Time Integration Algorithm for a Cyclic Damage Coupled Thermo-Viscoplasticity Model for 63Sn-37Pb Solder Applications

2004 ◽  
Vol 126 (1) ◽  
pp. 148-158 ◽  
Author(s):  
Xianjie Yang ◽  
C. L. Chow ◽  
K. J. Lau
Keyword(s):  
Time Integration ◽  
Numerical Procedure ◽  
Implicit Time ◽  
Integration Scheme ◽  
Iteration Algorithm ◽  
State Variables ◽  
Integration Algorithm ◽  
Mixed Hardening ◽  
Constitutive Material Model ◽  
Cyclic Damage

In this paper, a semi-implicit time integration scheme has been developed for a damage-coupled constitutive model to characterize the mechanical behavior of 63Sn-37Pb solder material under thermo-mechanical fatigue (TMF) loading. The scheme is developed to provide an efficient numerical procedure of integration and iteration for calculating stress and other associated state variables within a strain-driven format. In particular, a novel Newton-Raphson iteration algorithm for the damage coupled constitutive material model involving von Mises viscoplastic potential function with nonlinear mixed hardening is formulated. An algorithmic tangent stiffness tensor is derived and the model is implemented numerically into a commercial finite element (FE) code ABAQUS through its user-defined material subroutine. Several numerical simulations are conducted for validation of the proposed algorithm.

scholarly journals Investigation of Air Pocket Behavior in Pipelines Using Rigid Column Model and Contributions of Time Integration Schemes

Water ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 785
Author(s):  
Arman Rokhzadi ◽  
Musandji Fuamba
Keyword(s):  
Transient Flow ◽  
Time Integration ◽  
Driving Pressure ◽  
Implicit Time ◽  
Numerical Dissipation ◽  
Integration Scheme ◽  
Time Step ◽  
Column Model ◽  
Integration Schemes ◽  
Backward Euler

This paper studies the air pressurization problem caused by a partially pressurized transient flow in a reservoir-pipe system. The purpose of this study is to analyze the performance of the rigid column model in predicting the attenuation of the air pressure distribution. In this regard, an analytic formula for the amplitude and frequency will be derived, in which the influential parameters, particularly, the driving pressure and the air and water lengths, on the damping can be seen. The direct effect of the driving pressure and inverse effect of the product of the air and water lengths on the damping will be numerically examined. In addition, these numerical observations will be examined by solving different test cases and by comparing to available experimental data to show that the rigid column model is able to predict the damping. However, due to simplified assumptions associated with the rigid column model, the energy dissipation, as well as the damping, is underestimated. In this regard, using the backward Euler implicit time integration scheme, instead of the classical fourth order explicit Runge–Kutta scheme, will be proposed so that the numerical dissipation of the backward Euler implicit scheme represents the physical dissipation. In addition, a formula will be derived to calculate the appropriate time step size, by which the dissipation of the heat transfer can be compensated.

scholarly journals A Semi-Implicit Version of the MPAS-Atmosphere Dynamical Core

2015 ◽  
Vol 143 (9) ◽  
pp. 3838-3855 ◽  
Author(s):  
Steven Sandbach ◽  
John Thuburn ◽  
Danail Vassilev ◽  
Michael G. Duda
Keyword(s):  
Time Integration ◽  
Standard Test ◽  
Newton Iteration ◽  
Atmospheric Modeling ◽  
Implicit Time ◽  
Integration Scheme ◽  
Baroclinic Wave ◽  
Time Step ◽  
Integration Schemes ◽  
Helmholtz Problem

