scholarly journals Modeling of failure at the interface of ductile materials by applying the cohesive discontinuous Galerkin method

2021 ◽  
Author(s):  
Hamid Reza Bayat ◽  
Ali Rajaei Harandi ◽  
Shahed Rezaei ◽  
Tim Brepols ◽  
Stefanie Reese
Keyword(s):  
Discontinuous Galerkin ◽  
Material Model ◽  
Isotropic Hardening ◽  
Failure Behavior ◽  
Elastoplastic Material ◽  
Ductile Materials ◽  
Nonmatching Meshes ◽  
Dg Method ◽  
Conventional Models ◽  
Hardening Rules

In this study, the failure behavior at the interface of ductile materials is investigated. In order to capture the degradation of the tractions at the interface, a cohesive zone (CZ) model is applied. The choice of the type of the CZ approach, i.e. either intrinsic or extrinsic, brings about different drawbacks. The former includes an elastic regime at the interface prior to the failure, which can result in numerical difficulties whereas the latter necessitates the re-meshing of the structure during crack propagation. In order to overcome these problems, the incomplete interior penalty Galerkin variant of the discontinuous Galerkin (DG) method is applied both at the interface and in the bulk instead of the standard conforming finite element method. In addition, the application of the DG method enables to use nonmatching meshes in the discretized model. To treat the bulk, an elastoplastic material model with isotropic hardening as well as different hardening rules for small strains is incorporated into the DG framework. Two numerical examples are computed to study the convergence behavior of the new cohesive discontinuous Galerkin (CDG) method in comparison to that of the conventional models. The new CDG method outperforms the conventional CZ continuous Galerkin elements in the presence of locking effects as well as hanging nodes.

Nonlinear Material Model in Part Variation Simulations of Sheet Metals

2019 ◽  
Vol 19 (2) ◽  
Author(s):  
Soner Camuz ◽  
Samuel Lorin ◽  
Kristina Wärmefjord ◽  
Rikard Söderberg
Keyword(s):  
Material Model ◽  
Nonlinear Material ◽  
Isotropic Hardening ◽  
Elastoplastic Material ◽  
Processing Unit ◽  
Central Processing ◽  
Physical Experiments ◽  
Linear Relationships ◽  
Influence Coefficients ◽  
Variation Simulation

Current methodologies for variation simulation of compliant sheet metal assemblies and parts are simplified by assuming linear relationships. From the observed physical experiments, it is evident that plastic strains are a source of error that is not captured in the conventional variational simulation methods. This paper presents an adaptation toward an elastoplastic material model with isotropic hardening in the method of influence coefficients (MIC) methodology for variation simulations. The results are presented in two case studies using a benchmark case involving a two-dimensional (2D) quarter symmetric plate with a centered hole, subjected to both uniaxial and biaxial displacement. The adaptation shows a great reduction in central processing unit time with limited effect on the accuracy of the results compared to direct Monte Carlo simulations.

FE Prediction and Extrapolation of Multiaxial Ratcheting for R7T Steel

2019 ◽  
Vol 810 ◽  
pp. 76-81 ◽  
Author(s):  
Radim Halama ◽  
Jana Bartecká ◽  
Petr Gál
Keyword(s):  
Experimental Testing ◽  
Kinematic Hardening ◽  
Cyclic Creep ◽  
Material Model ◽  
Rolling Contact ◽  
Isotropic Hardening ◽  
Proportional Loading ◽  
Space Material ◽  
Hardening Rules ◽  
With Memory

Wear of materials in rail/wheel industry is closely related to the cyclic creep. This contribution presents main results of experimental testing on R7T wheel steel. The cyclic creep is investigated under non-proportional loading conditions simulating a line rolling contact case. McDowell extrapolation was successfully applied to the calculation of twist. Cyclic material model MAKOC and MAKOC with memory surface were used for cyclic creep prediction. The plasticity model is based on AbdelKarim-Ohno kinematic hardening and Calloch isotropic hardening rules. Second material model was extended with Jiang-Sehitoglu memory surface, which is introduced in stress space. Material models were successfully used for predicting accumulation of shear strain.

