{"title":"A Stochastic Method of Moving Asymptotes for Topology Optimization Under Uncertainty","authors":"Lukas Pflug, Michael Stingl, Andrian Uihlein","doi":"10.1002/nme.70109","DOIUrl":"https://doi.org/10.1002/nme.70109","url":null,"abstract":"<p>Topology optimization under uncertainty or reliability-based topology optimization is usually numerically very expensive. This is mainly due to the fact that an accurate evaluation of the probabilistic model requires the system to be simulated for a large number of varying parameters. Traditional gradient-based optimization schemes thus face the difficulty that reasonable accuracy and numerical efficiency often seem mutually exclusive. In this work, we propose a stochastic optimization technique to tackle this problem. To be precise, we combine the well-known method of moving asymptotes (MMA) with a stochastic sample-based integration strategy. By adaptively recombining gradient information from previous steps, we obtain a noisy gradient estimator that is asymptotically correct, that is, the approximation error vanishes over the course of iterations. As a consequence, the resulting stochastic method of moving asymptotes (sMMA) allows us to solve chance constraint topology optimization problems for a fraction of the cost compared to traditional approaches from literature. To demonstrate the efficiency of sMMA, we analyze structural optimization problems in two and three dimensions.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 16","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70109","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144892478","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Axel Bral, Jozef Peeters, Lode Daelemans, Joris Degroote
{"title":"Development and Validation of an Actuator Line Method for Fuzzy Yarns in High-Speed Air Flow","authors":"Axel Bral, Jozef Peeters, Lode Daelemans, Joris Degroote","doi":"10.1002/nme.70108","DOIUrl":"https://doi.org/10.1002/nme.70108","url":null,"abstract":"<div>\u0000 \u0000 <p>Air-jet weaving relies on high-speed air flow to propel the weft yarns through the machine, achieving high insertion rates but at the cost of a significant energy demand. Capturing the interactions between the air jets and the weft yarns, which often have a fuzzy surface structure, is therefore vital in improving the air-jet weaving process. To achieve this, this work introduces a cost-efficient method to represent fuzzy staple-fibre yarns in Computational Fluid Dynamics (CFD) simulations by adapting the Actuator Line Method (ALM). The methodology addresses the drag-dominated aerodynamic forces acting on the yarn by introducing an upstream velocity sampling procedure. These forces are then introduced in the flow domain in a smooth and continuous manner using the actuator curve embedding principle, allowing relatively coarse mesh resolutions while still providing a correct prediction of the aerodynamic forces. The method is validated numerically through comparison with high-fidelity fibre-resolved simulations in uniform flow. Results show maximal errors in the force prediction of approximately <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>15</mn>\u0000 <mo>%</mo>\u0000 </mrow>\u0000 <annotation>$$ 15% $$</annotation>\u0000 </semantics></math> in cross flow with narrow force regularization kernels and a force distribution error below <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 <mo>%</mo>\u0000 </mrow>\u0000 <annotation>$$ 1% $$</annotation>\u0000 </semantics></math> while reducing the cell count by two orders of magnitude. Additionally, the methodology was also validated experimentally in non-uniform flow and the simulations of these jet flow experiments show excellent agreement with the measured aerodynamic forces on the yarns for various orientations and supply pressures. This actuator line approach significantly reduces the computational cost by bypassing the need for microscale flow resolution around fuzzy yarn surfaces. For this reason, it opens the door to large-scale coupled fluid-structure interaction (FSI) simulations of the yarn insertion process in air-jet weaving.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 16","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144881127","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Nonlinear Dynamics and Control of Reissner's 2D Geometrically Exact Beam by Distributed Port-Hamiltonian System","authors":"Suljo Ljukovac, Adnan Ibrahimbegovic, Maida Cohodar Husic","doi":"10.1002/nme.70103","DOIUrl":"https://doi.org/10.1002/nme.70103","url":null,"abstract":"<div>\u0000 \u0000 <p>Port Hamiltonian systems formalism [1] is proposed for providing the general control theory for finite-dimensional systems, with the models typically used in multibody dynamics (such as rigid components interconnected with flexible joints, or ports). Many present applications require better modeling of the system flexibility (and risk of damage), and one has to consider infinite-dimensional systems. The nonlinear dynamics and control of such a system in terms of Reissner's geometrically exact beam are studied in this work. More precisely, we first present the