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On the incorporation of a micromechanical material model into the inherent strain method—Application to the modeling of selective laser melting 材料微力学模型与固有应变法的结合——在选择性激光熔化过程建模中的应用
Q1 Mathematics Pub Date : 2021-12-03 DOI: 10.1002/gamm.202200002

In Noll et al.,1 an error was published in the Acknowledgement section. The name “Lena Koppka” was misspelled in the original publication.

The correct Acknowledgement section is presented below:

在Noll et al. 1中,在Acknowledgement部分发布了一个错误。莉娜·科普卡这个名字在最初的出版物中拼写错误。正确的确认部分如下:
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引用次数: 1
Analysis of the sound sources of lean premixed methane–air flames 贫预混甲烷-空气火焰声源分析
Q1 Mathematics Pub Date : 2021-11-23 DOI: 10.1002/gamm.202200001
Sohel Herff, Konrad Pausch, Matthias Meinke, Wolfgang Schröder

Two investigations on the sound generation mechanisms of lean methane–air flames are reviewed and linked. A two-step approach is used for the analysis. First, the compressible conservation equations are solved in a large-eddy simulation formulation to compute the acoustic source terms of the reacting fluid. Second, the acoustic source terms are used in computational aeroacoustics simulations to determine the acoustic field by solving the acoustic perturbation equations. To identify the contributions of the different source terms to the overall sound emission of the flames different source term formulations are considered in the computational aeroacoustics simulations. The results of various flames of increasing complexity are shown: harmonically excited laminar flames, a turbulent jet flame, and an unconfined and a confined swirl flame. The results show that in general the heat release source alone does not determine the acoustic emission of the flame. Only the acoustic emission of the unconfined swirl flame could be computed by the heat release source. To accurately predict the phase and the amplitude of the sound emission of the other flames the acceleration of density gradients occurring at the flame front must be included in the considered set of source terms.

综述了两项关于贫甲烷-空气火焰产生声音机理的研究。分析使用了两步方法。首先,用大涡模拟公式求解可压缩守恒方程,计算反应流体的声源项。其次,将声源项用于计算气动声学模拟,通过求解声扰动方程来确定声场。为了确定不同源项对火焰整体声发射的贡献,在计算气动声学模拟中考虑了不同的源项公式。显示了各种复杂火焰的结果:谐波激发层流火焰,湍流射流火焰,无约束和有约束旋流火焰。结果表明,一般情况下,热源本身不能决定火焰的声发射。只有无约束旋流火焰的声发射可以通过热源计算得到。为了准确地预测其他火焰声发射的相位和振幅,必须在考虑的源项集合中包括发生在火焰前缘的密度梯度加速度。
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引用次数: 2
Simulation-supported characterization of 3D-printed biodegradable structures 模拟支持的3d打印可生物降解结构表征
Q1 Mathematics Pub Date : 2021-11-15 DOI: 10.1002/gamm.202100018
Richard Wolfgang Schirmer, Martin Abendroth, Stephan Roth, Lisa Kühnel, Henning Zeidler, Bjoern Kiefer

In this article, a proof-of-concept study is presented, in which in-situ full-field deformation measurements via digital image correlation, finite element analysis, and nonlinear optimization techniques are combined to characterize the heterogeneous structural behavior of a bio-based material 3D-printed via binder jetting. The special features of this composite material are its biodegradability and its easy manufacturability using conventional 3D printers. The binder-jetting process enables innovative applications such as additively manufactured, highly customized, recyclable, or compostable packaging solutions. Compared to other 3D printing techniques, it is relatively fast and inexpensive and can make use of raw material powders that are by-products of the food or other industries. As an initial step towards gaining a simulation-supported understanding of the complex process-structure-property relations, a first quantitative assessment of the effective behavior of a bio-based binder-jetted material is conducted under the following operating assumptions: (i) Its mechanical response can be described by means of a nonlinear elasto-plastic constitutive law, enriched by a cohesive damage model capturing failure on the structural level, (ii) established mechanical tests on a 3D-printed component, involving standardized sample geometries, and optical measurements, should yield sufficient information to allow the identification of the corresponding material parameters. First, experimental results of optically monitored four-point bending tests, with varying alignments of loading axes and printing directions, are presented in detail. Then the proposed parameter identification strategy is explained and its capabilities and limitations, as made evident from quantitative case studies based on the measured structural response data, are thoroughly discussed.

