Journal of The Mechanics and Physics of Solids最新文献

{"title":"Effects of nonlinearities and geometric imperfections on multistability and deformation localization in wrinkling films on planar substrates","authors":"","doi":"10.1016/j.jmps.2024.105774","DOIUrl":"10.1016/j.jmps.2024.105774","url":null,"abstract":"<div><p>Compressed elastic films on soft substrates release part of their strain energy by wrinkling, which represents a loss of symmetry, characterized by a pitchfork bifurcation. Its development is well understood at the onset of supercritical bifurcation, but not beyond, or in the case of subcritical bifurcation. This is mainly due to nonlinearities and the extreme imperfection sensitivity. In both types of bifurcations, the energy–displacement diagrams that can characterize an energy landscape are non-convex, which is notoriously difficult to determine numerically or experimentally, let alone analytically. To gain an elementary understanding of such potential energy landscapes, we take a thin beam theory suitable for analyzing large displacements under small strains and significantly reduce its complexity by reformulating it in terms of the tangent rotation angle. This enables a comprehensive analytical and numerical analysis of wrinkling elastic films on planar substrates, which are effective stiffening and/or softening due to either geometric or material nonlinearities. We also validate our findings experimentally. We explicitly show how effective stiffening nonlinear behavior (e.g., due to substrate or membrane deformations) leads to a supercritical post-bifurcation response, makes the energy landscape non-convex through energy barriers causing multistability, which is extremely problematic for numerical computation. Moreover, this type of nonlinearity promotes uni-modal, uniformly distributed, periodic deformation patterns. In contrast, nonlinear effective softening behavior leads to subcritical post-bifurcation behavior, similarly divides the energy landscape by energy barriers and conversely promotes localization of deformations. With our theoretical model we can thus explain an experimentally observed phenomenon that in structures with effective softening followed by an effective stiffening behavior, the symmetry is initially broken by localizing the deformation and later restored by forming periodic, distributed deformation patterns as the load is increased. Finally, we show that initial imperfections can significantly alter the local or global energy-minimizing deformation pattern and completely remove some energy barriers. We envision that this knowledge can be extrapolated and exploited to convexify extremely divergent energy landscapes of more sophisticated systems, such as wrinkling compressed films on curved substrates (e.g., on cylinders and spheres) and that it will enable elementary analysis and the development of specialized numerical tools.</p></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":null,"pages":null},"PeriodicalIF":5.0,"publicationDate":"2024-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0022509624002400/pdfft?md5=480a8025e39753a1ffe41a914966e4be&pid=1-s2.0-S0022509624002400-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141639399","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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":"Imbibition of water into a cellulose foam: The kinetics","authors":"","doi":"10.1016/j.jmps.2024.105763","DOIUrl":"10.1016/j.jmps.2024.105763","url":null,"abstract":"<div><p>Cellulose foams are representative of many porous engineering solids that can absorb a large quantity of fluid such as water. Experiments are reported to give insight into water rise in cellulose foams and the underlying mechanisms. The water rise characteristic of water height <em>h</em> versus time <em>t</em> displays a distinct knee on a log-log plot; this knee separates an initial regime where <em>h</em> scales as <em>t</em>^1/2 from a subsequent regime where <em>h</em> scales as <em>t</em>^1/4. The rate of water rise below the knee is consistent with the Washburn law of water rise in a single dominant capillary, and the knee in the <em>h</em>(<em>t</em>) curve suggests that the Jurin height of this large capillary has been attained. Water rise in the foam above the knee of the <em>h</em>(<em>t</em>) curve is interpreted as water rise in a population of small capillaries with a wide range of radius that feed off the dominant capillary. A series of critical experiments support this interpretation, including water rise in inclined columns, and water rise from a limited reservoir of water. A simple analytical model is used to provide a physical explanation for the observations. Additionally, X-ray computer tomography is used to deduce the probability density function of the small capillaries. The experimental findings are in support of the hypothesis that water rise in the cellulose foam is driven by capillary action and not by diffusion.</p></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":null,"pages":null},"PeriodicalIF":5.0,"publicationDate":"2024-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0022509624002291/pdfft?md5=a06aae4dc21a0129dc3b3adf59301efc&pid=1-s2.0-S0022509624002291-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141689948","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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":"Deformation, shape transformations, and stability of elastic rod loops within spherical confinement","authors":"","doi":"10.1016/j.jmps.2024.105771","DOIUrl":"10.1016/j.jmps.2024.105771","url":null,"abstract":"<div><p>Mechanical insight into the packing of slender objects within confinement is essential for understanding how polymers, filaments, or wires organize and rearrange in limited space. Here we combine theoretical modeling, numerical optimization, and experimental studies to reveal spherical packing behavior of thin elastic rod loops of