{"title":"Discovering uncertainty: Bayesian constitutive artificial neural networks","authors":"Kevin Linka , Gerhard A. Holzapfel , Ellen Kuhl","doi":"10.1016/j.cma.2024.117517","DOIUrl":"10.1016/j.cma.2024.117517","url":null,"abstract":"<div><div>Understanding uncertainty is critical, especially when data are sparse and variations are large. Bayesian neural networks offer a powerful strategy to build predictable models from sparse data, and inherently quantify both, aleatoric uncertainties of the data and epistemic uncertainties of the model. Yet, classical Bayesian neural networks ignore the fundamental laws of physics, they are non-interpretable, and their parameters have no physical meaning. Here we integrate concepts of Bayesian learning and constitutive neural networks to discover interpretable models, parameters, and uncertainties that best explain soft matter systems. Instead of training an individual constitutive neural network and learning point values of the network weights, we train an ensemble of networks and learn probability distributions of the weights, along with their means, standard deviations, and credible intervals. We use variational Bayesian inference and adopt an efficient backpropagation-compatible algorithm that approximates the true probability distributions by simpler distributions and minimizes their divergence through variational learning. When trained on synthetic data, our Bayesian constitutive neural network successfully rediscovers the initial model, even in the presence of noise, and robustly discovers uncertainties, even from incomplete data. When trained on real data from healthy and aneurysmal human arteries, our network discovers a model with more stretch stiffening, more anisotropy, and more uncertainty for diseased than for healthy arteries. Our results demonstrate that Bayesian constitutive neural networks can successfully discriminate between healthy and diseased arteries, robustly discover interpretable models and parameters for both, and efficiently quantify uncertainties in model discovery. We anticipate our approach to generalize to other soft biomedical systems for which real-world data are rare and inter-personal variations are large. Ultimately, our calculated uncertainties will help enhance model robustness, promote personalized predictions, enable informed decision-making, and build confidence in automated model discovery and simulation. Our source code, data, and examples are available at <span><span>https://github.com/LivingMatterLab/CANN</span><svg><path></path></svg></span>.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"433 ","pages":"Article 117517"},"PeriodicalIF":6.9,"publicationDate":"2024-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142637444","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Vincent C. Scholz , Yaohua Zang , Phaedon-Stelios Koutsourelakis
{"title":"Weak neural variational inference for solving Bayesian inverse problems without forward models: Applications in elastography","authors":"Vincent C. Scholz , Yaohua Zang , Phaedon-Stelios Koutsourelakis","doi":"10.1016/j.cma.2024.117493","DOIUrl":"10.1016/j.cma.2024.117493","url":null,"abstract":"<div><div>In this paper, we introduce a novel, data-driven approach for solving high-dimensional Bayesian inverse problems based on partial differential equations (PDEs), called Weak Neural Variational Inference (WNVI). The method complements real measurements with virtual observations derived from the physical model. In particular, weighted residuals are employed as probes to the governing PDE in order to formulate and solve a Bayesian inverse problem <em>without</em> ever formulating nor solving a forward model. The formulation treats the state variables of the physical model as latent variables, inferred using Stochastic Variational Inference (SVI), along with the usual unknowns. The approximate posterior employed uses neural networks to approximate the inverse mapping from state variables to the unknowns. We illustrate the proposed method in a biomedical setting where we infer spatially-varying, material properties from noisy, tissue deformation data. We demonstrate that WNVI is not only as accurate and more efficient than traditional methods that rely on repeatedly solving the (non)linear forward problem as a black-box, but it can also handle ill-posed forward problems (e.g., with insufficient boundary conditions).</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"433 ","pages":"Article 117493"},"PeriodicalIF":6.9,"publicationDate":"2024-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142637446","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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":"Convolution tensor decomposition for efficient high-resolution solutions to the Allen–Cahn equation","authors":"Ye Lu , Chaoqian Yuan , Han Guo","doi":"10.1016/j.cma.2024.117507","DOIUrl":"10.1016/j.cma.2024.117507","url":null,"abstract":"<div><div>This paper presents a convolution tensor decomposition based model reduction method for solving the Allen–Cahn equation. The Allen–Cahn equation is usually used to characterize phase separation or the motion of anti-phase boundaries in materials. Its solution is time-consuming when high-resolution meshes and large time scale integration are involved. To resolve these issues, the convolution tensor decomposition method is developed, in conjunction with a stabilized semi-implicit scheme for time integration. The development enables a powerful computational framework for high-resolution solutions of Allen–Cahn problems, and allows the use of relatively large time increments for time integration without violating the discrete energy law. To further improve the efficiency and robustness of the method, an adaptive algorithm is also proposed. Numerical examples have confirmed the efficiency of the method in both 2D and 3D problems. Orders-of-magnitude speedups were obtained with the method for high-resolution problems, compared to the finite element method. The proposed computational framework opens numerous opportunities for simulating complex microstructure formation in materials on large-volume high-resolution meshes at a deeply reduced computational cost.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"433 ","pages":"Article 117507"},"PeriodicalIF":6.9,"publicationDate":"2024-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142637445","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Luyu Li , Zhihao Yan , Shichao Wang , Xue Zhang , Xinglang Fan
