Comparison of Two Time-Integration Algorithms for an Anisotropic Damage Model Coupled with Plasticity

2015 ◽  
Vol 784 ◽  
pp. 292-299 ◽  
Author(s):  
Stephan Wulfinghoff ◽  
Marek Fassin ◽  
Stefanie Reese
Keyword(s):  
Evolution Equations ◽  
Damage Model ◽  
Time Integration ◽  
Three Dimensional ◽  
Anisotropic Damage ◽  
Euler Scheme ◽  
The Finite Element Method ◽  
Time Step ◽  
Implicit Euler Scheme ◽  
Integration Algorithms

In this work, two time integration algorithms for the anisotropic damage model proposed by Lemaitre et al. (2000) are compared. Specifically, the standard implicit Euler scheme is compared to an algorithm which implicitly solves the elasto-plastic evolution equations and explicitly computes the damage update. To this end, a three dimensional bending example is solved using the finite element method and the results of the two algorithms are compared for different time step sizes.

Time and space meshes adaptivity for the resolution of a semi-linear heat equation

2021 ◽  
pp. 1-10
Author(s):  
Nejmeddine Chorfi
Keyword(s):  
Parabolic Equation ◽  
Heat Equation ◽  
Order Of Convergence ◽  
Linear Parabolic Equation ◽  
Spectral Elements ◽  
Euler Scheme ◽  
Time Step ◽  
Implicit Euler Scheme ◽  
Linear Heat ◽  
Error Indicators

The aim of this work is to highlight that the adaptivity of the time step when combined with the adaptivity of the spectral mesh is optimal for a semi-linear parabolic equation discretized by an implicit Euler scheme in time and spectral elements method in space. The numerical results confirm the optimality of the order of convergence. The later is similar to the order of the error indicators.

Numerical Implementation of Continuum Dislocation Dynamics with the Discontinuous-Galerkin Method.

2014 ◽  
Vol 1651 ◽  
Author(s):  
Alireza Ebrahimi ◽  
Mehran Monavari ◽  
Thomas Hochrainer
Keyword(s):  
Discontinuous Galerkin ◽  
Crystal Plasticity ◽  
Evolution Equations ◽  
Total Curvature ◽  
Time Integration ◽  
Three Dimensional ◽  
Conserved Quantity ◽  
Dislocation Dynamics ◽  
Slip Systems ◽  
Continuum Dislocation Dynamics

ABSTRACTIn the current paper we modify the evolution equations of the simplified continuum dislocation dynamics theory presented in [T. Hochrainer, S. Sandfeld, M. Zaiser, P. Gumbsch, Continuum dislocation dynamics: Towards a physical theory of crystal plasticity. J. Mech. Phys. Solids. (in print)] to account for the nature of the so-called curvature density as a conserved quantity. The derived evolution equations define a dislocation flux based crystal plasticity law, which we present in a fully three-dimensional form. Because the total curvature is a conserved quantity in the theory the time integration of the equations benefit from using conservative numerical schemes. We present a discontinuous Galerkin implementation for integrating the time evolution of the dislocation state and show that this allows simulating the evolution of a single dislocation loop as well as of a distributed loop density on different slip systems.

scholarly journals Numerical Analysis of the Brittle-Ductile Transition in the Failure-Mode in Polymeric Materials

2014 ◽  
Vol 566 ◽  
pp. 310-315
Author(s):  
Josué Aranda-Ruiz ◽  
J.A. Loya
Keyword(s):  
Failure Mode ◽  
Damage Model ◽  
Three Dimensional ◽  
Polymeric Materials ◽  
Material Behavior ◽  
The Finite Element Method ◽  
Brittle Ductile Transition ◽  
User Subroutine ◽  
The Difference ◽  
Three Dimensional Models

In this paper we analyze, using the Finite Element Method, the process of brittle-ductile transition in the failure mode observed in polycarbonate notched specimens under impact loads. In order to analyze this transition we have implemented, through a user subroutine, a damage model which combines a tensional fracture criterion and an energetic, acting simultaneously. The competition between both criteria predicts the difference in material behavior from a critical impact velocity, and how this transition is produced on different planes through the thickness of the specimen. These results show the necessity of employing three-dimensional models for its study.