在本文中,提出了一项概念验证研究,其中结合了通过数字图像相关,有限元分析和非线性优化技术进行现场全场变形测量,以表征通过粘合剂喷射3d打印的生物基材料的非均质结构行为。这种复合材料的特点是它的可生物降解性和使用传统3D打印机易于制造。粘合剂喷射工艺使创新应用成为可能,如增材制造、高度定制、可回收或可堆肥的包装解决方案。与其他3D打印技术相比,它相对快速且便宜,并且可以利用食品或其他行业的副产品原料粉末。作为获得对复杂工艺-结构-性能关系的模拟支持理解的第一步,在以下操作假设下对生物基粘合剂喷射材料的有效行为进行了第一次定量评估:(i)其机械响应可以通过非线性弹塑性本构律来描述,并通过在结构层面上捕获故障的内聚损伤模型来丰富;(ii)对3d打印部件进行的已建立的机械测试,包括标准化的样品几何形状和光学测量,应产生足够的信息,以便确定相应的材料参数。首先,详细介绍了不同加载轴向和打印方向的光学监测四点弯曲试验结果。然后,对所提出的参数识别策略进行了解释,并从基于实测结构响应数据的定量案例研究中,对其能力和局限性进行了深入讨论。
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引用次数: 4
On accurate time integration for temperature evolutions in additive manufacturing 增材制造温度演变的精确时间积分研究
Q1 Mathematics Pub Date : 2021-11-08 DOI: 10.1002/gamm.202100019
Stefan Kollmannsberger, Philipp Kopp

We investigate two numerical challenges in thermal finite element simulations of laser powder bed fusion (LPBF) processes. First, we compare the behavior of first- and second-order implicit time-stepping schemes on a fixed domain. While both methods yield comparable accuracies in the pre-asymptotic regime, the second-order method eventually outperforms the first-order method. However, the oscillations present in the pre-asymptotic range of the second-order method can render it less suitable for simulating LPBF processes. Then, we consider sudden domain extensions resulting from subsequently adding new layers of material with ambient temperature. We model this extension on the continuous level in an energy conservative manner. The discontinuities introduced here reduce the convergence order for both time-stepping schemes to 0.75. First and second order accuracy could only be achieved by strongly grading the time-steps towards the domain expansion.

