Computer Methods in Applied Mechanics and Engineering最新文献

{"title":"Approach for multi-valued integer programming in multi-material topology optimization: Random discrete steepest descent (RDSD) algorithm","authors":"Zeyu Deng,&nbsp;Zhenzeng Lei,&nbsp;Gengdong Cheng,&nbsp;Yuan Liang","doi":"10.1016/j.cma.2024.117449","DOIUrl":"10.1016/j.cma.2024.117449","url":null,"abstract":"<div><div>The present study models the multi-material topology optimization problems as the multi-valued integer programming (MVIP) or named as combinatorial optimization. By extending classical convex analysis and convex programming to discrete point-set functions, the discrete convex analysis and discrete steepest descent (DSD) algorithm are introduced. To overcome combinatorial complexity of the DSD algorithm, we employ the sequential approximate integer programming (SAIP) to explicitly and linearly approximate the implicit objective and constraint functions. Considering the multiple potential changed directions for multi-valued design variables, the random discrete steepest descent (RDSD) algorithm is proposed, where a random strategy is implemented to select a definitive direction of change. To analytically calculate multi-material discrete variable sensitivities, topological derivatives with material contrast is applied. In all, the MVIP is finally transferred as the linear 0–1 programming that can be efficiently solved by the canonical relaxation algorithm (CRA). Explicit nonlinear examples demonstrate that the RDSD algorithm owns nearly three orders of magnitude improvement compared with the commercial software (GUROBI). The proposed approach, without using any continuous variable relaxation and interpolation penalization schemes, successfully solves the minimum compliance problem, strength-related problem, and frequency-related optimization problems. Given the algorithm efficiency, mathematical generality and merits over other algorithms, the proposed RDSD algorithm is meaningful for other structural and topology optimization problems involving multi-valued discrete design variables.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"432 ","pages":"Article 117449"},"PeriodicalIF":6.9,"publicationDate":"2024-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142446239","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":"Deep learning-driven domain decomposition (DLD3): A generalizable AI-driven framework for structural analysis","authors":"Balavignesh Vemparala ,&nbsp;Ming Yang ,&nbsp;Soheil Soghrati","doi":"10.1016/j.cma.2024.117446","DOIUrl":"10.1016/j.cma.2024.117446","url":null,"abstract":"<div><div>A novel, generalizable Artificial Intelligence (AI)-driven technique, termed Deep Learning-Driven Domain Decomposition (DLD<span><math><msup><mrow></mrow><mrow><mn>3</mn></mrow></msup></math></span>), is introduced for simulating two-dimensional linear elasticity problems with arbitrary geometries and boundary conditions (BCs). The DLD<span><math><msup><mrow></mrow><mrow><mn>3</mn></mrow></msup></math></span> framework leverages trained AI models to predict the displacement field within small subdomains, each characterized by varying geometries and BCs. To enforce continuity across the entire domain, the overlapping Schwarz domain decomposition method (DDM) iteratively updates the BCs of each subdomain, thus approximating the overall solution. After evaluating multiple model architectures, the Fourier Neural Operator (FNO) was selected as the AI engine for the DLD<span><math><msup><mrow></mrow><mrow><mn>3</mn></mrow></msup></math></span> method, owing to its data efficiency and high accuracy. We also present a framework that utilizes geometry reconstruction and automated meshing algorithms to generate millions of training data points from high-fidelity finite element (FE) simulations. Several case studies are provided to demonstrate the DLD<span><math><msup><mrow></mrow><mrow><mn>3</mn></mrow></msup></math></span> algorithm’s ability to accurately predict displacement fields in problems involving complex geometries, diverse BCs, and material properties.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"432 ","pages":"Article 117446"},"PeriodicalIF":6.9,"publicationDate":"2024-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142446237","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":"DiffMat: Data-driven inverse design of energy-absorbing metamaterials using diffusion model","authors":"Haoyu Wang ,&nbsp;Zongliang Du ,&nbsp;Fuyong Feng ,&nbsp;Zhong Kang ,&nbsp;Shan Tang ,&nbsp;Xu Guo","doi":"10.1016/j.cma.2024.117440","DOIUrl":"10.1016/j.cma.2024.117440","url":null,"abstract":"<div><div>Energy-absorbing materials and structures are widely applied in industrial areas. Presently, design methods of energy-absorbing metamaterials mainly rely on empirical or bio-inspired configurations. Inspired by AI-generated content, this paper proposes a novel inverse design framework for energy-absorbing metamaterial using diffusion model called DiffMat, which can be customized to generate microstructures given desired stress–strain curves. DiffMat learns the conditional distribution of microstructure given mechanical properties and can realize the one-to-many mapping from properties to geometries. Numerical simulations and experimental validations demonstrate the capability of DiffMat to generate a diverse array of microstructures based on given mechanical properties. This indicates the validity and high accuracy of DiffMat in generating metamaterials that meet the desired mechanical properties. The successful demonstration of the proposed inverse design framework highlights its potential to revolutionize the development of energy-absorbing metamaterials and underscores the broader impact of integrating AI-inspired methodologies into metamaterial design and engineering.