key feature of the proposed beamformer is that it operates blindly, i.e., it neither requires knowledge about the array geometry nor an explicit estimation of the transfer functions from source to sensors or the direction-of-arrival.}},
  author       = {{Warsitz, Ernst and Haeb-Umbach, Reinhold}},
  journal      = {{IEEE Transactions on Audio, Speech, and Language Processing}},
  keywords     = {{acoustic signal processing, arbitrary transfer function, array signal processing, blind acoustic beamforming, direction-of-arrival, direction-of-arrival estimation, eigenvalues and eigenfunctions, generalized eigenvalue decomposition, gradient ascent adaptation algorithm, microphone arrays, microphones, narrowband array beamforming, sensor array, single-channel post-filter, spatially colored noise, transfer functions}},
  number       = {{5}},
  pages        = {{1529--1539}},
  title        = {{{Blind Acoustic Beamforming Based on Generalized Eigenvalue Decomposition}}},
  doi          = {{10.1109/TASL.2007.898454}},
  volume       = {{15}},
  year         = {{2007}},
}

@inproceedings{11930,
  abstract     = {{For human-machine interfaces in distant-talking environments multichannel signal processing is often employed to obtain an enhanced signal for subsequent processing. In this paper we propose a novel adaptation algorithm for a filter-and-sum beamformer to adjust the coefficients of FIR filters to changing acoustic room impulses, e.g. due to speaker movement. A deterministic and a stochastic gradient ascent algorithm are derived from a constrained optimization problem, which iteratively estimates the eigenvector corresponding to the largest eigenvalue of the cross power spectral density of the microphone signals. The method does not require an explicit estimation of the speaker location. The experimental results show fast adaptation and excellent robustness of the proposed algorithm.}},
  author       = {{Warsitz, Ernst and Haeb-Umbach, Reinhold}},
  booktitle    = {{IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2005)}},
  keywords     = {{acoustic filter-and-sum beamforming, acoustic room impulses, acoustic signal processing, adaptive principal component analysis, adaptive signal processing, architectural acoustics, constrained optimization problem, cross power spectral density, deterministic algorithm, deterministic algorithms, distant-talking environments, eigenvalues and eigenfunctions, eigenvector, enhanced signal, filter-and-sum beamformer, FIR filter coefficients, FIR filter coefficients, FIR filters, gradient methods, human-machine interfaces, iterative estimation, iterative methods, largest eigenvalue, microphone signals, multichannel signal processing, optimisation, principal component analysis, spectral analysis, stochastic gradient ascent algorithm, stochastic processes}},
  pages        = {{iv/797--iv/800 Vol. 4}},
  title        = {{{Acoustic filter-and-sum beamforming by adaptive principal component analysis}}},
  doi          = {{10.1109/ICASSP.2005.1416129}},
  volume       = {{4}},
  year         = {{2005}},
}