Error estimates of an Euler method for a quasistatic elastic-visco- plastic problem. (English) Zbl 0712.73028

Ionescu, I. R.

Z. Angew. Math. Mech. 70, No. 3, 173-180 (1990).

It is often necessary to use numerical methods to find the solution of problems of deformation of rate-dependent materials, particularly of the kind discussed here. Here, the author applies rigorous numerical analysis to the application of Euler’s method to such problems. An explicit Euler method is used to develop a recursive sequence of linear elliptic boundary value problems; an estimation of error is also given. A final error estimate is also given for an algebraic process leading to the displacements and stresses in such problems. Numerical examples are described.
Of particular interest to specialists in numerical analysis and computational methods of structural analysis.

Reviewer: R.H.Lance

MSC:

74S30	Other numerical methods in solid mechanics (MSC2010)
74C10	Small-strain, rate-dependent theories of plasticity (including theories of viscoplasticity)
74C15	Large-strain, rate-independent theories of plasticity (including nonlinear plasticity)
74C20	Large-strain, rate-dependent theories of plasticity
74S05	Finite element methods applied to problems in solid mechanics

Keywords:

initial and boundary value problem; internal; external approximation techniques; error estimated over finite time interval; viscoelastic case; estimated over infinite time interval; rate-dependent materials; explicit Euler method; recursive sequence of linear elliptic boundary value problems; displacements; stresses

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