{"title":"A novel data-driven framework of elastoplastic constitutive model based on geometric physical information","authors":"Luyu Li , Zhihao Yan , Shichao Wang , Xue Zhang , Xinglang Fan","doi":"10.1016/j.cma.2024.117513","DOIUrl":"10.1016/j.cma.2024.117513","url":null,"abstract":"<div><div>The advantages of data science have inspired the development of data-driven approaches for solving constitutive modeling problems, which have become a new research focus in engineering mechanics. These approaches help fully utilize the information inherent in the data, bypassing the traditional modeling processes.</div><div>In order to advance the development of Constitutive Model Based on Data-Driven (CMBDD), we introduced a novel framework called the Geometric Physical <strong>I</strong>nformation-enhanced <strong>D</strong>ata-<strong>D</strong>riven <strong>E</strong>lasto<strong>P</strong>lastic constitutive model (IDD-EP) under hysteretic loading paths. IDD-EP adopts an ”Encoder-Decoder” framework, with the information transmission between the encoder and decoder facilitated by the ”Geometric Physical Information” proposed in this paper. Specifically, IDD-EP-I, serving as the encoder, extracts Geometric Physical Information from experimental constitutive images, which is then transmitted to the modular data-driven decoder IDD-EP-II, designed based on physical mechanisms, to compute material responses under arbitrary paths. IDD-EP aims to establish a constitutive model relying solely on a single small sample without using deep learning techniques and avoids the challenge of model parameter fitting in classical models through a non-mathematical model design.</div><div>In addition to discussing the general framework of IDD-EP, this paper specifically demonstrates a specialized version of the IDD-EP framework based on uniaxial buckling-restrained braces (BRBs), which are commonly used in structural vibration control, in order to showcase a specific implementation example of the IDD-EP model. The IDD-EP method in this paper accurately predicts the mechanical response of the BRB using only one constitutive experimental image, without the need to pre-select a base constitutive model or fit model parameters. This innovative approach to IDD-EP opens a new avenue for constitutive modeling of elastoplastic materials and may offer solutions to a wider range of history-dependent constitutive modeling challenges in the future.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"433 ","pages":"Article 117513"},"PeriodicalIF":6.9,"publicationDate":"2024-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142637365","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Liming Chen , Qingshan Wang , Zan Yang , Haobo Qiu , Liang Gao
{"title":"Optimization of expensive black-box problems with penalized expected improvement","authors":"Liming Chen , Qingshan Wang , Zan Yang , Haobo Qiu , Liang Gao","doi":"10.1016/j.cma.2024.117521","DOIUrl":"10.1016/j.cma.2024.117521","url":null,"abstract":"<div><div>This paper proposes a new infill criterion for the optimization of expensive black-box design problems. The method complements the classical Efficient Global Optimization algorithm by considering the distribution of improvement instead of merely the expectation. During the optimization process, we maximize a penalized expected improvement acquisition function from a specially collected infill candidate set. Specifically, the acquisition function is formulated by penalizing the expected improvement with the variation of improvement, and the infill candidate set is composed of some global and local maxima of the expected improvement function which are identified to be “mutually non-dominated”. Some conditions necessary for setting the penalty coefficient of the acquisition function are investigated, and the definition of “mutually non-dominated infill candidates” is presented. The proposed method is demonstrated with a 1-D analytical function and benchmarked using six 10-D analytical functions and an underwater vehicle structural optimization problem. The results show that the proposed method is efficient for the optimization of expensive black-box design problems.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"433 ","pages":"Article 117521"},"PeriodicalIF":6.9,"publicationDate":"2024-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142637443","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Peridynamic modelling of time-dependent behaviour and creep damage in hyper-viscoelastic solids with pre-cracks","authors":"Luyu Wang , Zhen-Yu Yin","doi":"10.1016/j.cma.2024.117512","DOIUrl":"10.1016/j.cma.2024.117512","url":null,"abstract":"<div><div>Time-dependent deformation and damage in viscoelastic materials exhibit distinct characteristics compared to purely brittle or ductile materials, especially under large deformations. These behaviours become even more complex in the presence of pre-cracks. To model this process, we propose an improved non-ordinary state-based peridynamics (NOSB-PD) with implicit adaptive time-stepping (IATS). The proposed formulation encompasses several key aspects, including peridynamic governing equations, improvements to the conventional NOSB-PD, incorporation of a hyper-viscoelastic constitutive model, and an implicit discretization method. The highlights of this study include: (1) Proposing an improved NOSB-PD integrated with a stabilised bond-associated (BA) scheme; (2) Incorporating a hyper-viscoelastic constitutive model combined with a damage model into the framework; (3) Developing a novel IATS method for efficient simulation of time-dependent behaviours; and (4) Exploring the effects of crack patterns and material properties on damage evolution, offering key insights into underlying mechanisms. Then, numerical examples are conducted using the proposed IATS BA-NOSB-PD to simulate hyper-viscoelastic deformation and creep damage. Numerical performance is thoroughly evaluated through benchmark tests, demonstrating that the proposed method effectively simulates creep processes under stepwise loading and unloading conditions. The effects of crack patterns, critical energy release rate, and shear modulus on creep damage are explored in-depth. The results reveal that the propagation and coalescence of multiple cracks take longer compared to a single crack. The influence of crack patterns becomes more pronounced when multiple cracks are present.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"433 ","pages":"Article 117512"},"PeriodicalIF":6.9,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142594137","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Modeling pulmonary perfusion and gas exchange in alveolar microstructures","authors":"Bastián Herrera , Daniel E. Hurtado","doi":"10.1016/j.cma.2024.117499","DOIUrl":"10.1016/j.cma.2024.117499","url":null,"abstract":"<div><div>Pulmonary capillary perfusion and gas exchange are physiological processes that take place at the alveolar level and that are fundamental to sustaining life. Present-day computational simulations of these phenomena are based on low-dimensional mathematical models solved in idealized alveolar geometries, where the chemical reactions between O<span><math><msub><mrow></mrow><mrow><mn>2</mn></mrow></msub></math></span>-CO<span><math><msub><mrow></mrow><mrow><mn>2</mn></mrow></msub></math></span> and hemoglobin are simplified. While providing general insights, current modeling efforts fail to capture the complex chemical reactions that take place in pulmonary capillary blood flow on arbitrary geometries and ignore the crucial impact of microstructural morphology on pulmonary function. Here, we propose a coupled continuum perfusion and gas exchange model that captures complex gas and hemoglobin dynamics in realistic geometries of alveolar tissue. To this end, we derive appropriate governing equations incorporating a two-way Hill-like relationship between gas partial pressures and hemoglobin saturations. We numerically solve the resulting boundary-value problem using a non-linear finite-element approach to simulate and validate velocity, partial pressure, and hemoglobin saturation fields in simple geometries. We further perform sensitivity studies to understand the impact of blood speed and acidity variability on key physiological fields. Notably, we simulate perfusion and gas exchange on anatomical alveolar domains constructed from 3D <span><math><mi>μ</mi></math></span>-computed-tomography images of murine lungs. Based on these models, we show that morphological variations decrease O<span><math><msub><mrow></mrow><mrow><mn>2</mn></mrow></msub></math></span> and CO<span><math><msub><mrow></mrow><mrow><mn>2</mn></mrow></msub></math></span> diffusing capacity, predicting trends and values that are consistent with current medical knowledge. We envision that our model will provide an effective in silico framework to study how exercise and pathological conditions affect perfusion dynamics and the overall gas exchange function of the respiratory system. Source code is available at <span><span>https://github.com/comp-medicine-uc/alveolar-perfusion-transport-modeling</span><svg><path></path></svg></span>.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"433 ","pages":"Article 117499"},"PeriodicalIF":6.9,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142586657","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Data-driven projection pursuit adaptation of polynomial chaos expansions for dependent high-dimensional parameters","authors":"Xiaoshu Zeng, Roger Ghanem","doi":"10.1016/j.cma.2024.117505","DOIUrl":"10.1016/j.cma.2024.117505","url":null,"abstract":"<div><div>Uncertainty quantification (UQ) and inference involving a large number of parameters are valuable tools for problems associated with heterogeneous and non-stationary behaviors. The difficulty with these problems is exacerbated when these parameters are statistically dependent requiring statistical characterization over joint measures. Probabilistic modeling methodologies stand as effective tools in the realms of UQ and inference. Among these, polynomial chaos expansions (PCE), when adapted to low-dimensional quantities of interest (QoI), provide effective yet accurate approximations for these QoI in terms of an adapted orthogonal basis. These adaptation techniques have been cast as projection pursuits in Gaussian Hilbert space in what has been referred to as a projection pursuit adaptation (PPA) by Xiaoshu Zeng and Roger Ghanem (2023). The PPA method efficiently identifies an optimal low-dimensional space for representing the QoI and simultaneously evaluates an optimal PCE within that space. The quality of this approximation clearly depends on the size of the training dataset, which is typically a function of the adapted reduced dimension. The complexity of the problem is thus mediated by the complexity of the low-dimensional quantity of interest and not the complexity of the high-dimensional parameter space.