Direct Numerical Simulation of the Interaction of an Ultra Short-Pulsed Intense Laser With a H2+ Molecule

2008 ◽  
Author(s):  
Y.-M. Lee ◽  
J.-S. Wu ◽  
T.-F. Jiang ◽  
Y.-S. Chen
Keyword(s):  
Domain Decomposition Method ◽  
Time Integration ◽  
Three Dimensional ◽  
Time Algorithm ◽  
Intense Laser ◽  
Angle Of Incidence ◽  
Step Size ◽  
Time Step ◽  
Time Step Size ◽  
H2 Molecule

In this paper, interactions of a linearly polarized ultra short-pulsed intense laser with a single H2+ molecule at various angles of incidence are studied by directly solving the time-dependent three-dimensional Schrodinger equation (TDSE), assuming Born-Oppenheimer approximation. An explicit stagger-time algorithm is employed for time integration of the TDSE, in which the real and imaginary parts of the wave function are defined at alternative times, while a cell-centered finite-volume method is utilized for spatial discretization of the TDSE on Cartesian grids. The TDSE solver is then parallelized using domain decomposition method on distributed memory machines by applying a multi-level graph-partitioning technique. The solver is applied to simulate laser-molecular interaction with test conditions including: laser intensity of 0.5*1014 W/cm2, wavelength of 800 nm, three pulses in time, angle of incidence of 0–90° and inter-nuclear distance of 2 a.u.. Simulation conditions include 4 million hexahedral cells, 90 a.u. long in z direction, and time-step size of 0.005 a.u.. Ionization rates, harmonic spectra and instantaneous distribution of electron densities are then obtained from the solution of the TDSE. Future possible extension of the present method is also outlined at the end of this paper.

scholarly journals Effective Method for Analysis of Electrothermally Coupled Fields

1995 ◽  
Vol 2 (3) ◽  
pp. 219-225
Author(s):  
Jacek Korytkowski ◽  
Stanisław Wincenciak
Keyword(s):  
Physical Phenomenon ◽  
Three Dimensional ◽  
Main Idea ◽  
The Finite Element Method ◽  
Temperature Dependent ◽  
Time Step ◽  
Coupled Fields ◽  
Strongly Nonlinear ◽  
Step Selection ◽  
Raphson Method

An effective method is presented for solving a nonlinear system of partial differential equations that describe the time-dependent electrothermally coupled fields for passage of constant electric current in a three-dimensional conductive medium. A numerical model of this physical phenomenon was obtained by the finite element method, which takes into account the temperature-dependent characteristics describing the material parameters and conditions of heat transmission outside of the analyzed objects. These characteristics and conditions make the problem strongly nonlinear. The solution uses the Newton-Raphson method with the appropriate procedure for determining the Jacobian matrix elements. The main idea of the proposed method is the use of an automatic time step selection algorithm to solve heat conduction equations. The influence of the assumed accuracy value on the final result of the nonlinear calculation is discussed. The theoretical results were confirmed by the numerical experiments performed with selected physical objects.

Subcycled Hourglass Control for Explicit Time Integration of Dynamic Relaxation Equations

2002 ◽  
Author(s):  
D. R. Metzger ◽  
S. Gao
Keyword(s):  
Temporal Integration ◽  
Time Integration ◽  
Three Dimensional ◽  
Internal Force ◽  
Time Interval ◽  
Time Step ◽  
Central Difference ◽  
Finite Element Program ◽  
Explicit Finite Element ◽  
Hourglass Control

Explicit methods, such as the central difference operator, rely on the economical evaluation of internal forces at each time step of a transient dynamic problem. One-point quadrature applied to the spatial discretization provides the greatest efficiency, but hourglass control is required to eliminate spurious zero energy modes. Computationally practical hourglass control methods involve considerable approximation in evaluating the internal force. Thus, a small additional approximation due to an alternative temporal integration of the hourglass force may not seriously affect the accuracy of the analysis. In particular, the possibility of evaluating the hourglass terms on a larger time interval than the usual stable time step could provide significant efficiencies. The proposed approach of subcycling the hourglass terms is examined in detail with respect to stability and accuracy. Implementation into an explicit finite element program is demonstrated on a three-dimensional example that involves several hourglass modes, and the new method proves to be beneficial for noninertial problems where artificial damping is used.

