We develop a weak Galerkin (WG) finite element method for the Biot’s consolidation model in the classical displacement–pressure two-field formulation. Weak Galerkin linear finite elements are used ...for both displacement and pressure approximations in spatial discretizations. Backward Euler scheme is used for temporal discretization in order to obtain an implicit fully discretized scheme. We study the well-posedness of the linear system at each time step and also derive the overall optimal-order convergence of the WG formulation. Such WG scheme is designed on general shape regular polytopal meshes and provides stable and oscillation-free approximation for the pressure without special treatment. Numerical experiments are presented to demonstrate the efficiency and accuracy of the proposed weak Galerkin finite element method.
•We provided a theoretical description of the anisotropic change of food dimensions.•We estimated the interactions between transport phenomena and food structure modifications.•We developed a ...computational tool describing the performance of real driers.•We determined the effects of operating conditions on shrinkage and on transfer rates.•The fluid–food interactions were modeled considering the time change of integration domains.
The aim of the present work was the formulation of a theoretical model predicting the behavior of a convective drier over a wide range of process conditions. The proposed approach was based on the coupling of a transport phenomena model, describing the simultaneous transfer of momentum, heat and mass both in the drying chamber and in the food, and of a structural mechanics model aimed at estimating food sample deformations, as due to moisture loss. The effects of food shrinkage on drying performance were ascertained by analyzing the spatial distributions of temperature, moisture content, strain and stress, as a function of operating conditions. The agreement between model predictions and a set of experimental data collected during drying of cylindrical potatoes was good as far as the time evolutions of food average moisture content and of its main dimensions, i.e. length and diameter, were concerned.
In the present study, both experimental and numerical examinations were performed to understand the hypereutectic Al–Mg2Si composite's microstructural morphology, mechanical properties and fracture ...correlation. The innovation of this research includes the micromechanics studies and failure initiation in hypereutectic Al–Mg2Si composite through the compiled induce stress, deformation plasticity and energy dissipation theory subjected to tension. Ultimate tensile strength (UTS), toughness and elongation have decreased, but the yield strength has increased up to 25% Mg2Si addition and then decreased at the composites with 30 wt% Mg2Si because the brittle fracture increases due to the presence of comparatively coarser and dendritic primary Mg2Si particles. Additionally, an increase in the microporosity with the increase in Mg2Si concentration also affects the same. Finite element analysis (FEA) was performed using the Ramberg-Osgood constitutive model and actual microstructure 2D representative volume elements model. The FEA and experimental results have a satisfactory agreement. The fractography unveils the presence of a mix-mode of fracture, i.e. the ductile and the brittle fracture of the composites. Mises and Tresca failure criteria reveal that the distribution of stress is non-homogeneous and stress is localized in the narrow eutectic and irregular Mg2Si phase region, which acts as a crack initiation site. Analysis of the stress triaxiality and equivalent plastic strain distribution shows that void initiation and growth take place during the deformation of the Al–Mg2Si composites. The plastic dissipated energy distribution in deformed RVEs interestingly consents to the von mises stress, plastic strain and stress triaxiality analysis findings.
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•The influence of Mg2Si wt. % was investigated both experimentally and numerically.•The most desirable mechanical properties were achieved in the Al–15Mg2Si composite.•Eutectic Mg2Si leads to the failure initiation of the composite.•Primary Mg2Si drives the final failure of the composite.•Energy dissipation is low in composite near the pseudo-eutectic region.
Magnetoelectric (ME) composites exhibiting strain-mediated coupling are gaining increasing interest for applications. The most interesting ones are composed of piezoelectric polymers and ...magnetostrictive particles. In particular, low dimensional ME materials, such as the ones in the form of micro- and nano-spheres, show strong potentials for improved energy harvesters with higher volume efficiency, sensors and actuators. Nevertheless the ME characterization of such low dimensional ME structures remain a difficult and challenging task and, therefore, the use of mathematical models and simulations are an interesting and viable option to better understand and tailor materials towards applications.
In this context, the ME coupling on microspheres based on piezoelectric poly(vinylidene fluoride) (PVDF) and magnetostrictive CoFe2O4 (CFO) particles was theoretically studied based on Finite Element Methods (FEM). The effect of sphere size and filler content on the ME response was evaluated, showing that the ME response of CFO/PVDF microspheres is strongly influenced by the magnetic field intensity, sphere diameter and CFO content, being the highest ME response achieved on composite sphere with 90 wt% of CFO and 1.2 μm.
