scholarly journals Computer Simulation of Stochastic Energy Fluctuations in Tensile Test of Elasto-Plastic Porous Metallic Material

Energies ◽  
2020 ◽  
Vol 13 (2) ◽  
pp. 485
Author(s):  
Marcin Kamiński ◽  
Michał Strąkowski
Keyword(s):  
Finite Element ◽  
Volume Fraction ◽  
Plasticity Model ◽  
Metallic Material ◽  
Porous Plasticity ◽  
Probabilistic Technique ◽  
Computational Implementation ◽  
Element System ◽  
Porous Metallic Material

The main aim of this work is the computational implementation and numerical simulation of a metal porous plasticity model with an uncertain initial microdefects’ volume fraction using the Stochastic Finite Element Method (SFEM) based on the semi-analytical probabilistic technique. The metal porous plasticity model applied here is based on Gurson–Tvergaard–Needleman theory and is included in the ABAQUS finite element system, while the external probabilistic procedures were programmed in the computer algebra system MAPLE 2017. Hybrid usage of these two computer systems enabled the determination of fluctuations in elastic and plastic energies due to initial variations in the ratio of the metal micro-voids, and the calculation of the first four probabilistic moments and coefficients of these energies due to Gaussian distribution of this ratio. A comparison with the Monte-Carlo simulation validated the numerical efficiency of the proposed approach for any level of input uncertainty and for the first four probabilistic characteristics traditionally seen in the experimental series.

scholarly journals Estimation of the physical properties of nanocomposites by finite-element discretization and Monte Carlo simulation

2013 ◽  
Vol 371 (1993) ◽  
pp. 20120494 ◽  
Author(s):  
P. Spanos ◽  
P. Elsbernd ◽  
B. Ward ◽  
T. Koenck
Keyword(s):  
Finite Element ◽  
Monte Carlo ◽  
Electrical Properties ◽  
Volume Fraction ◽  
Effective Conductivity ◽  
Numerical Models ◽  
Strain Curve ◽  
Identification Algorithm ◽  
Element Discretization

This paper reviews and enhances numerical models for determining thermal, elastic and electrical properties of carbon nanotube-reinforced polymer composites. For the determination of the effective stress–strain curve and thermal conductivity of the composite material, finite-element analysis (FEA), in conjunction with the embedded fibre method (EFM), is used. Variable nanotube geometry, alignment and waviness are taken into account. First, a random morphology of a user-defined volume fraction of nanotubes is generated, and their properties are incorporated into the polymer matrix using the EFM. Next, incremental and iterative FEA approaches are used for the determination of the nonlinear properties of the nanocomposite. For the determination of the electrical properties, a spanning network identification algorithm is used. First, a realistic nanotube morphology is generated from input parameters defined by the user. The spanning network algorithm then determines the connectivity between nanotubes in a representative volume element. Then, interconnected nanotube networks are converted to equivalent resistor circuits. Finally, Kirchhoff's current law is used in conjunction with FEA to solve for the voltages and currents in the system and thus calculate the effective electrical conductivity of the nanocomposite. The model accounts for electrical transport mechanisms such as electron hopping and simultaneously calculates percolation probability, identifies the backbone and determines the effective conductivity. Monte Carlo analysis of 500 random microstructures is performed to capture the stochastic nature of the fibre generation and to derive statistically reliable results. The models are validated by comparison with various experimental datasets reported in the recent literature.

Local Approach of Fracture in the Ductile Regime and Application to VVER Materials

2002 ◽  
Author(s):  
B. Z. Margolin ◽  
V. I. Kostylev ◽  
E. Keim ◽  
R. Chaouadi
Keyword(s):  
Finite Element ◽  
Crack Resistance ◽  
Ductile Fracture ◽  
Finite Element Simulation ◽  
Volume Fraction ◽  
Stress Triaxiality ◽  
Local Approach ◽  
Gurson Model ◽  
Element Simulation

Within the TACIS R2.06/96 project: “Surveillance Program for VVER 1000 Reactors”, sponsored by the European Commission, the local approach of fracture has been applied in the ductile regime. Two different models were applied and compared, namely Tvergaard-Needleman-Gurson versus Prometey model. The main tasks are: • perform special Local Approach experiments on smooth and notched cylindrical specimens; • predict JR-curve on the basis of the ductile fracture models; • compare two models of ductile fracture, namely, the Tvergaard-Needleman-Gurson model and the Prometey model. In this paper, the Tvergaard-Needleman-Gurson and Prometey models are briefly described. The parameters of both models were calibrated by using experimental data obtained on tensile specimens. While only smooth tensile specimens are used to calibrate the Tvergaard-Needleman-Gurson model, notched tensile in addition to smooth tensile specimens are used to calibrate the Prometey model. In the latter, standard smooth tensile specimens are used to determine the mechanical properties (the yield stress σy, the ultimate stress σu, the ultimate elongation δu, the area reduction Z) and notched cylindrical specimens to determine the strain at rupture. The numerical analysis comprises essentially two steps: • Step 1: finite element simulation of the smooth tensile specimen (determination of true stress-strain curve and critical void volume fraction for the Tvergaard-Needleman-Gurson model) and simulation of the notched cylindrical specimen up to rupture (determination of stress triaxiality for the Prometey model); • Step 2: finite element simulation of the 2T CT specimen and determination of the crack resistance behaviour in the ductile regime (J-Δa curve). It is found that both models were able to correctly predict the crack resistance behaviour of the investigated materials. The numerical and the experimental results were in very good agreement. The main difference between the two models is that the required number of calibrated parameters in the Prometey model is less than in the Tvergaard-Needleman-Gurson model but additional tests on notched specimens are required for the Prometey model.