Predictions of microtorsional experiments by micropolar plasticity

2005 ◽  
Vol 461 (2053) ◽  
pp. 189-205 ◽  
Author(s):  
Paschalis Grammenoudis ◽  
Charalampos Tsakmakis
Keyword(s):  
Size Effects ◽  
Bauschinger Effect ◽  
Kinematic Hardening ◽  
Circular Cylinders ◽  
Isotropic Hardening ◽  
Gradient Plasticity ◽  
Material Response ◽  
Micropolar Plasticity ◽  
Classical Plasticity ◽  
Hardening Rules

Kinematic hardening rules are employed in classical plasticity to capture the so–called Bauschinger effect. They are important when describing the material response during reloading. In the framework of thermodynamically consistent gradient plasticity theories, kinematic hardening effects were first incorporated into a micropolar plasticity model by Grammenoudis and Tsakmakis. The aim of the present paper is to investigate this model by predicting size effects in torsional loading of circular cylinders. It is shown that kinematic hardening rules compared with isotropic hardening rules, as adopted in the paper, provide more possibilities for modelling size effects in the material response, even if only monotonous loading conditions are considered.

scholarly journals Consistent Weighted Average Flux of Well-Balanced TVD-RK Discontinuous Galerkin Method for Shallow Water Flows

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Thida Pongsanguansin ◽  
Montri Maleewong ◽  
Khamron Mekchay
Keyword(s):  
Shallow Water ◽  
Discontinuous Galerkin ◽  
Numerical Solutions ◽  
Order Approximation ◽  
Weighted Average ◽  
Flat Bottom ◽  
Flux Function ◽  
Dg Method ◽  
Average Flux ◽  
Steady Solutions

A well-balanced scheme with total variation diminishing Runge-Kutta discontinuous Galerkin (TVD-RK DG) method for solving shallow water equations is presented. Generally, the flux function at cell interface in the TVD-RK DG scheme is approximated by using the Harten-Lax-van Leer (HLL) method. Here, we apply the weighted average flux (WAF) which is higher order approximation instead of using the HLL in the TVD-RK DG method. The consistency property is shown. The modified well-balanced technique for flux gradient and source terms under the WAF approximations is developed. The accuracy of numerical solutions is demonstrated by simulating dam-break flows with the flat bottom. The steady solutions with shock can be captured correctly without spurious oscillations near the shock front. This presents the other flux approximations in the TVD-RK DG method for shallow water simulations.

scholarly journals NUMERICAL SIMULATION OF A MASSIVE IMPACTOR FALLING ONTO A REINFORCED CONCRETE BEAM

2020 ◽  
Vol 82 (1) ◽  
pp. 5-15
Author(s):  
S.M. Gertsik ◽  
Yu.V. Novozhilov
Keyword(s):  
Finite Elements ◽  
Concrete Beam ◽  
Time Integration ◽  
Volumetric Strain ◽  
Failure Criteria ◽  
Tensile Failure ◽  
Low Velocity Impact ◽  
Isotropic Hardening ◽  
Elastoplastic Material ◽  
Low Velocity

The paper presents the results of numerically modeling the dynamics of a concrete beam reinforced by longitudinal rods and transversal frames of rods under the effect of a falling massive impactor. The dynamic behavior of the material of concrete is described using the Holmquist - Johnson - Cook model. The reinforcement of the beam is modeled by beam elements, using the bilinear model of elastoplastic material with isotropic hardening. Binding between the reinforcement and concrete is described by introducing additional kinematic equations that couple degrees of freedom of the related nods of the beam and volumetric finite elements. The mathematical model makes it possible to introduce additional failure criteria to predict propagation of tensile cracking. Pressure lower than the minimal one (failure only in the tension zone) and volumetric strain higher than the threshold value are taken as a criterion of tensile failure. Failure is modeled by removing elements from the computational pattern, when the above failure criteria are satisfied. The effect of accounting for failure on the response of the beam is analyzed. Numerical modeling is done using the finite-element method with explicit time integration in the LOGOS and LS-DYNA systems. Concrete is modeled using linear four-node finite elements with one integration point. The impactor is modeled as an absolutely solid body with a detailed description of the impacting end. The obtained results are compared with experimental data. It is demonstrated that the Holmquist - Johnson - Cook material model developed for analyzing high-velocity impacts can also be applied to problems of low-velocity impact.