Predicting the structural performance of a joint requires mechanical characterization of the interface that results from the joining process. Use of the cohesive zone model (CZM) is a popular ...approach for investigating fractures, seams, and joints in the structures. The CZM requires a cohesive constitutive law, which, in the context of a welded joint, relates the traction at the interface to the separation displacement of the two surfaces. Additionally, typical congurations for fracture testing to obtain the parameters for a cohesive law involve assumptions including large weld areas and undisturbed substrate, making those techniques unsuitable for friction stir welded joints. This paper presents an approach of experimentation combined with nite element modeling to determine the cohesive law parameters to mechanically characterize the interface obtained in friction stir welded joints.
The phenomenology of population extinction is one of the central themes in population biology which it is an inherently stochastic event. In the present investigation, we study this problem for three ...different stochastic models built from a single Lotka–Volterra deterministic model. More concretely, we study their mean-extinction time which satisfies the backward Kolmogorov differential equation, a linear second-order partial differential equation with variable coefficients; hence, we can only compute numerical approximations. We suggest a finite element method using FreeFem++. Our analysis and numerical results allow us to conclude that there are important differences between the three models. These differences enable us to choose the most “natural way” to turn a the deterministic model into a stochastic model.
•Stabilized finite element method for viscoplastic flows using equal order polynomials.•Computational cost is considerably reduced.•Increased numerical stability in critical flow conditions, i.e., ...bubble entrapment•Numerical results in quantitative agreement with other popular methods
Ideal viscoplastic models present an inherent discontinuity at the yielded/unyielded interface, which poses great numerical difficulties. In this work, the recently proposed method for the solution of viscoplastic flows, the Penalized Augmented Lagrangian (PAL) method (Dimakopoulos et al. (2018)) is coupled with a new projection-based finite element formulation that allows for equal order interpolants in all variables. The accuracy of the new finite element formulation is assessed by comparing its numerical results to those of the literature in three problems: (a) the buoyancy-driven bubble rise through a viscoplastic medium, (b) the steady-state lid-driven cavity and its transient counterpart, and (c) the transient gas-assisted displacement of a viscoplastic material in straight and corrugated tubes. The method presents increased numerical stability and reduced computational cost without hindering the accuracy of the solution. By changing the solution procedure, we are able to obtain solutions that are as accurate as those obtained with the Augmented Lagrangian (AL) method. In addition, we show that the optimal value of the penalty parameter is correlated with the mesh and the critical dimensionless numbers that correspond in each problem.
Generalized laws of Fourier and Fick based on thermal and solutal relaxation times are used in the development of the system of PDEs related to simultaneous transport of heat and species in Maxwell ...fluid with mono and hybrid nano particles. The developed systems of PDEs are solved numerically by using the finite element method (FEM). Implementation of the FEM algorithm is discussed. The parametric study is carried out by performing various theoretical and numerical experiments. Related outcomes are presented in the form of graphs and numerical data. Convergence is ensured and grid-independent solutions are derived. Thermal relaxation parameter tends to lower down the temperature of the fluid and thermal boundary layer becomes shorter for higher values of thermal relaxation parameter. Concentration relaxation parameter has shown a decreasing impact on the diffusion of species in Maxwell fluid. Deborah number has reduced the diffusion of momentum in Maxwell fluid. Convective transport of both heat and species is compromised when Deborah's number is increased. It is also noticed from simulations that Deborah number for mono nano-Maxwell fluid has greater value relative to that for hybrid nano-Maxwell fluid. The simulations have also confirmed that the effective thermal conductivity of the Maxwell fluid due to the simultaneous dispersion of copper and aluminium oxide is greater than the thermal conductivity of pure Maxwell fluid and mono nano-Maxwell fluid. Therefore, simultaneous dispersion of copper and aluminium oxide for optimized heat transfer. Thermal and concentration relaxation memory effects are responsible for reducing thermal and concentration boundary layer thickness respectively. It is also noted that heat transport rate in hybrid nano-Maxwell fluid is greater than that in mono nano-Maxwell fluid and pure Maxwell fluid. Thermal memory effects play significant role in increasing the wall heat flux.
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