本文研究了激光粉末床熔合(LPBF)过程热有限元模拟中的两个数值问题。首先,我们比较了一阶和二阶隐式时间步进格式在固定域上的行为。虽然两种方法在前渐近区域产生相当的精度,但二阶方法最终优于一阶方法。然而,二阶方法的前渐近范围内存在振荡,使得它不太适合模拟LPBF过程。然后,我们考虑了由于随后在环境温度下添加新材料层而导致的突然域扩展。我们以能量守恒的方式在连续水平上对这种扩展进行建模。这里引入的不连续将两种时间步进方案的收敛阶降低到0.75。一阶和二阶精度只能通过向域展开方向强烈分级时间步来实现。
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引用次数: 5
Preface on mechanics of additive manufacturing—Part II 增材制造力学前言——第二部分
Q1 Mathematics Pub Date : 2021-11-04 DOI: 10.1002/gamm.202100020
Thorsten Bartel, Markus Kästner, Björn Kiefer, Andreas Menzel
In the first part of this two-part special issue, the focus is on the modeling and simulation of elementary processes within various materials that can be used for additive manufacturing. It comprises selective laser sintering of polymers, topology optimization in the context of additively manufactured structures, a general overview on the challenges related to the modeling and simulation of powder bed fusion additive manufacturing as well as the modeling of phase changes during Selective Laser Melting and the related analysis of process-induced inherent strains. As sophisticated as these models may be, they also require experimental data for verification and validation. The more complex the modeled and simulated processes, as well as the material models themselves, become the more important becomes the sound and comprehensive experimental characterization and experimental investigation of the effective material behavior. Even with accurate and experimentally verified material and process models successfully developed and established the general challenge of their algorithmic implementation remains. In this context, it is essential to establish efficient and robust numerical methods, some of which have to be newly developed due to the high numerical complexity. The contributions of this Part II of the Special Issue of the Surveys for Applied Mathematics and Mechanics (GAMM-Mitteilungen) mainly focus on these above-mentioned aspects: The paper referenced by Kollmannsberger and Kopp [1] elaborates advanced modeling and simulation approaches with emphasis on different time scales. This includes, among other topics, the investigation and comparison of different time-stepping schemes with special focus on robustness, prevention of oscillating solutions and general applicability. In Zhou et al. [2], a multilayer phase-field simulation of selective sintering process and the calculation of effective mechanical properties and residual stresses is proposed. In this regard, quantitative relations between the process parameters and the microstructure and its properties are established. The contribution of Schirmer et al. [3] addresses the additive manufacturing of a novel class of bio-based materials via binder-jetting. The highly customizable printed structures are recyclable and use renewable raw materials that are often industrial by-products. The article presents a proof-of-concept study, in which digital image correlation, finite element analysis and optimization techniques are combined to characterize the heterogeneous structural behavior of such 3D-printed biodegradable materials. The work presented in Raßloff et al. [4] aims at the prediction of structure–property linkages for additively manufactured materials with a particular focus on process-induced imperfections like pores. It uses light microscopy and X-ray computed tomography to determine microstructure characteristics of Ti–6Al–4V in combination with microscale simulations to assess the influe
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引用次数: 0
3D-multilayer simulation of microstructure and mechanical properties of porous materials by selective sintering 选择性烧结多孔材料微观结构和力学性能的三维多层模拟
Q1 Mathematics Pub Date : 2021-10-19 DOI: 10.1002/gamm.202100017
Xiandong Zhou, Yangyiwei Yang, Somnath Bharech, Binbin Lin, Jörg Schröder, Bai-Xiang Xu

This work presents multilayer phase-field simulation of selective sintering process and the calculation of effective mechanical properties and residual stress of the microstructure using the finite element method. The dependence of the effective properties and residual stress on the process parameters, such as beam power and scan speed, are analyzed. Significant partial melting of powders is observed for large beam power and low scan speed, which results in low porosity of the microstructure. Nonlinear relationship between the effective mechanical properties and process parameters is observed. The increasing rate of effective mechanical properties decreases with increasing beam power, while increases with decreasing scan speed. The dependence of effective Young's modulus and Poisson's ratio on porosity are well established using power law models. Stress concentrations are found at the necking region of powders and the intensity increases with the level of partial melting, which results in increasing residual stress in the microstructure. The numerical results reveal quantitatively the process-microstructure-property relation, which implies the feasibility of the subsequent data-driven approach.

