A phase field model based on a regularized version of the variational formulation of brittle fracture is introduced. The influences of the regularization parameter that controls the interface width ...between broken and undamaged material and of the mobility constant of the evolution equation are studied in finite element simulations. A generalized Eshelby tensor is derived and analyzed for mode I loading in order to evaluate the energy release rate of the diffuse phase field cracks. The numerical implementation is performed with finite elements and an implicit time integration scheme. The configurational forces are computed in a postprocessing step after the coupled problem of mechanical balance equations and the evolution equation is solved. Some of the numerical results are compared to analytical results from classical Griffith theory.
The definitive guide to unsaturated soil— from the world's experts on the subjectThis book builds upon and substantially updates Fredlund and Rahardjo's publication, Soil Mechanics for Unsaturated ...Soils, the current standard in the field of unsaturated soils. It provides readers with more thorough coverage of the state of the art of unsaturated soil behavior and better reflects the manner in which practical unsaturated soil engineering problems are solved. Retaining the fundamental physics of unsaturated soil behavior presented in the earlier book, this new publication places greater emphasis on the importance of the 'soil-water characteristic curve' in solving practical engineering problems, as well as the quantification of thermal and moisture boundary conditions based on the use of weather data. Topics covered include:Theory to Practice of Unsaturated Soil MechanicsNature and Phase Properties of Unsaturated SoilState Variables for Unsaturated SoilsMeasurement and Estimation of State VariablesSoil-Water Characteristic Curves for Unsaturated SoilsGround Surface Moisture Flux Boundary ConditionsTheory of Water Flow through Unsaturated SoilsSolving Saturated/Unsaturated Water Flow ProblemsAir Flow through Unsaturated SoilsHeat Flow Analysis for Unsaturated SoilsShear Strength of Unsaturated SoilsShear Strength Applications in Plastic and Limit EquilibriumStress-Deformation Analysis for Unsaturated SoilsSolving Stress-Deformation Problems with Unsaturated SoilsCompressibility and Pore Pressure ParametersConsolidation and Swelling Processes in Unsaturated SoilsUnsaturated Soil Mechanics in Engineering Practiceis essential reading for geotechnical engineers, civil engineers, and undergraduate- and graduate-level civil engineering students with a focus on soil mechanics.
This paper presents discrete element method (DEM) simulations with experimental comparisons at multiple length scales—underscoring the crucial role of particle shape. The simulations build on ...technological advances in the DEM furnished by level sets (LS-DEM), which enable the mathematical representation of the surface of arbitrarily-shaped particles such as grains of sand. We show that this ability to model shape enables unprecedented capture of the mechanics of granular materials across scales ranging from macroscopic behavior to local behavior to particle behavior. Specifically, the model is able to predict the onset and evolution of shear banding in sands, replicating the most advanced high-fidelity experiments in triaxial compression equipped with sequential X-ray tomography imaging. We present comparisons of the model and experiment at an unprecedented level of quantitative agreement—building a one-to-one model where every particle in the more than 53,000-particle array has its own avatar or numerical twin. Furthermore, the boundary conditions of the experiment are faithfully captured by modeling the membrane effect as well as the platen displacement and tilting. The results show a computational tool that can give insight into the physics and mechanics of granular materials undergoing shear deformation and failure, with computational times comparable to those of the experiment. One quantitative measure that is extracted from the LS-DEM simulations that is currently not available experimentally is the evolution of three dimensional force chains inside and outside of the shear band. We show that the rotations on the force chains are correlated to the rotations in stress principal directions.
Energy harvesting is one of the most promising research areas to produce sustainable power sources from the ambient environment. Which found applications to attain the extensive lifetime self-powered ...operations of various devices such as MEMS wireless sensors, medical implants and wearable electronic devices. Piezoelectric nanogenerators can efficiently convert the vastly available mechanical energy into electrical energy to meet the requirements of low-powered electronic devices. Among the piezoelectric materials, poly (vinylidene fluoride) (PVDF) and its copolymers are extensively studied for the development of energy harvesting devices. Due to the outstanding properties such as high flexibility, ease of processing, long-term stability, biocompatibility makes them a promising candidate for piezoelectric generators. Nevertheless, compared to piezoceramic materials, PVDF based generators produce lower piezoresponse. Over the last decades, tremendous research activities have been reported to endorse the performance of PVDF based energy harvesters. This review article mainly focused on the recent progress in the performance improvement with processing methods, piezoelectric materials, different filler loading. The new developments and design structures will lead to an increase in piezoelectricity, alignment of dipoles, dielectric properties and subsequently enhance the output performance of the device. Electronic circuits play a vital role in energy harvesting to efficiently collect the developed charge from the device. Here, we have proposed a detailed description of the electronic circuits. Also, in the application part deals with the recent progress in flexible, biomedical and hybrid generators based on PVDF polymers.