homogeneous or inhomogeneous stiffness. Across varying loop lengths, a rich array of configurations including circle, saddle, figure-eight, and more intricate patterns are identified. A theoretical framework rooted in the local equilibrium of force and moment is proposed for the rod loop deformation, facilitating the determination of internal and contact forces experienced by the rods during deformation. For the confined homogeneous rod loops, their stable and metastable configurations are well described using proposed Euler rotation curves, which offer a concise and effective approach for configuration prediction. Moreover, formulated analysis on the stability and critical force for homogeneous rod loops on great circles of the spherical confinement are performed. For inhomogeneous rod loops with two segments of differing stiffness, the stiffer segment exhibits less deviation from the great circle, while the softer segment undergoes more pronounced deformation. These findings not only enhance our understanding of buckling and post-buckling phenomena but also offer insights into filament patterning within confining environments.</p></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":null,"pages":null},"PeriodicalIF":5.0,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141639396","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Statistical mechanics of plasticity: Elucidating anomalous size-effects and emergent fractional nonlocal continuum behavior","authors":"","doi":"10.1016/j.jmps.2024.105747","DOIUrl":"10.1016/j.jmps.2024.105747","url":null,"abstract":"<div><p>Extensive experiments over the decades unequivocally point to a pronounced scale-dependency of plastic deformation in metals. This observation is fairly general, and broadly speaking, strengthening against deformation is observed with the decrease in the size of a relevant geometrical feature of the material, e.g., the thickness of a thin film. The classical theory of plasticity is size-independent, and this has spurred extensive research into an appropriate continuum theory to elucidate the observed size effects. This pursuit has led to the emergence of strain gradient plasticity, along with its numerous variants, as the paradigm of choice. Recognizing the constrained shear of a thin metallic film as the model problem to understand the observed size-effect, all conventional (and reasonable candidate) theories of strain gradient plasticity predict a scaling of yield strength that inversely varies with the film thickness <span><math><mrow><mo>∼</mo><msup><mrow><mi>h</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></math></span>. Experimental findings indicate a considerably diminished scaling, the magnitude of which can exhibit significant variation based on processing conditions or even the mode of deformation. As an example, the scaling exponent as low as <span><math><mrow><mo>−</mo><mn>0</mn><mo>.</mo><mn>2</mn></mrow></math></span> has been observed for as-deposited copper thin films. Two perspectives have been posited to explain this perplexing anomaly. Kuroda and Needleman (2019) argue that the conventional boundary conditions used in strain gradient plasticity theory are not meaningful for the canonical constrained thin film problem and propose a physically motivated alternative. Dahlberg and Ortiz (2019) contend that the intrinsic differential calculus structure of all strain gradient plasticity theories will invariably lead to the incorrect (or rather inadequate) explanation of the size-scaling. They propose a fractional strain gradient plasticity framework where the fractional derivative order is a material property that correlates with the scaling exponent. In this work, we present an alternative approach that complements the existing explanations. We create a statistical mechanics model for interacting microscopic units that deform and yield with the rules of <em>classical plasticity</em>, and plastic yielding is treated as a phase transition. We coarse-grain the model to precisely elucidate the microscopic interactions that can lead to the emergent size-effects observed experimentally. Specifically, we find that depending on the nature of the long-range microscopic interactions, the emergent coarse-grained theory can be of fractional differential type or alternatively a form of integral nonlocal model. Our theory, therefore, provides a partial (and microscopic) justification for the fractional derivative model and makes clear the precise microscopic interactions that must be operative for a continuum plasticity theor","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":null,"pages":null},"PeriodicalIF":5.0,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141639398","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Predicting mechanical properties of mitotic spindles with a minimal constitutive model","authors":"","doi":"10.1016/j.jmps.2024.105770","DOIUrl":"10.1016/j.jmps.2024.105770","url":null,"abstract":"<div><p>The mitotic spindle, crucial for precise chromosome segregation and cytoplasmic partitioning during cell division, demands stability against forces arising from chromosomal movements and thermal fluctuations. Despite its central role, the mechanical properties of spindles remain largely elusive. In this study, we delve into the mechanical properties of spindles through a comprehensive model encompassing interactions among centrosomes, microtubules, chromosomes, and molecular motors. Our model successfully reproduces the 3D self–assembly of spindles and their responses to mechanical forces. We find that the spindle exhibits viscoelastic properties, responding distinctively to stretch and compression. Rapid stretch induces transient softening of the spindle, while compression leads to temporary hardening. Based on the viscoelastic responses of spindles under constant–force and constant–displacement loadings, we propose a minimal constitutive model for the spindle structure. This constitutive model can not only accurately recapture the viscoelastic responses of spindles under stretch and compression but also predict the mechanical behaviors of spindles under constant–rate loadings and cyclic loadings, which are further verified by simulations. Therefore, our validated constitutive model can replace complex simulations, providing more interesting predictions and guidance for future experiments.