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On time integration of viscoplastic constitutive models suitable for creep
Author(s) -
Schreyer H. L.
Publication year - 2001
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.293
Subject(s) - viscoplasticity , constitutive equation , creep , stability (learning theory) , conjugate gradient method , algebraic equation , mathematics , computer science , nonlinear system , mathematical optimization , finite element method , engineering , structural engineering , materials science , physics , composite material , quantum mechanics , machine learning
Creep of critical components such as electrical solder connections may occur over long periods of time. Efficient numerical simulations of such problems generally require the use of quasi‐static formulations with conjugate‐gradient techniques for solving the large number of algebraic equations. Implicit in the approach is the need to solve the constitutive equation several times for large time steps and for loading directions that may have no resemblance to the actual solution. Therefore, an unconditionally stable and efficient algorithm for solving the constitutive equation is essential for the overall efficiency of the solution procedure. Unfortunately, constitutive equations suitable for simulating the materials of interest are notoriously difficult to solve numerically and most existing algorithms have a stability limit on the time step which may be several orders of magnitude smaller than the desired time step. Here an algorithm is proposed which is a combination of the use of a trapezoidal rule and an iterative Newton–Raphson method for solving implicitly the non‐linear equations. The key to the success of the proposed approach is to always use an initial guess based on the steady‐state solution to the constitutive equation. A representative viscoplastic constitutive equation is used as a model for illustrating the approach. The algorithm is developed and typical numerical results are provided to substantiate the claim that stability has been achieved. Copyright © 2001 John Wiley & Sons, Ltd.