Subdifferential‐based implicit return‐mapping operators in computational plasticity

Sysala, Stanislav; Čermák, Martin; Koudelka, Tomáš; Kruis, Jaroslav; Zeman, Jan; Blaheta, Radim

doi:10.1002/zamm.201500305

Cited by 20 publications

(38 citation statements)

References 33 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, this investigation seems to be more involved and we shall not go into details here. The semismoothness of elastoplastic constitutive operators has been analyzed, e.g., in [8,18,27,31,32,34].…”

Section: Commentsmentioning

confidence: 99%

“…The main aim of this paper is to simplify the handling such criteria by using a specific form of the subdifferential of the eigenvalue yield function. A similar idea was introduced in the recent paper [34] for yield criteria containing one or two singular points (apices) on the yield surface (e.g., the Drucker-Prager or the Menétrey-Willam ones). It led to simpler and more correct implicit constitutive solution schemes, and it enabled a deeper analysis of the stress-strain operator.…”

Section: Introductionmentioning

confidence: 99%

“…Such a formulation is independent of the unknown stress position, contains just one plastic multiplier, and thus it is more convenient for mathematical analysis of the constitutive operators. In [34], it was shown that this formulation is also convenient for solution of some constitutive problems. Finally, in some special cases, the constitutive problem can also be defined by using the principle of maximum plastic dissipation [17,19] or the theory of bipotentials [3,38] and solved by techniques based on mathematical programming.The (fully) implicit Euler discretization of the flow rule is frequently used in elastoplasticity.…”

mentioning

confidence: 99%

See 2 more Smart Citations

Subdifferential‐based implicit return‐mapping operators in Mohr‐Coulomb plasticity

2017

Self Cite

View full text Add to dashboard Cite

Key wordsInfinitesimal plasticity, Mohr-Coulomb yield surface, implicit return-mapping scheme, consistent tangent operator, semismooth Newton method, incremental limit analysis, slope stability. MSC (2010) 35Q74, 74C05, 74S05, 90C25The paper is devoted to constitutive solution, limit load analysis and Newton-like methods in elastoplastic problems containing the Mohr-Coulomb yield criterion. Within the constitutive problem, we introduce a self-contained derivation of the implicit return-mapping solution scheme using a recent subdifferential-based treatment. Unlike conventional techniques based on Koiter's rules, the presented scheme a priori detects a position of the unknown stress tensor on the yield surface even if the constitutive solution cannot be found in a closed form. This eliminates blind guesswork from the scheme and enables to analyze properties of the constitutive operator. It also simplifies the construction of the consistent tangent operator, which is important for the semismooth Newton method when applied to the incremental boundary-value elastoplastic problem. The incremental problem in Mohr-Coulomb plasticity is combined with limit load analysis. Beside a conventional direct method of incremental limit analysis, a recent indirect one is introduced and its advantages are described. The paper contains 2D and 3D numerical experiments on slope stability with publicly available Matlab implementations. / www.zamm-journal.org 1503 respectively. It is worth mentioning that the solution schemes depend mainly on the formulation of the plastic flow rule, its discretization and eventual other approximations. Let us now briefly discuss these aspects.The plastic flow rule is usually formulated by using the so-called Koiter rule in engineering practice. This rule was introduced for associative models with multisurface yield criteria in [23] and consequently extended to nonassociative models, see, e.g., [15]. It consists of several formulas that depend on a position of the unknown stress tensor on the yield surface. These formulas have a different number of plastic multipliers. Within the Mohr-Coulomb pyramid, one plastic multiplier is used for the smooth portions, two multipliers at the edge points, and six multipliers at the apex. Therefore, the resulting solution schemes are different for each Koiter's formula. However, only one of them usually leads to the correct stress tensor. Moreover, handling different numbers of plastic multipliers is not suitable for analyzing the stress-strain operator even if the solution can be found in a closed form. If the elastoplastic model contains a convex plastic potential as the Mohr-Coulomb one, then it is possible to replace the Koiter rule with a subdifferential of the potential (see, e.g., [17]). Such a formulation is independent of the unknown stress position, contains just one plastic multiplier, and thus it is more convenient for mathematical analysis of the constitutive operators. In [34], it was shown that this formulation is also convenient for solution of some con...

show abstract

Section: Commentsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

See 1 more Smart Citation

Subdifferential‐based implicit return‐mapping operators in Mohr‐Coulomb plasticity

2017

Self Cite

View full text Add to dashboard Cite

show abstract

“…The consistent tangent operator is used for assembling of the tangent stiffness matrix which is important for solving this problem by Newton-like methods [2,4,5].…”

Section: Useful Theoretical Resultsmentioning

confidence: 99%

“…To improve this conventional scheme, we use the subdifferential formulation of the flow rule instead of the multisurface one. The subdifferential-based implicit solution concept was proposed in [5] for yield criteria containing 1 or 2 singular points on the yield surface. Then it was extended to the Mohr-Coulomb problem in [4].…”

Section: Introductionmentioning

confidence: 99%

Implicit constitutive solution scheme for Mohr-Coulomb plasticity

Sysala¹,

Čermák²

2017

Programs and Algorithms of Numerical Mathematics 18

Self Cite

View full text Add to dashboard Cite

Optimization and variational principles for the shear strength reduction method

Sysala

Hrubešová

Michalec

et al. 2021

Num Anal Meth Geomechanics

Self Cite

View full text Add to dashboard Cite

In this paper, a modified shear strength reduction method (MSSR) and its optimization variant (OPT‐MSSR) are suggested. The idea of MSSR is to approximate the standard shear strength reduction to be more stable and rigorous from the numerical point of view. The MSSR method consists of a simplified associated elasto‐plastic model completed by the strength reduction depending on the dilatancy angle. Three Davis' modifications suggested by Tschuchnigg et al. (2015) are interpreted as special cases of MSSR and their factors of safety are compared. The OPT‐MSSR method is derived from MSSR on the basis of rigid plastic assumption, similarly as in limit analysis. Using the variational approach, the duality between the static and kinematic principles of OPT‐MSSR is shown. The numerical solution of OPT‐MSRR is obtained by performing a regularization method in combination with the finite element method, mesh adaptivity and a damped Newton method. In‐house codes (Matlab) are used for the implementation of this solution concept. Finally, two slope stability problems are considered, one of which follows from analysis of a real slope. The softwares packages Plaxis and Comsol Multiphysics are used for comparison of the results.

show abstract

Subdifferential‐based implicit return‐mapping operators in computational plasticity

Cited by 20 publications

References 33 publications

Subdifferential‐based implicit return‐mapping operators in Mohr‐Coulomb plasticity

Subdifferential‐based implicit return‐mapping operators in Mohr‐Coulomb plasticity

Implicit constitutive solution scheme for Mohr-Coulomb plasticity

Optimization and variational principles for the shear strength reduction method

Contact Info

Product

Resources

About