Finite Element Simulation Analysis on Residual Stress Relief of 7075 Aluminum Alloy Ring

2021 ◽  
Vol 1032 ◽  
pp. 135-140
Author(s):  
Shao Feng Wu ◽  
Xiang Sheng Gao ◽  
Xian Rang Zhang ◽  
Han Jun Gao
Keyword(s):  
Residual Stress ◽  
Aluminum Alloy ◽  
Simulation Analysis ◽  
Material Model ◽  
Stress Relief ◽  
Isotropic Hardening ◽  
7075 Aluminum Alloy ◽  
Vibration Stress ◽  
Structural Parts ◽  
Creep Constitutive Model

Vibration stress relief (VSR) and thermal stress relief (TSR) are important method to eliminate the residual stress of structural parts. The thermal vibratory stress relief (TVSR) is a new method to decrease and homogenize the residual stress. Based on the stress relaxation tests and the equivalent vibration equation of modal analysis, the creep constitutive model and the bilinear isotropic hardening plasticity material model (BISO) are combined to establish the numerical simulation model of TVSR of 7075 aluminum alloy ring part. The simulation results show that four different initial blank residual stress levels are obtained after quenching process, and the residual stress elimination and homogenization effect of TSR and TVSR is better than that of VSR. TVSR has a better effect on both residual stress elimination and homogenization, and the residual stress relief rate can reach more than 20%.

scholarly journals A discontinuous Galerkin fast-sweeping eikonal solver for fast and accurate traveltime computation in 3D tilted anisotropic media

Geophysics ◽  
2019 ◽  
Vol 84 (2) ◽  
pp. C107-C118 ◽  
Author(s):  
Philippe Le Bouteiller ◽  
Mondher Benjemaa ◽  
Ludovic Métivier ◽  
Jean Virieux
Keyword(s):  
Discontinuous Galerkin ◽  
Seismic Anisotropy ◽  
Computational Cost ◽  
Anisotropic Media ◽  
Finite Difference Schemes ◽  
Seismic Amplitude ◽  
Fast Sweeping ◽  
Complex Models ◽  
Dg Method ◽  
Sweeping Method

We tackle the challenging problem of efficient and accurate seismic traveltime computation in 3D anisotropic media by applying the fast-sweeping method to a discontinuous Galerkin (DG)-based eikonal solver. Using this method leads to a stable and highly accurate scheme, which is faster than finite-difference schemes for a given precision, and with a low computational cost compared to the standard Runge-Kutta DG formulation. The integral formulation of the DG method also makes it easy to handle seismic anisotropy and complex topographies. Several numerical tests on complex models, such as the 3D SEG advanced modeling model, are given as illustration, highlighting the efficiency and the accuracy of this new approach. In the near future, these results will be used together with accurate solvers for seismic amplitude and take-off angle computation to revisit asymptotic inversion (traveltime/slope tomography) and imaging approaches (quantitative migration involving amplitudes and angles).

Discontinuous Galerkin approximation for excitatory-inhibitory networks with delay and refractory periods

2020 ◽  
Vol 31 (03) ◽  
pp. 2050041
Author(s):  
Dipty Sharma ◽  
Paramjeet Singh
Keyword(s):  
Discontinuous Galerkin ◽  
Galerkin Approximation ◽  
Strong Stability ◽  
Weno Scheme ◽  
Transmission Delays ◽  
Weighted Essentially Nonoscillatory ◽  
Refractory Periods ◽  
Dg Method ◽  
Analysis Of Stability ◽  
Inhibitory Networks

In this study, we consider the network of noisy leaky integrate-and-fire (NNLIF) model, which governs by a second-order nonlinear time-dependent partial differential equation (PDE). This equation uses the probability density approach to describe the behavior of neurons with refractory states and the transmission delays. A numerical approximation based on the discontinuous Galerkin (DG) method is used for the spatial discretization with the analysis of stability. The strong stability-preserving explicit Runge–Kutta (SSPERK) method is performed for the temporal discretization. Finally, some test examples and numerical simulations are given to examine the behavior of the solution. The execution of the constructed scheme is measured by the quantitative comparison with the existing finite difference technique, namely weighted essentially nonoscillatory (WENO) scheme.

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