theoretical formulation for nonlinear dynamics for a 2D Reissner's beam constructed as a port-Hamiltonian system. This results in a highly nonlinear problem due to nonlinear beam kinematics capable of representing finite displacements, rotations, and strains. The port Hamiltonian formulation suitable for the (nonlinear) control problems is then developed by selecting appropriate effort and flow variables, and the model is reformulated as a coupled system of first-order partial differential equations in a structure-preserving format in a continuum setting. We then develop an expanded format required for a nonlinear system and the corresponding variational formulation by using the principle of virtual power, with the boundary conditions defining the port variables that are used in control. The final step is the finite element discretization by using finite element interpolations for such a nonlinear port-Hamiltonian formulation, resulting in a set of nonlinear ordinary differential equations with nodal degrees that count displacements, rotation, linear and angular velocities, forces, and moments, which provides the greatest flexibility in choosing control strategies. This set of differential equations is here integrated by the backward Euler scheme, resulting in a nonlinear system of algebraic equations. The consistent linearization of such a system provides a robust performance for the proposed port Hamiltonian formulation. This is illustrated with the results of several numerical simulations that confirm the improved performance in energy conservation, which is superior to those provided previously by energy-conserving time integration schemes that have been constructed for fully discretized problems [2].</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 16","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144869757","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Thi-Hoa Nguyen, Bruno A. Roccia, Dominik Schillinger, Cristian G. Gebhardt
{"title":"A Study on Nodal and Isogeometric Formulations for Nonlinear Dynamics of Shear- and Torsion-Free Rods","authors":"Thi-Hoa Nguyen, Bruno A. Roccia, Dominik Schillinger, Cristian G. Gebhardt","doi":"10.1002/nme.70104","DOIUrl":"https://doi.org/10.1002/nme.70104","url":null,"abstract":"<div>\u0000 \u0000 <p>In this work, we compare the nodal and isogeometric spatial discretization schemes for the nonlinear formulation of shear- and torsion-free rods introduced in Gebhardt and Romero (see Reference no. 31). We investigate the resulting discrete solution space, the accuracy, and the computational cost of these spatial discretization schemes. To fulfill the required <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mi>C</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$$ {C}^1 $$</annotation>\u0000 </semantics></math> continuity of the rod formulation, the nodal scheme discretizes the rod in terms of its nodal positions and directors using cubic Hermite splines. Isogeometric discretizations naturally fulfill this with smooth spline basis functions and discretize the rod only in terms of the positions of the control points (see Nguyen et al. in Reference no. 41), which leads to a discrete solution in multiple copies of the Euclidean space <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mi>ℝ</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>3</mn>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$$ {mathbb{R}}^3 $$</annotation>\u0000 </semantics></math>. They enable the employment of basis functions of one degree lower, that is, quadratic <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mi>C</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$$ {C}^1 $$</annotation>\u0000 </semantics></math> splines, and possibly reduce the number of degrees of freedom (dofs). When using the nodal scheme, since the defined director field is in the unit sphere <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mi>S</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$$ {S}^2 $$</annotation>\u0000 </semantics></math>, preserving this for the nodal director variable field requires an additional constraint of unit nodal directors. This leads to a discrete solution in multiple copies of the manifold <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mrow","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 16","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144869756","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Real-World Steel Frame Optimization Using a Hybrid Leader Selection-Based Multi-Objective Flow Direction Algorithm","authors":"Truong Vu-Huu, Samir Khatir, Thanh Cuong-Le","doi":"10.1002/nme.70098","DOIUrl":"https://doi.org/10.1002/nme.70098","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper presents a novel Multi-Objective Flow Direction Algorithm (MOFDA) for complex engineering optimization problems. The key innovation is a hybrid leader selection mechanism, which replaces the conventional roulette wheel selection and significantly enhances convergence and diversity in identifying Pareto-optimal solutions. The proposed MOFDA is rigorously evaluated on 31 standard benchmark problems and 11 constrained