A return mapping algorithm for unified strength theory model

Chen, Lin; Li, Yueming

doi:10.1002/nme.4937

Cited by 12 publications

(9 citation statements)

References 19 publications

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“…In engineering practice, there is a broad class of yield criteria that are formulated in terms of principal stresses (i.e., in terms of eigenvalues of stress tensors). We mention the Mohr-Coulomb, the Tresca, the Rankine, the Hoek-Brown or the unified strength ones [13,17,24,25], for example. Such criteria usually have a multisurface representation leading to nonsmooth yield surfaces with relatively complex structures of singular points.…”

Section: Introductionmentioning

confidence: 99%

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

2017

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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...

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Section: Introductionmentioning

confidence: 99%

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

2017

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“…where σt is tensile yield strength, α is tensile-compressive strength ratio to reflect SD property, and b is a parameter that describes the effect of intermediate principal stress on the failure of material. The return mapping algorithm model is proposed by Chen et al [12] for simulation. The details of the algorithm model is in Reference [12].…”

Section: Mechanical Behavior Modelingmentioning

confidence: 99%

“…The return mapping algorithm model is proposed by Chen et al [12] for simulation. The details of the algorithm model is in Reference [12]. Here, only the brief processes of stress-update are introduced in Appendix A.…”

Section: Mechanical Behavior Modelingmentioning

confidence: 99%

See 1 more Smart Citation

Oxidation Simulation of Thermal Barrier Coatings with Actual Microstructures Considering Strength Difference Property and Creep-Plastic Behavior

Chen

Chai

2018

Coatings

Self Cite

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A scanning electron microscope (SEM) image based direct finite element (FE) mesh reconstruction method is employed to reflect microstructure features of thermal barrier coatings (TBC). The creep-plastic assumption of thermally grown oxide (TGO) scale and metallic bond coat (BC) as well as the strength difference (SD) property of ceramic top coat (TC) are considered to simulate the mechanical behavior. A diffusion oxidation model considering oxygen consumption is proposed to characterize TGO growth. The oxidation simulation of TBC is carried out under the consideration of actual microstructure features. The results revealed that the interface defects increase the surface-area-to-volume ratio of BC exposed to oxygen anion. This leads to the non-uniform TGO growth, which has also been observed in experimental studies. The microstructures and mechanical behavior strongly affect stress evolution in TBC. The consideration of actual microstructure features and reasonable mechanical behaviors, including the creep-plastic behavior and SD property, is helpful for the accurate evaluation of interface stress.

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“…Clausen et al [10,11] proposed a kind of implicit integration algorithm for the linear yield criteria with multiple yield planes built upon the works of Pankaj and Bićanić [19]. Lin and Li [20] presented a return mapping algorithm for unified strength theory; this algorithm is suitable not only for the unified strength theory but also for other criteria (e.g., the Mohr-Coulomb (M-C) yield criterion and the Tresca yield criterion) due to the flexibility of unified strength theory. Fang et al [21] proposed an implicit numerical integration algorithm for the unified yield criterion in the principal stress space; this algorithm is more useful and convenient than the algorithm proposed by Lin and Li [20], as linear isotropic hardening and nonassociated plasticity can be considered.…”

Section: Introductionmentioning

confidence: 99%

A Return Mapping Algorithm for Nonlinear Yield Criteria with the Equivalent Mohr–Coulomb Strength Parameters

et al. 2020

Advances in Civil Engineering

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This paper proposes a modified return mapping algorithm for a series of nonlinear yield criteria. The algorithm is established in the principal stress space and ignores the effect of the intermediate principal stress. Three stress return schemes are derived in this paper: return to the yield surface, return to the curve, and return to the apex point. The conditions used for determining the correct stress return type are also constructed. After the proposed algorithm is programmed in the finite element software, we merely need the equivalent Mohr–Coulomb (M-C) strength parameters, the derivatives of their functions, and the tensile strength of these nonlinear yield criteria. In addition, the Hoek–Brown (H-B) yield criterion is taken as an example to validate the proposed method. The results show that the updated stresses and the final principal stresses obtained by the proposed method are in good agreement with those obtained by other methods. Furthermore, the proposed method is more suitable for the associated plastic-flow rule.

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A return mapping algorithm for unified strength theory model

Cited by 12 publications

References 19 publications

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

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

Oxidation Simulation of Thermal Barrier Coatings with Actual Microstructures Considering Strength Difference Property and Creep-Plastic Behavior

A Return Mapping Algorithm for Nonlinear Yield Criteria with the Equivalent Mohr–Coulomb Strength Parameters

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