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"432 ","pages":"Article 117440"},"PeriodicalIF":6.9,"publicationDate":"2024-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142446238","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":"A new exploration of mesoscopic structure in the nonlocal macro-meso-scale consistent damage model for quasi-brittle materials","authors":"Jianbing Chen,&nbsp;Jiankang Xie,&nbsp;Guangda Lu","doi":"10.1016/j.cma.2024.117456","DOIUrl":"10.1016/j.cma.2024.117456","url":null,"abstract":"<div><div>In the present study, a new exploration of the mesoscopic structure is proposed for the nonlocal macro‑meso-scale consistent damage (NMMD) model, and the definition from mesoscopic damage to macroscopic damage in the original NMMD model is expanded. In the proposed model, material points are divided into two types: macroscopic and mesoscopic. For each macroscopic material point, there are mesoscopic material points within its influence domain, and every two different mesoscopic material points form a material point pair. The macroscopic damage at a macroscopic material point is also evaluated as the weighted average of mesoscale damage over material point pairs in the influence domain. However, compared with the original NMMD model, the mesoscale damage of material point pairs is determined by the motion of mesoscopic material points, rather than macroscopic material points. The macroscopic material points in the proposed model only represent the nonlocal effect and the macroscopic damage. Moreover, the shape of the influence domain and the arrangement of material point pairs are arbitrary and not fixed, i.e., the unified mesoscopic structure is abstract. To verify the proposed model, a specific mesoscopic structure is generated for quasi-brittle materials without considering the randomness of material properties. In this mesoscopic structure, the shape of the influence domain is a circle, and the mesoscopic material points are generated by the tangent sphere method. The numerical results indicate that the proposed model can accurately capture the crack patterns of quasi-brittle materials and exhibits excellent numerical robustness. Meanwhile, through a mode-I failure example, it is demonstrated that the computational efficiency of the proposed model is not lower than the original NMMD model. More importantly, the framework of mesoscopic structure modeling provides a new feasible approach for the extension of other models, e.g., virtual internal bond model and peridynamics. The urgent work within the NMMD model framework is to extend the proposed model to anisotropic, composite materials and dynamic crack simulation of large structures in the future.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"432 ","pages":"Article 117456"},"PeriodicalIF":6.9,"publicationDate":"2024-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142441851","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":"Topology optimization of structures guarding against brittle fracture via peridynamics-based SIMP approach","authors":"Weisheng Zhang ,&nbsp;Yuan Liu ,&nbsp;Jian Zhang ,&nbsp;Jialun Li ,&nbsp;Xu Guo ,&nbsp;Sung-Kie Youn","doi":"10.1016/j.cma.2024.117438","DOIUrl":"10.1016/j.cma.2024.117438","url":null,"abstract":"<div><div>Fracture resistance of structures consisting of brittle materials is significantly important in engineering practice. In this work, we explore the application of peridynamics (PD) in the optimization of structures against brittle fracture. A fracture resistance topology optimization scheme under the PD-based analysis framework is proposed, where two fracture-based strategies are adopted to improve the structural fracture behavior. The first one sets the conventional fracture energy as a constraint. While the second constraint is the bond stretch established on the unique concept “bond” of the PD framework, which smoothly transfers the energy-based fracture resistance control to an intuitive and mathematically tractable geometric expression. The topology optimization is carried out under the SIMP framework, where densities are assigned to the bonds via material points to represent the topology changes and crack generation. Numerical examples and experiments demonstrate that the proposed strategies can guarantee the safety of the optimized structure against the occurrence of fracture failure.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"432 ","pages":"Article 117438"},"PeriodicalIF":6.9,"publicationDate":"2024-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142441962","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":"Reliability-based topology optimization using LRPIM surrogate model considering local stress and displacement constraints","authors":"Dianyin Hu ,&nbsp;Yi Wang ,&nbsp;Xi Liu ,&nbsp;Cuiying Gong ,&nbsp;Jinchao Pan ,&nbsp;Dong Mi ,&nbsp;Rongqiao Wang","doi":"10.1016/j.cma.2024.117460","DOIUrl":"10.1016/j.cma.2024.117460","url":null,"abstract":"<div><div>This paper presents a novel decoupled framework for reliability-based topology optimization (RBTO) that aims to find optimal material configurations while meeting local stiffness and strength constraints. To effectively address the nonlinear displacement and stress reliability constraints, the proposed framework replaces the conventional first-order reliability method (FORM) with the more accurate Local Radial Point Interpolation Method (LRPIM). This substitution overcomes the limitations of FORM in approximating high-dimensional nonlinear problems. The framework includes the qp-relaxation criterion and a global stress aggregation technique to avoid stress singularities. For multi-constrained optimization, the adjoint vector method is used for design sensitivity analysis, followed by a gradient-based algorithm to solve the structural optimization problem. Numerical examples are presented to validate the effectiveness of the proposed RBTO methodology, demonstrating its superiority in both accuracy and reliability compared to the Sequential Optimization and Reliability Assessment (SORA) method. The comparative analysis highlights the efficiency and precision of the proposed method across different reliability approaches, making it a robust tool for addressing complex engineering challenges.