engineering design cases—including truss optimization, welded beam design, and a large-scale steel frame structure—to assess its accuracy, stability, and solution diversity comprehensively. Comparative studies with state-of-the-art multi-objective algorithms such as MOMVO, MOMSA, MSSA, and MOGNDO further highlight the strong performance of MOFDA. In addition, MOFDA is integrated into a MATLAB–SAP2000 framework and applied to the real-world structural optimization of the Dong Bai ferry terminal steel frame in Vietnam. The results show that MOFDA consistently achieves competitive or superior outcomes on benchmark functions, delivers substantial weight reduction, and improves structural efficiency in engineering applications. These findings demonstrate both the proposed approach's technical novelty and practical effectiveness. Source codes of MOFDA is publicly available at \u0000https://ceats.ou.edu.vn/us/codes.html.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 15","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144782437","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Generalized Summation Rule-Based Nonlocal Quasicontinuum Approach (GSR-QC) for Efficient Modeling of Architected Lattice Structures","authors":"Zi Li, Fan Yang, Qingcheng Yang","doi":"10.1002/nme.70093","DOIUrl":"https://doi.org/10.1002/nme.70093","url":null,"abstract":"<div>\u0000 \u0000 <p>To address the substantial computational cost in modeling the mechanical behavior of large-scale architected lattice structures, this work introduces a concurrent multiscale framework: the generalized summation rule-based nonlocal quasicontinuum (GSR-QC) method. The core innovation is a generalized summation rule that enables accurate coarse-graining consistent with general finite element shape functions. While a few existing approaches have explored summation rules for higher-order interpolation, such efforts remain limited and are typically tailored to specific element types or applications. In contrast, the proposed framework provides a unified and systematic approach that ensures compatibility with general shape functions, significantly enhancing the flexibility and applicability of nonlocal quasicontinuum methods. The GSR-QC method features: (1) constitutive-model consistency, employing the same discrete lattice model in both fully resolved and coarse-grained regions; (2) shape-function-consistent energy sampling, aligned rigorously with the interpolation order of general finite elements; and (3) interfacial compatibility, enabling seamless energy and force transfer across regions of differing resolutions without additional interface treatment. The performance of GSR-QC is validated using bilinear quadrilateral and quadratic triangular elements across benchmark problems—including uniaxial tension, clamped bending, three-point bending, and crack propagation in truss-based lattice structures—demonstrating good accuracy. Additionally, the error analysis and convergence behavior of GSR-QC are investigated.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 15","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144782417","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The Novel High-Order Updated-Lagrangian Nonlocal General Particle Dynamics for Transient Anisotropic Seepage Problems in Unsaturated Porous Media","authors":"Peng Yin, Xiao-Ping Zhou","doi":"10.1002/nme.70091","DOIUrl":"https://doi.org/10.1002/nme.70091","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, the novel high-order updated Lagrangian nonlocal general particle dynamics (UL-NGPD) is first proposed to solve anisotropic transient seepage flow problems, in which the novel high-order spatially nonlocal operators are first established to obtain accurate second-order nonlocal differential derivatives. The novel high-order UL-NGPD formulation and its corresponding numerical implementations of boundary conditions and time integration for seepage problems are established, which are capable of automatically capturing seepage surfaces without extra treatments and consider the complete time-dependent transition from unsaturated to saturated states. The capabilities of the proposed high-order UL-NGPD method in solving the complex seepage flow problems are verified by several examples. The numerical results are in good agreement with theoretical solutions. This indicates that the newly proposed high-order UL-NGPD method is powerful and suitable for solving complex transient seepage flow problems, which marks a significant milestone for its future application to solving fully coupled flow deformation problems involving large deformation and failure of porous media.