Premium
Numerical solution of viscoplastic constitutive equations with internal state variables Part I: algorithms and implementation
Author(s) -
Fritzen Peter,
Wittekindt Jörg
Publication year - 1997
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/(sici)1099-1476(19971110)20:16<1411::aid-mma930>3.0.co;2-0
Subject(s) - viscoplasticity , mathematics , constitutive equation , state variable , algorithm , calculus (dental) , finite element method , physics , thermodynamics , medicine , dentistry
This article treats the initial‐boundary‐value problem of viscoplasticity using unified constitutive models without a yield surface. Semi‐discretization with the finite element method (FEM) leads to a system of differential‐algebraic equations (DAE) with strongly non‐linear evolution equations for the internal state variables. A special family of partitioned Runge–Kutta methods is introduced which allows an efficient time integration of the semidiscrete system. Coefficients for methods of order one, two, and three are given. Finally, numerical results for some two‐ and three‐dimensional examples using the model of Hart are presented. In a second part we will give the theoretical background and state a proof of convergence for the algorithm presented in this paper. © 1997 by B. G. Teubner Stuttgart–John Wiley & Sons Ltd.