1991
DOI: 10.1002/nme.1620310110
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Convergence of the Newton‐Raphson algorithm in elastic‐plastic incremental analysis

Abstract: SUMMARYA spatially continuous, time discrete formulation of the loading of an elastic, perfectly plastic body governed by a von Mises yield condition is presented. It is assumed that incremental changes in strain occur along minimum work paths, which is equivalent to a backward difference implicit integration algorithm or the radial return method. This assumption permits the incremental problem to be formulated as a convex non-linear programming problem. The classical Newton-Raphson algorithm can be adopted to… Show more

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Cited by 36 publications
(21 citation statements)
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“…The algorithm studied is stable, but can present numerical dissipation at the interface (see (49)). Expression (49) shows that if the velocity of subdomain A is constant on the coarse time scale, then the numerical dissipation equals zero; otherwise, energy dissipates at the interface.…”
Section: Stability and Convergence Studymentioning
confidence: 99%
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“…The algorithm studied is stable, but can present numerical dissipation at the interface (see (49)). Expression (49) shows that if the velocity of subdomain A is constant on the coarse time scale, then the numerical dissipation equals zero; otherwise, energy dissipates at the interface.…”
Section: Stability and Convergence Studymentioning
confidence: 99%
“…Expression (49) shows that if the velocity of subdomain A is constant on the coarse time scale, then the numerical dissipation equals zero; otherwise, energy dissipates at the interface. In other terms, when the displacement of subdomain A is not linear with time, the smaller the local radius of curvature, the higher the numerical dissipation.…”
Section: Stability and Convergence Studymentioning
confidence: 99%
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“…In the numerical model the integrals (19) are approximate by following formula: (20) where s+1 is the actual time step, s -previous time step, mit is the number of iteration in the increase of time Δt s+1 . In the iterative process of evaluation of plastic strains, the modified Newton-Raphson algorithm is used [22,25].…”
Section: Model Of Thermo-elasto-plastic Stress and Strainmentioning
confidence: 99%
“…The scalar plastic multiplier in the model of an isotropic and kinematic hardening can be determined by using the Newton-Raphson method [1,7].…”
Section: Kinematic Hardeningmentioning
confidence: 99%