</p></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":null,"pages":null},"PeriodicalIF":5.0,"publicationDate":"2024-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141622876","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 micromagnetic-mechanically coupled phase-field model for fracture and fatigue of magnetostrictive alloys","authors":"Shen Sun ,&nbsp;Qihua Gong ,&nbsp;Yong Ni ,&nbsp;Min Yi","doi":"10.1016/j.jmps.2024.105767","DOIUrl":"https://doi.org/10.1016/j.jmps.2024.105767","url":null,"abstract":"<div><p>Magnetostrictive alloys are usually brittle materials with micromagnetic structures. Their structural reliability and durability depend on the complex micromagnetic-mechanical coupling at smaller length scales encompassing the evolution of micromagnetic structures. Herein we propose a micromagnetic-mechanically coupled phase-field model for fracture and fatigue behavior of magnetostrictive alloys with evolution of the micromagnetic structure. The thermodynamically-consistent model is derived from microforce theory, laws of thermodynamics, and Coleman–Noll analysis. The evolution of crack phase-field and magnetization-vector order parameters that are fully coupled is governed by history field dependent Allen–Cahn and Landau–Lifshitz–Gilbert equations, respectively. The model is extended to fatigue by introducing a degradation prefactor for the fracture energy as a function of positive elastic energy. One-dimensional analyses are then presented to anatomize the crack driving forces in terms of fully coupled micromagnetic-mechanical and pure mechanical driving force. We demonstrate the model capabilities by finite-element numerical studies on the micromagnetic domain evolution during the crack propagation and the influence of external magnetic field for type-I, type-II, and three-point bending fracture, as well as for the fracture of a single-edge notched specimen with an elliptical inclusion. The simulation result shows that depending on how micromagnetic domains are switched under micromagnetic-mechanical coupling, the magnetic field can enhance or decrease the critical load. In the presence of inclusion with larger fracture toughness, a crack is found to nucleate in the tri-junction of multi-domain micromagnetic structure owing to the high elastic strain around the tri-junction point. It is further found that a suitable magnetic field promoting magnetization-vector rotation around the crack tip could remarkably improve the fracturing load and fatigue life. The results demonstrate the model promising for the study of micromagnetic-mechanically coupled fracture and fatigue in magnetostrictive alloys.</p></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":null,"pages":null},"PeriodicalIF":5.0,"publicationDate":"2024-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141607806","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Active interfacial degradation/deposition of an elastic matrix by a fluid inclusion: Theory and pattern formation","authors":"","doi":"10.1016/j.jmps.2024.105773","DOIUrl":"10.1016/j.jmps.2024.105773","url":null,"abstract":"<div><p>During collective invasion in 3D, cohesive cellular tissues migrate within a fibrous extracellular matrix (ECM). This process requires significant remodeling of the ECM by cells, notably proteolysis at the cell–ECM interface by specialized molecules. Motivated by this problem, we develop a theoretical framework to study the dynamics of a fluid inclusion (modeling the cellular tissue) embedded in an elastic matrix (the ECM), which undergoes surface degradation/deposition. To account for the active nature of this process, we develop a continuum theory based on irreversible thermodynamics, leading to a kinetic relation for the degradation front that locally resembles the force–velocity relation of a molecular motor. We further study the effect of mechanotransduction on the stability of the cell–ECM interface, finding a variety of self-organized dynamical patterns of collective invasion. Our work identifies ECM proteolysis as an active process possibly driving the self-organization of cellular tissues.</p></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":null,"pages":null},"PeriodicalIF":5.0,"publicationDate":"2024-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141639400","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Physics-based discrete models for magneto-mechanical metamaterials","authors":"","doi":"10.1016/j.jmps.2024.105759","DOIUrl":"10.1016/j.jmps.2024.105759","url":null,"abstract":"<div><p>Magneto-mechanical metamaterials are emerging smart materials whose mechanical responses can be tailored through structure architecture and magnetic interactions. The latter provides additional freedom in the material design space and leads to novel behaviors due to its nonlocal nature. The enriched functionalities open new possibilities in various applications, such as actuators, energy absorbers, and soft robots. However, the nonlinear and nonlocal coupling between elastic and magnetic forces poses a great challenge in the modeling and simulation of these systems, further hindering theory-based rational design strategies. Here, we focus on a class of magneto-mechanical metamaterials comprising elastic solids embedded with rigid permanent magnets. The clear separation between elastic and magnetic forces simplifies the design and fabrication process, yet their nonlocal interplay still allows for complex behaviors. We present a simulation framework for such magneto-mechanical