Line‐search methods in general return mapping algorithms with application to porous plasticity

Abstract

The present paper focuses on the application of line-search methods in general return mapping algorithms. Two inexact line-search methods and an exact line-search method are investigated regarding their convergence properties within an automatic time incrementation in finite element calculations. As an example for the assessment of the algorithms, an elastic-plastic and an elastic-viscoplastic version of Gurson's porous plasticity model are used in simulations of the necking of a tensile bar. It is shown that larger time increments are possible and, therefore, a smaller number of increments are required when using line-search methods. The exact line-search method shows the best performance concerning the required number of increments, but takes more CPU time to complete the simulation. The application of the inexact line search methods in general lowers the number of increments along with a reduction in the CPU time, as compared with the case when no line-search is used

Consistent linearization and finite element implementation of an incrementally objective canonical form return mapping algorithm for large deformation inelasticity

“…[27, p. 116, 28, p. 29]. The line-search algorithm turned out to be useful in combination with Gurson-type constitutive models [15]. The Jacobian of the Newton scheme is given by…”

“…In this paper, the fully incrementally objective Hughes and Winget algorithm is consistently linearized using a canonical form return mapping algorithm within the rotated configuration, described in [9,10,15]. Thus, in contrast to Fish and Shek [13], where the linearization is derived for a specific finite deformation plasticity model, a general and modular algorithmic setting is presented, which is in particular desirable in the development of constitutive equations.…”

A consistent u‐p formulation for porous media with hysteresis

“…The consistency of algorithms to solve nonlinear differential equations via the FEM is essential to achieve quadratic convergence; a discovery that is well known particularly in solid mechanics [1,2]. Therefore, the derivation of consistent tangent operators for material models has become a classical topic in computational plasticity [3][4][5]; see also [6,7]. In porous media mechanics, a consistent algorithm has to define operators corresponding to the update of the solid and fluid material laws; both are required for quadratic convergence.…”

Implicit Damping Iterative Algorithm to Solve Elastoplastic Static and Dynamic Equations

“…Researches on the Newton-Raphson method are focused on two aspects, namely, the computational efficiency and the stability of the solution. The Aitken acceleration method [3] and linear-search method [4,5] are used in conjunction with Newton's method to reduce the number of computational iterations. Wempner [6] and Riks [7] proposed the arc-length method, and Forde and Stiemer [8], Müller [9], and others improved it.…”