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"432 ","pages":"Article 117460"},"PeriodicalIF":6.9,"publicationDate":"2024-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142441963","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":"A novel mesh regularization approach based on finite element distortion potentials: Application to material expansion processes with extreme volume change","authors":"Abhiroop Satheesh,&nbsp;Christoph P. Schmidt,&nbsp;Wolfgang A. Wall,&nbsp;Christoph Meier","doi":"10.1016/j.cma.2024.117444","DOIUrl":"10.1016/j.cma.2024.117444","url":null,"abstract":"<div><div>The accuracy of finite element solutions is closely tied to the mesh quality. In particular, geometrically nonlinear problems involving large and strongly localized deformations often result in prohibitively large element distortions. In this work, we propose a novel mesh regularization approach allowing to restore a non-distorted high-quality mesh in an adaptive manner without the need for expensive re-meshing procedures. The core idea of this approach lies in the definition of a finite element distortion potential considering contributions from different distortion modes such as skewness and aspect ratio of the elements. The regularized mesh is found by minimization of this potential. Moreover, based on the concept of spatial localization functions, the method allows to specify tailored requirements on mesh resolution and quality for regions with strongly localized mechanical deformation and mesh distortion. In addition, while existing mesh regularization schemes often keep the boundary nodes of the discretization fixed, we propose a mesh-sliding algorithm based on variationally consistent mortar methods allowing for an unrestricted tangential motion of nodes along the problem boundary. Especially for problems involving significant surface deformation (e.g., frictional contact), this approach allows for an improved mesh relaxation as compared to schemes with fixed boundary nodes. To transfer data such as tensor-valued history variables of the material model from the old (distorted) to the new (regularized) mesh, a structure-preserving invariant interpolation scheme for second-order tensors is employed, which has been proposed in our previous work and is designed to preserve important properties of tensor-valued data such as objectivity and positive definiteness. As a practically relevant application scenario, we consider the thermo-mechanical expansion of materials such as foams involving extreme volume changes by up to two orders of magnitude along with large and strongly localized strains as well as thermo-mechanical contact interaction. For this scenario, it is demonstrated that the proposed regularization approach preserves a high mesh quality at small computational costs. In contrast, simulations without mesh adaption are shown to lead to significant mesh distortion, deteriorating result quality, and, eventually, to non-convergence of the numerical solution scheme.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"432 ","pages":"Article 117444"},"PeriodicalIF":6.9,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142441961","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":"PTPI-DL-ROMs: Pre-trained physics-informed deep learning-based reduced order models for nonlinear parametrized PDEs","authors":"Simone Brivio,&nbsp;Stefania Fresca,&nbsp;Andrea Manzoni","doi":"10.1016/j.cma.2024.117404","DOIUrl":"10.1016/j.cma.2024.117404","url":null,"abstract":"<div><div>Among several recently proposed data-driven Reduced Order Models (ROMs), the coupling of Proper Orthogonal Decompositions (POD) and deep learning-based ROMs (DL-ROMs) has proved to be a successful strategy to construct non-intrusive, highly accurate, surrogates for the <em>real time</em> solution of parametric nonlinear time-dependent PDEs. Inexpensive to evaluate, POD-DL-ROMs are also relatively fast to train, thanks to their limited complexity. However, POD-DL-ROMs account for the physical laws governing the problem at hand only through the training data, that are usually obtained through a full order model (FOM) relying on a high-fidelity discretization of the underlying equations. Moreover, the accuracy of POD-DL-ROMs strongly depends on the amount of available data. In this paper, we consider a major extension of POD-DL-ROMs by enforcing the fulfillment of the governing physical laws in the training process – that is, by making them physics-informed – to compensate for possible scarce and/or unavailable data and improve the overall reliability. To do that, we first complement POD-DL-ROMs with a <em>trunk net</em> architecture, endowing them with the ability to compute the problem’s solution at every point in the spatial domain, and ultimately enabling a seamless computation of the physics-based loss by means of the strong continuous formulation. Then, we introduce an efficient training strategy that limits the notorious computational burden entailed by a physics-informed training phase. In particular, we take advantage of the few available data to develop a low-cost pre-training procedure; then, we fine-tune the architecture in order to further improve the prediction reliability. Accuracy and efficiency of the resulting pre-trained physics-informed DL-ROMs (PTPI-DL-ROMs) are then assessed on a set of test cases ranging from non-affinely parametrized advection–diffusion–reaction equations, to nonlinear problems like the Navier–Stokes equations for fluid flows.