Strength Determination of Composite Flexible Joint

2016 ◽  
Vol 827 ◽  
pp. 149-156
Author(s):  
František Sedláček ◽  
Václava Lašová ◽  
Radek Kottner
Keyword(s):  
Finite Element ◽  
Maximum Stress ◽  
Strength Criterion ◽  
Compression Tests ◽  
Strength Criteria ◽  
Flexible Joint ◽  
Strength Determination ◽  
Element System ◽  
Static Tensile

This thesis deals with the design of a joint for composite flexible elements using an integrated connection. For the verification of the selected layout, a wrapping loop was chosen as a simplified member, which was created on a special form designed for these samples. The material used was unidirectional fibreglass and epoxy resin. These samples were then compared using quasi-static tensile and compression tests. The tests were carried out with the Zwick-Roell Z050 machine. The resulting data of the experiment were then compared with the data obtained from numerical simulations using the finite element system Siemens NX 10 and SIMULIA Abaqus 6.13. 3D strength criteria Maximum stress and direct-mode strength criterion LaRC04 were used for evaluation.

scholarly journals Random Stiffness Tensor of Particulate Composites with Hyper-Elastic Matrix and Imperfect Interface

Materials ◽  
2021 ◽  
Vol 14 (21) ◽  
pp. 6676
Author(s):  
Damian Sokołowski ◽  
Marcin Kamiński
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Analytical Method ◽  
Volume Fraction ◽  
Effective Stiffness ◽  
Particulate Composites ◽  
Stiffness Tensor ◽  
The Matrix ◽  
Hyper Elastic

The main aim of this study is determination of the basic probabilistic characteristics of the effective stiffness for inelastic particulate composites with spherical reinforcement and an uncertain Gaussian volume fraction of the interphase defects. This is determined using a homogenization method with a cubic single-particle representative volume element (RVE) of such a composite and the finite element method solution. A reinforcing particle is spherical, located centrally in the RVE, surrounded by the thin interphase of constant thickness, and remains in an elastic reversible regime opposite to the matrix, which is hyper-elastic. The interphase defects are represented as semi-spherical voids, which are placed on the outer surface of this particle. The interphase is modeled as hyper-elastic and isotropic, whose effective stiffness is calculated by the spatial averaging of hyper-elastic parameters of the matrix and of the defects. A constitutive relation of the matrix is recovered experimentally by its uniaxial stretch. The 3D homogenization problem solution is based upon a numerical determination of strain energy density in the given RVE under specific uniaxial and biaxial stretches as well as under shear deformations. The analytical relation of the effective composite stiffness to the input uncertain parameter is recovered via the response function method, using a polynomial basis and an optimized order. Probabilistic calculations are completed using three concurrent approaches, namely the iterative stochastic finite element method (SFEM), Monte Carlo simulation and by the semi-analytical method. Previous papers consider the composite fully elastic, which limits the applicability of the resulting effective stiffness tensor computed therein. The current study voids this assumption and defines the composite as fully hyper-elastic, thus extending applicability of this tensor to strains up to 0.25. The most important research finding is that (1) the effective stiffness tensor is sensitive to random interface defects in its hyper-elastic range, (2) its resulting randomness is not close to Gaussian, (3) the semi-analytical method is not perfectly suited to stochastic calculations in this region of strains, as opposed to the linear elastic region, and (4) that the increase in random dispersion of defects volume fraction has a much higher effect on the stochastic characteristics of this stiffness tensor than fluctuation of the strain.

scholarly journals A new analytical model to predict the formation of necking instabilities in porous plates subjected to dynamic biaxial loading

2021 ◽  
Author(s):  
Murlidhar Anil Kumar ◽  
Komi Espoir N'souglo ◽  
Jose Rodriguez-Martinez
Keyword(s):  
Finite Element ◽  
Stress State ◽  
Linear Stability ◽  
Analytical Model ◽  
Biaxial Loading ◽  
Volume Fraction ◽  
Hydrostatic Stress ◽  
Matrix Material ◽  
Loading Path ◽  
Porous Plasticity