</div><div>In this paper, our objective is to tackle the challenge of dependent parameters while constructing the PPA, utilizing a generative data-driven framework that requires a fixed number of pre-evaluated (parameter, QoI) pairs. While PCE approaches dealing with dependent input parameters have already been introduced by Christian Soize and Roger Ghanem (2004) their coupling with basis adaptation remains an outstanding task without which they remain plagued by the curse of dimensionality. For modest-sized parameters, mapping such as the Rosenblatt transformation can be employed to decouple the dependent variables. This strategy requires access to the joint distribution of the random variables which is usually lacking, requiring significantly more data than is typically available. To overcome these limitations, we propose leveraging multivariate Regular Vine (R-vine) copulas to encapsulate the dependency structure within parameters, manifested as a joint cumulative density function (CDF). The Rosenblatt transformation can then be applied to decouple the dependent input data, mapping them to samples from independent Gaussian variables. Conversely, we can generate dependent samples from independent Gaussian variables while maintaining the learned dependencies. This generative capability ensures that the reconstructed dependency structure is faithfully preserved in the generated samples. Endowed with the ability to diagonalize measures on product spaces, the R-vine copula blends seamlessly with the PPA method, resulting in a unified procedure for constructing optimally reduced PCE models tailored for high-dimensional problems with d","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"433 ","pages":"Article 117505"},"PeriodicalIF":6.9,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142586658","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Guangquan Yu , Ning Li , Cheng Chen , Xiaohang Zhang
{"title":"A novel global prediction framework for multi-response models in reliability engineering using adaptive sampling and active subspace methods","authors":"Guangquan Yu , Ning Li , Cheng Chen , Xiaohang Zhang","doi":"10.1016/j.cma.2024.117506","DOIUrl":"10.1016/j.cma.2024.117506","url":null,"abstract":"<div><div>The computational cost associated with structural reliability analysis increases substantially when dealing with multiple response metrics and high-dimensional input spaces. To address this challenge, an innovative global prediction framework is proposed which leverages multi-output Gaussian process (MOGP) modeling. This framework reduces the computational burden for high-dimensional, multi-response systems by incorporating active subspace and adaptive sampling. The adaptive sampling technique strategically selects the most informative new data points for multi-response prediction by leveraging correlations between responses. Notably, the framework prevents premature termination in low-dimensional scenarios with unknown distributions. Additionally, a multi-response dependent active subspace dimension reduction method is employed to manage high-dimensional data, enhancing the stability of projected structural responses in the reduced-dimensional subspace. The effectiveness of the proposed framework is demonstrated through comprehensive case studies and comparative analyses with traditional approaches. The results demonstrate significant advantages in model dimension reduction, improved accuracy of structural prediction, and enhanced stability, making it well-suited for structural performance prediction.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"433 ","pages":"Article 117506"},"PeriodicalIF":6.9,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142586659","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Thermo-plastic Nonuniform Transformation Field Analysis for eigenstress analysis of materials undergoing laser melt injection","authors":"Felix Fritzen , Julius Herb , Shadi Sharba","doi":"10.1016/j.cma.2024.117487","DOIUrl":"10.1016/j.cma.2024.117487","url":null,"abstract":"<div><div>In engineering applications, surface modifications of materials can greatly influence the lifetime of parts and structures. For instance, laser melt injection (LMI) of ceramic particles into a metallic substrate can greatly improve abrasive resistance. The LMI process is challenging to model due to the rapid temperature changes, which induce high mechanical stresses. Ultimately, this leads to plastification and residual eigenstresses in particles and matrix. These depend on the process parameters. In order to predict these stresses, we propose a major extension of the Nonuniform Transformation Field Analysis that enables the method to cope with strongly varying thermo-elastic material parameters over a large temperature range (here: 300 to 1300 K). The newly proposed <span><math><mi>θ</mi></math></span>-NTFA method combines the NTFA with a Galerkin projection to solve for the self-equilibrated fields needed to gain the NTFA system matrices. For that, we exploit our recent thermo-elastic reduced order model (Sharba et al., 2023) and extend it to allow for arbitrary polarization strains. An efficient implementation and a rigorous separation of the derivation of the reduced order model is proposed. The new <span><math><mi>θ</mi></math></span>-NTFA is then validated for various thermo-mechanical loadings and in thermo-mechanical two-scale simulations.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"433 ","pages":"Article 117487"},"PeriodicalIF":6.9,"publicationDate":"2024-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142578369","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}