Abstract
AbstractIn most finite-element codes, a Newton-Raphson procedure is used for solving the global equilibrium problem. To preserve quadratic convergence of the aforementioned iterative scheme, this paper presents an analytical full linearization of the principal of virtual work in an updated Lagrangian framework and develops tangent operators consistent with the integration algorithms. Four implementations of the most-used objective rates are described and are shown to be consistent, stable, and objective. The rigid body rotation tensor is obtained by a new computational implementation of polar decomposition scheme in two-dimensional problems. An automatic substepping algorithm is used for integrating elastoplastic constitutive laws in large deformation problems. Numerical examples are presented to test the algorithms, validate the proposed schemes, and compare their performance with other integration algorithms.
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