In this paper, we have developed a linear stability analysis to predict the formation of necking instabilities in porous ductile plates subjected to dynamic biaxial stretching. The mechanical behavior of the material is described with the Gurson-Tvergaard-Needleman constitutive relation for progressively cavitating solids (Gurson, 1977; Tvergaard, 1981, 1982; Tvergaard and Needleman, 1984) which considers the voids to be spherical and the matrix material isotropic with yielding defined by the von Mises (1928) criterion. The analytical model is formulated in a two-dimensional framework in which the multiaxial stress state that develops inside the necked region is approximated with the Bridgman (1952) correction factor, superimposing a hydrostatic stress state to the uniform stress field that develops in the plate before localization. As opposed to the linear stability models published so far to model dynamic necking in ductile plates, which consider the material to be fully dense and incompressible, the approach developed in this paper provides new insights into the interplay between porosity and inertia on plastic localization. In addition, the predictions of the theoretical model for the critical strain leading to necking formation have been compared with unit-cell finite element calculations performed in ABAQUS/Explicit (2019). Satisfactory quantitative and qualitative agreement has been found between the theoretical and computational approach for loading paths ranging from plane strain tension to nearly equibiaxial tension, loading rates varying from 100 s−1 to 10000 s−1, and different values of the initial void volume fraction ranging from 0.01 to 0.1. Both analytical and finite element results suggest that the influence of porosity on necking localization increases, due to early voids coalescence, as the loading rate increases and the loading path approaches equibiaxial tension. The original formulation developed in this paper serves as a basis for analytically modeling the dynamic formability of porous ductile plates, and it can be readily extended to consider more complex porous plasticity theories, e.g. constitutive models which consider the anisotropy of the material (Benzerga and Besson, 2001) and/or voids with different shapes (Gologanu et al., 1993; Monchiet et al., 2008).

An Eight-Node Hexahedral Finite Element with Rotational DOFs for Elastoplastic Applications

2019 ◽  
Vol 11 (1) ◽  
pp. 54-66
Author(s):  
Ayoub Ayadi ◽  
Kamel Meftah ◽  
Lakhdar Sedira ◽  
Hossam Djahara
Keyword(s):  
Mathematical Model ◽  
Finite Element ◽  
Plastic Zone ◽  
Displacement Vector ◽  
Small Strain ◽  
Benchmark Problems ◽  
Plasticity Model ◽  
Vector Approximation ◽  
Calculation Code

Abstract In this paper, the earlier formulation of the eight-node hexahedral SFR8 element is extended in order to analyze material nonlinearities. This element stems from the so-called Space Fiber Rotation (SFR) concept which considers virtual rotations of a nodal fiber within the element that enhances the displacement vector approximation. The resulting mathematical model of the proposed SFR8 element and the classical associative plasticity model are implemented into a Fortran calculation code to account for small strain elastoplastic problems. The performance of this element is assessed by means of a set of nonlinear benchmark problems in which the development of the plastic zone has been investigated. The accuracy of the obtained results is principally evaluated with some reference solutions.

Determination of Charge Coefficient of Piezoelectric Films Using a Combined Finite Element Model and Dynamic Loading Technique

2020 ◽  
Vol 835 ◽  
pp. 229-242
Author(s):  
Oboso P. Bernard ◽  
Nagih M. Shaalan ◽  
Mohab Hossam ◽  
Mohsen A. Hassan
Keyword(s):  
Finite Element ◽  
Dynamic Loading ◽  
Material Properties ◽  
Accurate Determination ◽  
Substrate Material ◽  
Experimental Results ◽  
Piezoelectric Composite ◽  
Piezoelectric Film ◽  
Piezoelectric Charge

Accurate determination of piezoelectric properties such as piezoelectric charge coefficients (d33) is an essential step in the design process of sensors and actuators using piezoelectric effect. In this study, a cost-effective and accurate method based on dynamic loading technique was proposed to determine the piezoelectric charge coefficient d33. Finite element analysis (FEA) model was developed in order to estimate d33 and validate the obtained values with experimental results. The experiment was conducted on a piezoelectric disc with a known d33 value. The effect of measuring boundary conditions, substrate material properties and specimen geometry on measured d33 value were conducted. The experimental results reveal that the determined d33 coefficient by this technique is accurate as it falls within the manufactures tolerance specifications of PZT-5A piezoelectric film d33. Further, obtained simulation results on fibre reinforced and particle reinforced piezoelectric composite were found to be similar to those that have been obtained using more advanced techniques. FE-results showed that the measured d33 coefficients depend on measuring boundary condition, piezoelectric film thickness, and substrate material properties. This method was proved to be suitable for determination of d33 coefficient effectively for piezoelectric samples of any arbitrary geometry without compromising on the accuracy of measured d33.

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