metamaterials by combining a lattice spring model for the elastic solid with the dipole model for the magnetic interactions and implementing it in the LAMMPS molecular dynamics software. We demonstrate the capabilities of our framework by simulating a few representative structures, including shape-locking lattice metamaterials, a soft cellular solid with controllable buckling, and a metamaterial chain with phase-transforming behavior. For the shape-locking lattice metamaterials, we successfully capture the magnetic-actuation-driven reconfiguration and the nonlinear mechanical response of the curved lattices. For the soft cellular solid, we identify its buckling patterns under external non-uniform magnetic fields and simulate a buckling evolution process consistent with experiments. For the metamaterial chain, we include the strong long-range interactions among the embedded magnets and reproduce the controllable phase transitions in the experiments. Our work provides a simple yet versatile simulation methodology to investigate the nonlinear mechanical behaviors in the presence of strong external and internal magnetic forces, which will facilitate the design and analysis of magneto-mechanical materials. It can also be applied to other magnetically-driven smart structures, such as soft robots.</p></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":null,"pages":null},"PeriodicalIF":5.0,"publicationDate":"2024-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141622875","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An asymptotically consistent morphoelastic shell model for compressible biological structures with finite-strain deformations","authors":"","doi":"10.1016/j.jmps.2024.105768","DOIUrl":"10.1016/j.jmps.2024.105768","url":null,"abstract":"<div><p>We derive an asymptotically consistent morphoelastic shell model to describe the finite deformations of biological tissues using the variational asymptotic method. Biological materials may exhibit remarkable compressibility when under large deformations, and we take this factor into account for accurate predictions of their morphoelastic changes. The morphoelastic shell model combines the growth model of Rodriguez et al. and a novel shell model developed by us. We start from the three-dimensional (3D) morphoelastic model and construct the optimal shell energy based on a series expansion around the middle surface. A two-step variational method is applied that retains the leading-order expansion coefficient while eliminating the higher-order ones. The main outcome is a two-dimensional (2D) shell energy depending on the stretching and bending strains of the middle surface. The derived morphoelastic shell model is asymptotically consistent with three-dimensional morphoelasticity and can recover various shell models in literature. Several examples are shown for the verification and illustration.</p></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":null,"pages":null},"PeriodicalIF":5.0,"publicationDate":"2024-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141697031","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Quantifying 3D time-resolved kinematics and kinetics during rapid granular compaction, Part I: Quasistatic and dynamic deformation regimes","authors":"","doi":"10.1016/j.jmps.2024.105765","DOIUrl":"10.1016/j.jmps.2024.105765","url":null,"abstract":"<div><p>Impacts in granular materials occur over a velocity range of a few hundred m/s in manufacturing processes to several km/s during asteroid impacts. Different energy dissipation mechanisms are activated during impacts based on the kinetic energy of the impactor and the properties of the granular material. Material response during impact can be classified into two broad regimes – quasi-static and dynamic – characterized by the nature of grain and pore deformation and the deformation morphology of grain interfaces. In the quasi-static regime, all energy from the impactor is utilized in pore (or void) collapse, while in the dynamic regime, excess energy after pore closure leads to material melting or jetting and often to non-planar grain interfaces. To understand the transition between the quasi-static and dynamic regimes, <em>in-situ</em> measurements of temperature, local stresses, and porosity at the grain scale are critical but often not possible due to short timescales and inherent heterogeneity of granular materials. In this work, we use X-ray phase contrast imaging (XPCI) to visualize grain-scale deformation during rapid granular compaction and observe phenomena such as plastic flow-induced pore collapse, compaction wave propagation, and the morphology of the grain-grain interfaces. Alongside these experiments, we develop and validate a mesoscale numerical model that incorporates each sample’s microstructure and captures realistic plasticity and thermal effects. Using this validated model, we quantify the temperatures, pressures, and porosity as granular materials are compacted in both quasi-static and dynamic deformation regimes. By comparing our results with existing theoretical models, we find that the continuum definitions of quasi-static and dynamic regimes needs to be updated for a realistic heterogeneous granular media. Specifically, the two regimes can coexist in the same assembly of grains at different time instants due to spatial heterogeneity and rapid dissipation of impact energy away from the point of impact. Finally, we quantify the energies associated with different dissipation mechanisms for individual grains using coupled numerical and analytical techniques. Our methodology allows us to obtain full 3D kinematics and kinetics of rapidly compacted granular materials at both the mesoscale and the grain scale.</p></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":null,"pages":null},"PeriodicalIF":5.0,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141708922","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}