Use of a Continuum Damage Model Based on Energy Equivalence to Predict the Response of a Single-Crystal Superalloy

2011 ◽  
Vol 133 (2) ◽  
Author(s):  
P. Grammenoudis ◽  
D. Reckwerth ◽  
Ch. Tsakmakis
Keyword(s):  
Equivalence Principle ◽  
Evolution Equations ◽  
Dynamic Recovery ◽  
Damage Model ◽  
Yield Function ◽  
Anisotropic Damage ◽  
Continuum Damage ◽  
Energy Equivalence ◽  
Deformation Processes ◽  
Multiple Holes

Anisotropic viscoplasticity coupled with anisotropic damage has been modeled in previous works by using the energy equivalence principle appropriately adjusted. Isotropic and kinematic hardenings are present in the viscoplastic part of the model and the evolution equations for the hardening variables incorporate both static and dynamic recovery terms. The main difference to other approaches consists in the formulation of the energy equivalence principle for the plastic stress power and the rate of hardening energy stored in the material. As a practical consequence, a yield function has been established, which depends, besides effective stress variables, on specific functions of damage. The present paper addresses the capabilities of the model in predicting responses of deformation processes with complex specimen geometry. In particular, multiple notched circular specimens and plates with multiple holes under cyclic loading conditions are considered. Comparison of predicted responses with experimental results confirms the convenience of the proposed theory for describing anisotropic damage effects.

Time-Varying Behavior of a Statically Indeterminate Shafting System in a Hydrodynamic Journal Bearing

1987 ◽  
Vol 109 (1) ◽  
pp. 115-123 ◽  
Author(s):  
Z. H. Karni ◽  
M. G. Parsons ◽  
Z. P. Mourelatos
Keyword(s):  
Control Method ◽  
Optimization Technique ◽  
Three Dimensional ◽  
Integration Time ◽  
Time Varying ◽  
The Finite Element Method ◽  
Time Step ◽  
Hydrodynamic Analysis ◽  
Oil Film ◽  
Hourglass Control

A new direct iterative method for obtaining the time-varying behavior of a statically indeterminate shafting system within one of its hydrodynamic journal bearings is described. A modified Newmark’s method is used to step in time. At each integration time step an optimization technique iterates between the shafting system and the oil film analyses until an equilibrium is achieved. The three-dimensional shafting system structural analysis and the two-dimensional oil film hydrodynamic analysis utilize the finite element method. The “hourglass control” method is employed for the construction of the oil film fluidity matrix. A numerical example illustrates the method.

A new progressive damage model for predicting the tensile behavior of the three-dimensional woven carbon/carbon composites using micromechanics method

2021 ◽  
pp. 105678952110354
Author(s):  
Kunlong Wei ◽  
Hongbin Shi ◽  
Jiang Li ◽  
Min Tang
Keyword(s):  
Evolution Equations ◽  
Damage Model ◽  
Three Dimensional ◽  
Failure Behavior ◽  
Progressive Damage ◽  
Cohesive Elements ◽  
Damage Initiation ◽  
Void Defects ◽  
Fiber Matrix ◽  
Progressive Damage Model

A new progressive damage model for the three-dimensional (3 D) woven carbon/carbon (C/C) composites is developed at fiber-matrix level using the micromechanics method. A woven architecture based Representative Volume Element (RVE) model composed of yarns, matrix and yarn/matrix interface is constructed, in which the manufacturing void defects are accounted for. The fiber-matrix concentric cylinder model is employed as a repeating unit cell to represent the yarn, and the matrix micro strain field is computed analytically by the micromechanics method. The maximum stain criteria is utilized for fiber longitudinal breakage, and the Von-Mises criterion is applied for the damage initiation of matrix in both intra-yarns and inter-yarns. The damaged fiber and matrix are modeled by the stiffness degradation method combined with exponential damage evolution equations. The zero thickness cohesive elements governed by bilinear traction-separation constitutive are adopted for yarn/matrix interfacial debonding behavior. The micro progressive damage and failure behavior of the 3 D woven C/C composites subjected to tension is implemented through a developed user-defined material subroutine in commercial software ABAQUS. The predicted stress-strain response is in a good agreement with experimental results. In addition, the effect of manufacturing void defects is also examined by the developed model.

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