A smooth hyperbolic approximation to the Mohr-Coulomb yield criterion

Abbo, Andrew J.; Sloan, Scott W.

doi:10.1016/0045-7949(94)00339-5

Cited by 229 publications

(137 citation statements)

References 2 publications

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“…The summation in brackets of equation (18) plays the same role that the inverse of the Jacobian of equation (6). In fact, equation (18) is identical to equation (6) if only one substep is considered, m = 1.…”

Section: The Consistent Tangent Modulimentioning

confidence: 80%

“…Equation (18) has the same structure of equation (6). The summation in brackets of equation (18) plays the same role that the inverse of the Jacobian of equation (6).…”

Section: The Consistent Tangent Modulimentioning

confidence: 89%

“…Note that the computation of the consistent tangent moduli involves matrix inversions, even in the case of single-step integration rules with no substepping, equation (6). It must be remarked, however, that small matrices are considered, so numerical inversion poses no difficulties.…”

Section: The Consistent Tangent Modulimentioning

confidence: 99%

“…In this subsection a rigid footing is analysed with the Rounded Hyperbolic Mohr-Coulomb model [6] and substepping. The consistent tangent matrix developed in section 3 is employed to achieve quadratic convergence at the global level.…”

Section: Simulation Of a Rigid Footing With The Rounded Hyperbolic Momentioning

confidence: 99%

“…As a consequence, the computational cost of substepping is marginal in comparison with the cost of global equilibrium iterations. These aspects are illustrated by means of some numerical examples regarding the Rounded Hyperbolic Mohr-Coulomb model [6].…”

Section: Introductionmentioning

confidence: 99%

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Consistent tangent matrices for substepping schemes

Foguet

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Huerta

2001

Computer Methods in Applied Mechanics and Engineering

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show abstract

Section: The Consistent Tangent Modulimentioning

confidence: 80%

“…Equation (18) has the same structure of equation (6). The summation in brackets of equation (18) plays the same role that the inverse of the Jacobian of equation (6).…”

Section: The Consistent Tangent Modulimentioning

confidence: 89%

Section: The Consistent Tangent Modulimentioning

confidence: 99%

Section: Simulation Of a Rigid Footing With The Rounded Hyperbolic Momentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Consistent tangent matrices for substepping schemes

Foguet

Ferran

Huerta

2001

Computer Methods in Applied Mechanics and Engineering

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Biot consolidation analysis with automatic time stepping and error control Part 2: applications

Sloan

Abbo²

1999

Int. J. Numer. Anal. Meth. Geomech.

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SUMMARYThe automatic time-stepping algorithms developed in a companion paper are used to study the behaviour of several problems involving the consolidation of porous media. The aim of these analyses is to demonstrate that the new procedures are robust, e$cient, and can control the global temporal discretization (or time-stepping) error in the displacements to lie near a prescribed error tolerance.

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An Automatic Load Stepping Algorithm With Error Control

Abbo

Sloan

1996

Int. J. Numer. Meth. Engng.

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SUMMARYThis paper presents an algorithm for controlling the error in non-linear finite element analysis which is caused by the use of finite load steps. In contrast to most recent schemes, the proposed technique is non-iterative and treats the governing load-deflection relations as a system of ordinary differential equations. This permits the governing equations to be integrated adaptively where the step size is controlled by monitoring the local truncation error. The latter is measured by computing the difference between two estimates of the displacement increments for each load step, with the initial estimate being found from the first-order Euler scheme and the improved estimate being found from the second-order modified Euler scheme. If the local truncation error exceeds a specified tolerance, then the load step is abandoned and the integration is repeated with a smaller load step whose size is found by local extrapolation. Local extrapolation is also used to predict the size of the next load step following a successful update. In order to control not only the local load path error, but also the global load path error, the proposed scheme incorporates a correction for the unbalanced forces. Overall, the cost of the automatic error control is modest since it requires only one additional equation solution for each successful load step. Because the solution scheme is non-iterative and founded on successful techniques for integrating systems of ordinary differential equations, it is particularly robust. To illustrate the ability of the scheme to constrain the load path error to lie near a desired tolerance, detailed results are presented for a variety of elastoplastic boundary value problems.

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A smooth hyperbolic approximation to the Mohr-Coulomb yield criterion

Cited by 229 publications

References 2 publications

Consistent tangent matrices for substepping schemes

Consistent tangent matrices for substepping schemes

Biot consolidation analysis with automatic time stepping and error control Part 2: applications

An Automatic Load Stepping Algorithm With Error Control

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