本文对选择性烧结过程进行了多层相场模拟,并采用有限元法计算了微观组织的有效力学性能和残余应力。分析了光束功率和扫描速度对有效性能和残余应力的影响。较大的光束功率和较低的扫描速度导致粉末明显的部分熔化,导致微观组织孔隙率低。观察到有效力学性能与工艺参数之间存在非线性关系。有效力学性能的增长速率随光束功率的增大而减小,随扫描速度的减小而增大。利用幂律模型很好地建立了有效杨氏模量和泊松比与孔隙度的关系。应力集中在粉末颈部,应力强度随部分熔化程度的增加而增大,导致显微组织中残余应力增大。数值结果定量地揭示了过程-微观结构-性能之间的关系,为后续数据驱动方法的可行性提供了依据。
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引用次数: 11
Preface on mechanics of additive manufacturing—Part I 增材制造力学前言——第一部分
Q1 Mathematics Pub Date : 2021-09-17 DOI: 10.1002/gamm.202100016
Thorsten Bartel, Markus Kästner, Björn Kiefer, Andreas Menzel
Additive manufacturing processes—often referred to as 3D printing—have developed since the 1980s into a promising and groundbreaking way of producing components and workpieces with geometries of almost any complexity. And the developments continue to advance! In the meantime, various methods that can be divided into different categories have been introduced. To cover just a few of the most common methods, inkjet technologies, material extrusion, powder bed fusion, direct energy deposition, and stereolithography shall be mentioned here. The latter is considered in some sources to be virtually the starting point of additive manufacturing. The category “powder bed fusion” includes processes such as selective laser sintering, selective laser melting, and electron beam melting. Laser cladding is an example of direct energy deposition. In conventional subtractive manufacturing processes, the final contour of the component is achieved by material removal. In contrast, additive manufacturing processes are characterized by the targeted addition of the respective material to the component layer by layer. The great potential of these processes is evident in the aerospace and automotive industries as well as in biomedical technology, and especially in the manufacturing of custom-made products and lightweight constructions. Developments have even gone so far that local material properties can be specifically adjusted by, for example, adapting the material feed. Moreover, no tools or joining processes are in principle required for direct manufacturing. Additive manufacturing processes can thus be initiated and adapted in a much faster and straight-forward way. For applied mathematics and mechanics, additive manufacturing opens up numerous new perspectives and opportunities, but also major challenges. Particularly in the field of topology optimization, additive manufacturing seems to overcome a previously existing and seemingly insurmountable limitation, namely that of realizability. Until recently, the mathematically optimal structure, for example, in the sense of an optimum density distribution within a given design space, was always subjected to the constraint that the structure must also be manufacturable via conventional methods. Among other things, voids were not allowed to become too small and the density distribution had to be binary—either “no material” or “full material”. Nowadays, additive manufacturing processes indeed enable the production of the mathematically/physically optimal structures. With regard to the modeling of the material and structural behavior of additively manufactured components, numerous new challenges arise. In order to be able to perform load-bearing capacity verifications, the constitutive behavior of the material finally obtained must be modeled and predicted as accurately as possible. In this context, the manufacturing process results in specific and spatially highly inhomogeneously distributed residual stresses, which can ha
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引用次数: 0
On the incorporation of a micromechanical material model into the inherent strain method—Application to the modeling of selective laser melting 材料微力学模型与固有应变法的结合——在选择性激光熔化过程建模中的应用
Q1 Mathematics Pub Date : 2021-09-09 DOI: 10.1002/gamm.202100015
Isabelle Noll, Thorsten Bartel, Andreas Menzel

When developing reliable and useful models for selective laser melting processes of large parts, various simplifications are necessary to achieve computationally efficient simulations. Due to the complex processes taking place during the manufacturing of such parts, especially the material and heat source models influence the simulation results. If accurate predictions of residual stresses and deformation are desired, both complete temperature history and mechanical behavior have to be included in a thermomechanical model. In this article, we combine a multiscale approach using the inherent strain method with a newly developed phase transformation model. With the help of this model, which is based on energy densities and energy minimization, the three states of the material, namely, powder, molten, and resolidified material, are explicitly incorporated into the thermomechanically fully coupled finite-element-based process model of the micromechanically motivated laser heat source model and the simplified layer hatch model.

在为大型零件的选择性激光熔化过程建立可靠和有用的模型时,为了实现计算效率的模拟,需要进行各种简化。由于此类零件的制造过程复杂,特别是材料模型和热源模型对仿真结果的影响较大。如果需要准确预测残余应力和变形,则必须在热力学模型中包括完整的温度历史和力学行为。本文将固有应变法的多尺度方法与新建立的相变模型相结合。利用该基于能量密度和能量最小化的模型,将材料的粉末、熔融和再凝固三种状态明确纳入微机械驱动激光热源模型的热力全耦合有限元过程模型和简化层hatch模型中。
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引用次数: 5
Physics-based modeling and predictive simulation of powder bed fusion additive manufacturing across length scales 基于物理的粉末床熔融增材制造跨长度尺度建模和预测仿真
Q1 Mathematics Pub Date : 2021-08-22 DOI: 10.1002/gamm.202100014
Christoph Meier, Sebastian L. Fuchs, Nils Much, Jonas Nitzler, Ryan W. Penny, Patrick M. Praegla, Sebastian D. Proell, Yushen Sun, Reimar Weissbach, Magdalena Schreter, Neil E. Hodge, A. John Hart, Wolfgang A. Wall

