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  • Springer Science and Business Media LLC  (29)
  • Wriggers, Peter  (29)
  • 2020-2024  (29)
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  • Springer Science and Business Media LLC  (29)
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  • 2020-2024  (29)
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  • 1
    Online Resource
    Online Resource
    Springer Science and Business Media LLC ; 2020
    In:  Computational Mechanics Vol. 66, No. 6 ( 2020-12), p. 1213-1235
    In: Computational Mechanics, Springer Science and Business Media LLC, Vol. 66, No. 6 ( 2020-12), p. 1213-1235
    Type of Medium: Online Resource
    ISSN: 0178-7675 , 1432-0924
    Language: English
    Publisher: Springer Science and Business Media LLC
    Publication Date: 2020
    detail.hit.zdb_id: 1458937-0
    detail.hit.zdb_id: 799787-5
    SSG: 11
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  • 2
    Online Resource
    Online Resource
    Springer Science and Business Media LLC ; 2023
    In:  Acta Mechanica Sinica Vol. 39, No. 4 ( 2023-04)
    In: Acta Mechanica Sinica, Springer Science and Business Media LLC, Vol. 39, No. 4 ( 2023-04)
    Abstract: 虚拟单元法在过去十年中得到了发展, 并应用于固体力学中的问题. 目前已使用了不同的公式来解释该方法的顺序和稳定性, 并应用到包括弹性和非弹性材料以及压裂过程的多种问题中. 本文利用虚拟单元法固有的可能性, 以简单有效的方式, 建立 C 1 连续的弹性函数, 研究固体高梯度弹性理论的虚拟单元公式.
    Type of Medium: Online Resource
    ISSN: 0567-7718 , 1614-3116
    Language: English
    Publisher: Springer Science and Business Media LLC
    Publication Date: 2023
    detail.hit.zdb_id: 2181030-8
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  • 3
    Online Resource
    Online Resource
    Springer Science and Business Media LLC ; 2021
    In:  Computational Particle Mechanics Vol. 8, No. 2 ( 2021-03), p. 369-388
    In: Computational Particle Mechanics, Springer Science and Business Media LLC, Vol. 8, No. 2 ( 2021-03), p. 369-388
    Abstract: Within this paper, the modelling and simulation of extrusion-based Additive Manufacturing (AM) processes of curing polymers is presented. The challenge of the AM is the adjustment of processing parameters. This includes the application of laser radiation to locally accelerate the curing in order to control the final geometry of the implant. Since complex multi-physical coupling effects are hardly predictable by operator experience, numerical simulations are beneficial. When the underlying physical effects of the AM processes are captured correctly within the simulations, a realistic representation of the process is possible. To model the material behaviour during the process, a process-dependent large strain curing model is formulated, considering the stress free curing behaviour of the material. State-of-the-art models are not able to model the fluid-like behaviour of low cured polymers. This needs a formulation that takes into account finite deformations. Hence, the current model is extended to finite plasticity using a process-dependent yield function. This allows the modelling of material spreading in the fluid-like state by simultaneously reducing the accumulation of elastic stored energy, which would lead to an unintentional and non-physical bounce-off behaviour otherwise. For the numerical simulations, an enhanced version of the peridynamic correspondence formulation using fractional subfamilies with associated volume weighting factors is introduced and implemented. Besides the specific laser modelling as a volumetric heat source, a local–non-local coupling of the arising thermo-chemo-mechanical coupled equations is introduced within the peridynamic framework. Within the simulations, the applicability of the plasticity-based approach to model material spreading in the fluid-like state is presented. Finally, the software for extrusion-based printing processes is developed and the complete thermo-chemo-mechanical coupled AM process is simulated. It is shown that higher geometrical precision is obtainable in terms of a reduced material spreading by the application of a laser radiation. The model constitutes the first step of the virtual implant development regarding the optimisation possibilities during the AM process.
    Type of Medium: Online Resource
    ISSN: 2196-4378 , 2196-4386
    Language: English
    Publisher: Springer Science and Business Media LLC
    Publication Date: 2021
    detail.hit.zdb_id: 2760376-3
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  • 4
    Online Resource
    Online Resource
    Springer Science and Business Media LLC ; 2023
    In:  Computational Mechanics Vol. 72, No. 1 ( 2023-07), p. 155-171
    In: Computational Mechanics, Springer Science and Business Media LLC, Vol. 72, No. 1 ( 2023-07), p. 155-171
    Abstract: Material modeling using modern numerical methods accelerates the design process and reduces the costs of developing new products. However, for multiscale modeling of heterogeneous materials, the well-established homogenization techniques remain computationally expensive for high accuracy levels. In this contribution, a machine learning approach, convolutional neural networks (CNNs), is proposed as a computationally efficient solution method that is capable of providing a high level of accuracy. In this work, the data-set used for the training process, as well as the numerical tests, consists of artificial/real microstructural images (“input”). Whereas, the output is the homogenized stress of a given representative volume element $$\mathcal {RVE}$$ RVE . The model performance is demonstrated by means of examples and compared with traditional homogenization methods. As the examples illustrate, high accuracy in predicting the homogenized stresses, along with a significant reduction in the computation time, were achieved using the developed CNN model.