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"432 ","pages":"Article 117404"},"PeriodicalIF":6.9,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142433311","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":"Divide and conquer: Learning chaotic dynamical systems with multistep penalty neural ordinary differential equations","authors":"Dibyajyoti Chakraborty ,&nbsp;Seung Whan Chung ,&nbsp;Troy Arcomano ,&nbsp;Romit Maulik","doi":"10.1016/j.cma.2024.117442","DOIUrl":"10.1016/j.cma.2024.117442","url":null,"abstract":"<div><div>Forecasting high-dimensional dynamical systems is a fundamental challenge in various fields, such as geosciences and engineering. Neural Ordinary Differential Equations (NODEs), which combine the power of neural networks and numerical solvers, have emerged as a promising algorithm for forecasting complex nonlinear dynamical systems. However, classical techniques used for NODE training are ineffective for learning chaotic dynamical systems. In this work, we propose a novel NODE-training approach that allows for robust learning of chaotic dynamical systems. Our method addresses the challenges of non-convexity and exploding gradients associated with underlying chaotic dynamics. Training data trajectories from such systems are split into multiple, non-overlapping time windows. In addition to the deviation from the training data, the optimization loss term further penalizes the discontinuities of the predicted trajectory between the time windows. The window size is selected based on the fastest Lyapunov time scale of the system. Multi-step penalty(MP) method is first demonstrated on Lorenz equation, to illustrate how it improves the loss landscape and thereby accelerates the optimization convergence. MP method can optimize chaotic systems in a manner similar to least-squares shadowing with significantly lower computational costs. Our proposed algorithm, denoted the Multistep Penalty NODE, is applied to chaotic systems such as the Kuramoto–Sivashinsky equation, the two-dimensional Kolmogorov flow, and ERA5 reanalysis data for the atmosphere. It is observed that MP-NODE provide viable performance for such chaotic systems, not only for short-term trajectory predictions but also for invariant statistics that are hallmarks of the chaotic nature of these dynamics.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"432 ","pages":"Article 117442"},"PeriodicalIF":6.9,"publicationDate":"2024-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142655320","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":"High-order multiscale method for elastic deformation of complex geometries","authors":"Sabit Mahmood Khan,&nbsp;Yashar Mehmani","doi":"10.1016/j.cma.2024.117436","DOIUrl":"10.1016/j.cma.2024.117436","url":null,"abstract":"<div><div>Computational methods, such as finite elements, are indispensable for modeling the mechanical compliance of elastic solids. However, as the size and geometric complexity of the domain increases, the cost of simulations becomes prohibitive. One example is the microstructure of a porous material, such as a piece of rock or bone sample, captured by an X-ray <span><math><mi>μ</mi></math></span>CT image. The solid geometry consists of numerous grains, cavities, and/or channels, with the domain large enough to allow inferring statistically converged macroscale properties. The pore-level multiscale method (PLMM) was recently proposed by the authors to reduce the associated computational cost through a divide-and-conquer strategy. The domain is decomposed into subdomains via watershed segmentation, and local basis and correction functions are built numerically, then assembled to obtain an approximate solution. However, PLMM is limited to domains corresponding to microscale porous media, incurs large errors when modeling loading conditions that generate significant bending/twisting moments locally, and it is equipped with only one mechanism to control approximation errors <em>during</em> a simulation. Here, we generalize PLMM into a high-order variant, called hPLMM, that removes these drawbacks. In hPLMM, appropriate mortar spaces are defined at subdomain interfaces that allow improving the boundary conditions used to solve local problems on the subdomains, thus the accuracy of the approximation. Moreover, errors can be reduced by a second mechanism wherein an upfront cost is paid <em>prior to</em> a simulation, useful if basis functions can be reused many times, e.g., across loading steps. Finally, the method applies not just to pore-scale, but also Darcy-scale and non-porous domains. We validate hPLMM against a range of complex 2D/3D geometries and discuss its convergence and algorithmic complexity. Implications for modeling failure and nonlinear problems are discussed.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"432 ","pages":"Article 117436"},"PeriodicalIF":6.9,"publicationDate":"2024-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142433309","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}