<正>Dyke swarms can be divided into three types:parallel dyke swarms,radiating dyke swarms and fan-shape dyke swarm,for which the mechanisms of formation are different(Fig.1).Parallel dyke ...swarms form in response
•High order schemes for a unified first order hyperbolic formulation of continuum mechanics.•The mathematical model applies simultaneously to fluid mechanics and solid mechanics.•Viscous fluids are ...treated in the frame of hyper-elasticity as generalized visco-plastic solids.•Formal asymptotic analysis reveals the connection with the Navier–Stokes equations.•The distortion tensor A in the model appears to be well-suited for flow visualization.
This paper is concerned with the numerical solution of the unified first order hyperbolic formulation of continuum mechanics recently proposed by Peshkov and Romenski 110, further denoted as HPR model. In that framework, the viscous stresses are computed from the so-called distortion tensor A, which is one of the primary state variables in the proposed first order system. A very important key feature of the HPR model is its ability to describe at the same time the behavior of inviscid and viscous compressible Newtonian and non-Newtonian fluids with heat conduction, as well as the behavior of elastic and visco-plastic solids. Actually, the model treats viscous and inviscid fluids as generalized visco-plastic solids. This is achieved via a stiff source term that accounts for strain relaxation in the evolution equations of A. Also heat conduction is included via a first order hyperbolic system for the thermal impulse, from which the heat flux is computed. The governing PDE system is hyperbolic and fully consistent with the first and the second principle of thermodynamics. It is also fundamentally different from first order Maxwell–Cattaneo-type relaxation models based on extended irreversible thermodynamics. The HPR model represents therefore a novel and unified description of continuum mechanics, which applies at the same time to fluid mechanics and solid mechanics. In this paper, the direct connection between the HPR model and the classical hyperbolic–parabolic Navier–Stokes–Fourier theory is established for the first time via a formal asymptotic analysis in the stiff relaxation limit.
From a numerical point of view, the governing partial differential equations are very challenging, since they form a large nonlinear hyperbolic PDE system that includes stiff source terms and non-conservative products. We apply the successful family of one-step ADER–WENO finite volume (FV) and ADER discontinuous Galerkin (DG) finite element schemes to the HPR model in the stiff relaxation limit, and compare the numerical results with exact or numerical reference solutions obtained for the Euler and Navier–Stokes equations. Numerical convergence results are also provided. To show the universality of the HPR model, the paper is rounded-off with an application to wave propagation in elastic solids, for which one only needs to switch off the strain relaxation source term in the governing PDE system.
We provide various examples showing that for the purpose of flow visualization, the distortion tensor A seems to be particularly useful.
The abundance of cellulose found in natural resources such as wood, and the wide spectrum of structural diversity of cellulose nanomaterials in the form of micro‐nano‐sized particles and fibers, have ...sparked a tremendous interest to utilize cellulose's intriguing mechanical properties in designing high‐performance functional materials, where cellulose's structure–mechanics relationships are pivotal. In this progress report, multiscale mechanics understanding of cellulose, including the key role of hydrogen bonding, the dependence of structural interfaces on the spatial hydrogen bond density, the effect of nanofiber size and orientation on the fracture toughness, are discussed along with recent development on enabling experimental design techniques such as structural alteration, manipulation of anisotropy, interface and topology engineering. Progress in these fronts renders cellulose a prospect of being effectuated in an array of emerging sustainable applications and being fabricated into high‐performance structural materials that are both strong and tough.
The structure–mechanics relationships of cellulose molecular chains give rise to unconventional cellulose‐based functional materials that possess multiple beneficial mechanical properties such as high strength and toughness, in addition to other fundamentally attractive properties such as low‐cost, lightweight, and sustainability.
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