Powder bed fusion additive manufacturing (PBFAM) of metals has the potential to enable new paradigms of product design, manufacturing and supply chains while accelerating the realization of new technologies in the medical, aerospace, and other industries. Currently, wider adoption of PBFAM is held back by difficulty in part qualification, high production costs and low production rates, as extensive process tuning, post-processing, and inspection are required before a final part can be produced and deployed. Physics-based modeling and predictive simulation of PBFAM offers the potential to advance fundamental understanding of physical mechanisms that initiate process instabilities and cause defects. In turn, these insights can help link process and feedstock parameters with resulting part and material properties, thereby predicting optimal processing conditions and inspiring the development of improved processing hardware, strategies and materials. This work presents recent developments of our research team in the modeling of metal PBFAM processes spanning length scales, namely mesoscale powder modeling, mesoscale melt pool modeling, macroscale thermo-solid-mechanical modeling and microstructure modeling. Ongoing work in experimental validation of these models is also summarized. In conclusion, we discuss the interplay of these individual submodels within an integrated overall modeling approach, along with future research directions.

金属粉末床熔融增材制造(pbam)有可能实现产品设计、制造和供应链的新范式,同时加速医疗、航空航天和其他行业新技术的实现。目前,由于在最终零件生产和部署之前需要进行大量的工艺调整、后处理和检查,零件鉴定困难、生产成本高和生产率低阻碍了pfam的广泛采用。基于物理的pbam建模和预测模拟提供了对引发工艺不稳定和导致缺陷的物理机制的基本理解的潜力。反过来,这些见解可以帮助将工艺和原料参数与产生的零件和材料特性联系起来,从而预测最佳加工条件,并激发改进加工硬件、策略和材料的发展。这项工作介绍了我们的研究团队在金属pfam过程跨长度尺度建模方面的最新进展,即中尺度粉末建模、中尺度熔池建模、宏观热固力学建模和微观结构建模。还总结了这些模型在实验验证方面正在进行的工作。最后,我们讨论了这些单独的子模型在集成的整体建模方法中的相互作用,以及未来的研究方向。
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引用次数: 19
Additive manufacturing applications of phase-field-based topology optimization using adaptive isogeometric analysis 增材制造中基于相场的自适应等几何分析拓扑优化应用
Q1 Mathematics Pub Date : 2021-08-12 DOI: 10.1002/gamm.202100013
Massimo Carraturo, Paul Hennig, Gianluca Alaimo, Leonhard Heindel, Ferdinando Auricchio, Markus Kästner, Alessandro Reali
In this contribution, we apply adaptive isogeometric analysis to a diffuse interface model for topology optimization. First, the influence of refinement and coarsening parameters on the optimization procedure are evaluated and discussed on a two‐dimensional problem and a possible workflow to convert smooth isogeometric solutions into 3D printed products is described. Second, to assess the required numerical accuracy of the proposed simulation framework, numerical results obtained adopting different stopping criteria are experimentally evaluated for a three‐dimensional benchmark problem.
在这篇贡献中,我们将自适应等几何分析应用于漫射界面模型的拓扑优化。首先,在二维问题上评估和讨论了精化和粗化参数对优化过程的影响,并描述了将光滑等几何解转化为3D打印产品的可能工作流程。其次,为了评估所提出的仿真框架所需的数值精度,对三维基准问题采用不同停止准则得到的数值结果进行了实验评估。
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引用次数: 10
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GAMM Mitteilungen
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