Abstract An important question for atmospheric modeling is the viability of semi-implicit time integration schemes on massively parallel computing architectures. Semi-implicit schemes can provide increased stability and accuracy. However, they require the solution of an elliptic problem at each time step, creating concerns about their parallel efficiency and scalability. Here, a semi-implicit (SI) version of the Model for Prediction Across Scales (MPAS) is developed and compared with the original model version, which uses a split Runge–Kutta (SRK3) time integration scheme. The SI scheme is based on a quasi-Newton iteration toward a Crank–Nicolson scheme. Each Newton iteration requires the solution of a Helmholtz problem; here, the Helmholtz problem is derived, and its solution using a geometric multigrid method is described. On two standard test cases, a midlatitude baroclinic wave and a small-planet nonhydrostatic gravity wave, the SI and SRK3 versions produce almost identical results. On the baroclinic wave test, the SI version can use somewhat larger time steps (about 60%) than the SRK3 version before losing stability. The SI version costs 10%–20% more per step than the SRK3 version, and the weak and strong scalability characteristics of the two versions are very similar for the processor configurations the authors have been able to test (up to 1920 processors). Because of the spatial discretization of the pressure gradient in the lowest model layer, the SI version becomes unstable in the presence of realistic orography. Some further work will be needed to demonstrate the viability of the SI scheme in this case.

Numerical Analysis of Solute Segregation in Directional Solidification under Static Magnetic Field

2011 ◽  
Vol 312-315 ◽  
pp. 253-258 ◽  
Author(s):  
Sabrina Nouri ◽  
Mouhamed Benzeghiba ◽  
Ahmed Benzaoui
Keyword(s):  
Magnetic Field ◽  
Static Magnetic Field ◽  
Time Integration ◽  
Magnetic Field Effect ◽  
Computer Code ◽  
Thermosolutal Convection ◽  
Implicit Time ◽  
Integration Scheme ◽  
Dimensional Solution ◽  
Time Integration Scheme

This paper addresses the effect of thermosolutal convection in the formation of defects in directionally solidified alloys. The numerical model is based on a bi-dimensional solution consisting of an implicit time integration scheme to couple thermal and solutal fields, which is supported by a finite volume numerical modeling technique. In this article, the macrosegregation phenomenon under a static magnetic field effect is analyzed numerically by a computer code developed and validated with experimental data. The numerically obtained results have been widely discussed in dependence of the characteristic parameters of the studied problem.

A Smoothing Scheme for Seismic Wave Propagation Simulation with a Mixed FEM of Diffusionized Wave Equation

2021 ◽  
pp. 2150061
Author(s):  
Ryuta Imai ◽  
Naoki Kasui ◽  
Masayuki Yamada ◽  
Koji Hada ◽  
Hiroyuki Fujiwara
Keyword(s):  
Wave Propagation ◽  
Wave Equation ◽  
Seismic Wave ◽  
Time Integration ◽  
Coupled System ◽  
Seismic Wave Propagation ◽  
Implicit Time ◽  
Integration Scheme ◽  
Weak Formulation ◽  
Mixed Fem

In this paper, we propose a smoothing scheme for seismic wave propagation simulation. The proposed scheme is based on a diffusionized wave equation with the fourth-order spatial derivative term. So, the solution requires higher regularity in the usual weak formulation. Reducing the diffusionized wave equation to a coupled system of diffusion equations yields a mixed FEM to ease the regularity. We mathematically explain how our scheme works for smoothing. We construct a semi-implicit time integration scheme and apply it to the wave equation. This numerical experiment reveals that our scheme is effective for filtering short wavelength components in seismic wave propagation simulation.

Dynamics of Disconnected Risers Under Rigid and Compliant Hang-Off

1990 ◽  
Vol 112 (2) ◽  
pp. 106-114
Author(s):  
N. M. Patrikalakis ◽  
D. Y. Yoon
Keyword(s):  
Efficient Solution ◽  
Time Integration ◽  
Implicit Time ◽  
Integration Scheme ◽  
Nonuniform Grid ◽  
Implicit Time Integration ◽  
Time Integration Scheme ◽  
Type Response ◽  
Nonlinear Motions ◽  
Excitation Conditions

An efficient solution scheme to simulate the nonlinear motions of hanging risers based on an adaptive nonuniform grid finite difference method and an implicit time integration scheme is presented. Dynamic buckling-type response of hanging risers under rigid hang-off due to heave acceleration of the support platform in extreme excitation conditions is studied, and the important parameters affecting the response are identified. Significant reduction of motions and resulting stresses is obtained by employing compliant hang-off.

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