    Type of Medium: Online Resource
    ISSN: 0178-7675 , 1432-0924
    Language: English
    Publisher: Springer Science and Business Media LLC
    Publication Date: 2023
    detail.hit.zdb_id: 1458937-0
    detail.hit.zdb_id: 799787-5
    SSG: 11
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  • 5
    Online Resource
    Online Resource
    Springer Science and Business Media LLC ; 2023
    In:  Biomechanics and Modeling in Mechanobiology
    In: Biomechanics and Modeling in Mechanobiology, Springer Science and Business Media LLC
    Abstract: This paper presents a mathematical model for arterial dissection based on a novel hypothesis proposed by a surgeon, Axel Haverich, see Haverich (Circulation 135(3):205–207, 2017. https://doi.org/10.1161/circulationaha.116.025407 ). In an attempt and based on clinical observations, he explained how three different arterial diseases, namely atherosclerosis, aneurysm and dissection have the same root in malfunctioning Vasa Vasorums (VVs) which are micro capillaries responsible for artery wall nourishment. The authors already proposed a mathematical framework for the modeling of atherosclerosis which is the thickening of the artery walls due to an inflammatory response to VVs dysfunction. A multiphysics model based on a phase-field approach coupled with mechanical deformation was proposed for this purpose. The kinematics of mechanical deformation was described using finite strain theory. The entire model is three-dimensional and fully based on a macroscopic continuum description. The objective here is to extend that model by incorporating a damage mechanism in order to capture the tearing (rupture) in the artery wall as a result of micro-injuries in VV. Unlike the existing damage-based model of the dissection in the literature, here the damage is driven by the internal bleeding (hematoma) rather than purely mechanical external loading. The numerical implementation is carried out using finite element method (FEM).
    Type of Medium: Online Resource
    ISSN: 1617-7959 , 1617-7940
    Language: English
    Publisher: Springer Science and Business Media LLC
    Publication Date: 2023
    detail.hit.zdb_id: 2064972-1
    SSG: 12
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  • 6
    Online Resource
    Online Resource
    Springer Science and Business Media LLC ; 2022
    In:  Archives of Computational Methods in Engineering Vol. 29, No. 6 ( 2022-10), p. 4285-4318
    In: Archives of Computational Methods in Engineering, Springer Science and Business Media LLC, Vol. 29, No. 6 ( 2022-10), p. 4285-4318
    Abstract: The complexity of many problems in computational mechanics calls for reliable programming codes and accurate simulation systems. Typically, simulation responses strongly depend on material and model parameters, where one distinguishes between backward and forward models. Providing reliable information for the material/model parameters, enables us to calibrate the forward model (e.g., a system of PDEs). Markov chain Monte Carlo methods are efficient computational techniques to estimate the posterior density of the parameters. In the present study, we employ Bayesian inversion for several mechanical problems and study its applicability to enhance the model accuracy. Seven different boundary value problems in coupled multi-field (and multi-physics) systems are presented. To provide a comprehensive study, both rate-dependent and rate-independent equations are considered. Moreover, open source codes ( https://doi.org/10.5281/zenodo.6451942 ) are provided, constituting a convenient platform for future developments for, e.g., multi-field coupled problems. The developed package is written in MATLAB and provides useful information about mechanical model problems and the backward Bayesian inversion setting.
    Type of Medium: Online Resource
    ISSN: 1134-3060 , 1886-1784
    Language: English
    Publisher: Springer Science and Business Media LLC
    Publication Date: 2022
    detail.hit.zdb_id: 2276736-8
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  • 7
    Online Resource
    Online Resource
    Springer Science and Business Media LLC ; 2023
    In:  Journal of Vibration Engineering & Technologies
    In: Journal of Vibration Engineering & Technologies, Springer Science and Business Media LLC
    Type of Medium: Online Resource
    ISSN: 2523-3920 , 2523-3939
    Language: English
    Publisher: Springer Science and Business Media LLC
    Publication Date: 2023
    detail.hit.zdb_id: 2941414-3
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  • 8
    Online Resource
    Online Resource
    Springer Science and Business Media LLC ; 2023
    In:  Scientific Reports Vol. 13, No. 1 ( 2023-07-22)
    In: Scientific Reports, Springer Science and Business Media LLC, Vol. 13, No. 1 ( 2023-07-22)
    Abstract: This paper deals with the mathematical modeling of bacterial co-aggregation and its numerical implementation in a FEM framework. Since the concept of co-aggregation refers to the physical binding between cells of different microbial species, a system composed of two species is considered in the modeling framework. The extension of the model to an arbitrary number of species is straightforward. In addition to two-species (multi-species growth) dynamics, the transport of a nutritional substance and the extent of co-aggregation are introduced into the model as the third and fourth primary variables. A phase-field modeling approach is employed to describe the co-aggregation between the two species. The mathematical model is three-dimensional and fully based on the continuum description of the problem without any need for discrete agents which are the key elements of the individual-based modeling approach. It is shown that the use of a phase-field-based model is equivalent to a particular form of classical diffusion-reaction systems. Unlike the so-called mixture models, the evolution of each component of the multi-species system is captured thanks to the inherent capability of phase-field modeling in treating systems consisting of distinct multi-phases. The details of numerical implementation in a FEM framework are also presented. Indeed, a new multi-field user element is developed and implemented in ANSYS for this multiphysics problem. Predictions of the model are compared with the experimental observations. By that, the versatility and applicability of the model and the numerical tool are well established.