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 15","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144782527","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Total Lagrangian Stochastic Finite Element Method for Hyperelastic Analysis With Uncertainties","authors":"Zhibao Zheng, Udo Nackenhorst","doi":"10.1002/nme.70090","DOIUrl":"https://doi.org/10.1002/nme.70090","url":null,"abstract":"<p>This article presents a total Lagrangian stochastic finite element method to solve hyperelastic problems with uncertainties. Similar to deterministic hyperelastic analysis, prescribed external forces or boundary values are applied through a series of load steps. By using a stochastic Newton-Raphson method, the stochastic hyperelastic analysis at each load step is linearized as a series of linear stochastic equations. To avoid the use of stochastic configurations from intermediate load steps, all analyses are performed on the initial configuration, thus referred to as a total Lagrangian method. Each stochastic increment of the stochastic solution is then approximated as the product of a random variable and a deterministic vector, and they are solved through a dedicated iteration. Specifically, the deterministic vector is solved using linear deterministic equations, and the corresponding random variable is calculated through one-dimensional stochastic algebraic equations that can be solved efficiently using a sample-based strategy, even for very high-dimensional random inputs. In this way, the proposed method avoids the curse of dimensionality to a great extent. 2D and 3D numerical examples with up to 100 stochastic dimensions demonstrate the promising performance of the proposed method.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 15","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70090","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144782526","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"An Enriched Equilibrium Finite Element Method for Crack Problems With Direct Access to Stress Intensity Factors and Strict Error Estimation","authors":"Qisheng Zheng, Jike Liu, Li Wang","doi":"10.1002/nme.70097","DOIUrl":"https://doi.org/10.1002/nme.70097","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper proposes an enriched equilibrium finite element method (EFEM) for addressing crack problems within the framework of linear elastic fracture mechanics and complementary energy principle. The key ingredient of enriched EFEM is to construct the equilibrated stress field using equilibrated tractions along with asymptotic enrichment. Specifically, an auxiliary field is employed to capture the asymptotic singular behavior of the near-tip stress field, while the traction-based equilibrium finite element accounts for the residual terms. The remarkable property of the proposed enriched EFEM is that the stress intensity factors (SIFs) and the stress fields are directly obtained with high accuracy, even on a very coarse mesh. Moreover, in combination with the compatible solution acquired by the enriched finite element method (FEM), strict estimation of the discretization error is obtained for crack problems by dual analysis. Numerical examples are finally conducted to verify the performance of the proposed method on strict error estimation and accurate computation of the SIFs.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 15","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144751670","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Celine Lauff, Maximilian Krause, Matti Schneider, Thomas Böhlke
{"title":"On the Influence of the Fiber Curvature on the Stiffness of Long Fiber Reinforced Composites","authors":"Celine Lauff, Maximilian Krause, Matti Schneider, Thomas Böhlke","doi":"10.1002/nme.70094","DOIUrl":"https://doi.org/10.1002/nme.70094","url":null,"abstract":"<p>The degree of curvature of fiber inclusions in fiber-reinforced composites impacts the elastic properties of the composite, but numerical studies of this effect are limited by the lack of efficient microstructure generators with fiber curvature control. We propose an extension to the fused Sequential Addition and Migration algorithm (<i>Int. J. Numer. Methods Eng.</i>, 125(22), e7573, 2024) to allow for the direct control of the average fiber curvature. To this end, we prescribe an averaged curvature parameter for the entire microstructure, while also constraining local curvature for every fiber to a maximum value. While local curvature is unambiguously defined, the choice of the averaged curvature parameter is not obvious. We introduce as a novel curvature measure the deviation from straight curve (DSC), which computes as the trace of the local second-order fiber orientation tensor's covariance for a single fiber. Averaging this over all fibers leads to a scalar averaged curvature parameter. Using this parameter, we define an optimization procedure for generating curved-fiber reinforced microstructures. We compare the microstructure generation capabilities of the proposed extension with the prior algorithm without curvature control and find that the extended algorithm is capable of realizing a significantly wider spectrum of curvatures. Finally, we study the influence of fiber curvature on elastic properties, and find that for an example composite of glass-fiber reinforced polypropylene, increased fiber curvature leads to a reduction of the Young's modulus by as much as 10%.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 15","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70094","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144751671","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}