    Type of Medium: Online Resource
    ISSN: 2045-2322
    Language: English
    Publisher: Springer Science and Business Media LLC
    Publication Date: 2023
    detail.hit.zdb_id: 2615211-3
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  • 9
    Online Resource
    Online Resource
    Springer Science and Business Media LLC ; 2023
    In:  Archives of Computational Methods in Engineering Vol. 30, No. 3 ( 2023-04), p. 2257-2288
    In: Archives of Computational Methods in Engineering, Springer Science and Business Media LLC, Vol. 30, No. 3 ( 2023-04), p. 2257-2288
    Abstract: Hyperelasticity is a common modeling approach to reproduce the nonlinear mechanical behavior of rubber materials at finite deformations. It is not only employed for stand-alone, purely elastic models but also within more sophisticated frameworks like viscoelasticity or Mullins-type softening. The choice of an appropriate strain energy function and identification of its parameters is of particular importance for reliable simulations of rubber products. The present manuscript provides an overview of suitable hyperelastic models to reproduce the isochoric as well as volumetric behavior of nine widely used rubber compounds. This necessitates firstly a discussion on the careful preparation of the experimental data. More specific, procedures are proposed to properly treat the preload in tensile and compression tests as well as to proof the consistency of experimental data from multiple experiments. Moreover, feasible formulations of the cost function for the parameter identification in terms of the stress measure, error type as well as order of the residual norm are studied and their effect on the fitting results is illustrated. After these preliminaries, invariant-based strain energy functions with decoupled dependencies on all three principal invariants are employed to identify promising models for each compound. Especially, appropriate parameter constraints are discussed and the role of the second invariant is analyzed. Thus, this contribution may serve as a guideline for the process of experimental characterization, data processing, model selection and parameter identification for existing as well as new materials.
    Type of Medium: Online Resource
    ISSN: 1134-3060 , 1886-1784
    Language: English
    Publisher: Springer Science and Business Media LLC
    Publication Date: 2023
    detail.hit.zdb_id: 2276736-8
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  • 10
    Online Resource
    Online Resource
    Springer Science and Business Media LLC ; 2023
    In:  Archives of Computational Methods in Engineering Vol. 30, No. 5 ( 2023-06), p. 2889-2927
    In: Archives of Computational Methods in Engineering, Springer Science and Business Media LLC, Vol. 30, No. 5 ( 2023-06), p. 2889-2927
    Abstract: In many aspects, elastomers and soft biological tissues exhibit similar mechanical properties such as a pronounced nonlinear stress–strain relation and a viscoelastic response to external loads. Consequently, many models use the same rheological framework and material functions to capture their behavior. The viscosity function is thereby often assumed to be constant and the corresponding free energy function follows that one of the long-term equilibrium response. This work questions this assumption and presents a detailed study on non-Newtonian viscosity functions for elastomers and brain tissues. The viscosity functions are paired with several commonly used free energy functions and fitted to two different types of elastomers and brain tissues in cyclic and relaxation experiments, respectively. Having identified suitable viscosity and free energy functions for the different materials, numerical aspects of viscoelasticity are addressed. From the multiplicative decomposition of the deformation gradient and ensuring a non-negative dissipation rate, four equivalent viscoelasticity formulations are derived that employ different internal variables. Using an implicit exponential map as time integration scheme, the numerical behavior of these four formulations are compared among each other and numerically robust candidates are identified. The fitting results demonstrate that non-Newtonian viscosity functions significantly enhance the fitting quality. It is shown that the choice of a viscosity function is even more important than the choice of a free energy function and the classical neo-Hooke approach is often a sufficient choice. Furthermore, the numerical investigations suggest the superiority of two of the four viscoelasticity formulations, especially when complex finite element simulations are to be conducted.
    Type of Medium: Online Resource
    ISSN: 1134-3060 , 1886-1784
    Language: English
    Publisher: Springer Science and Business Media LLC
    Publication Date: 2023
    detail.hit.zdb_id: 2276736-8
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