Mixed method and convex optimization for limit analysis of homogeneous Gurson materials: a kinematical approach

Pastor, Franck; Loute, Étienne; Pastor, J.; Trillat, Malorie

doi:10.1016/j.euromechsol.2008.02.008

Cited by 45 publications

(37 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…An extension to the discontinuous velocity case, based on the assumption that linear programming duality properties remain valid in non-linear programming, was proposed in [25]. A general extension-without any a priori assumption-to the discontinuous case using convex optimization was successfully experienced in [26] and [27] for homogeneous von Mises and Gurson materials in plane strain. This general formulation reads:…”

Section: The Mixed Kinematic Methodsmentioning

confidence: 99%

“…the velocity u is piecewise continuous with bounded discontinuities [u], and verifies the boundary conditions. Studies in [26] and [27] have demonstrated that the optimal velocity field will also be plastically admissible (PA), i.e. there exists a tensor σ or a vector T that are respectively associated with the strain rate tensor or to the velocity jump by the normality law corresponding to f (σ ) = 0 and f nt (T ) = 0.…”

Section: The Mixed Kinematic Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Numerical limit analysis and plasticity criterion of a porous Coulomb material with elliptic cylindrical voids

Pastor¹,

Pastor²,

Kondo³

2015

Comptes Rendus. Mécanique

View full text Add to dashboard Cite

The paper is devoted to a numerical Limit Analysis of a hollow cylindrical model with a Coulomb solid matrix (of confocal boundaries) considered in the case of a generalized plane strain. To this end, the static approach of Pastor et al. (2008) [18] for Drucker-Prager materials is first extended to Coulomb problems. A new mixed-but rigorously kinematiccode is elaborated for Coulomb problems in the present case of symmetry, resulting also in a conic programming approach. Owing to the good conditioning of the resulting optimization problems, both methods give very close bounds by allowing highly refined meshes, as verified by comparing to existing exact solutions. In a second part, using the identity of Tresca (as special case of Coulomb) and von Mises materials in plane strain, the codes are used to assess the corresponding results of Mariani and Corigliano (2001) [13] and of [11] for circular and elliptic cylindrical voids in a von Mises matrix. Finally, the Coulomb problem is investigated, also in terms of projections on the coordinate planes of the principal macroscopic stresses.

show abstract

Section: The Mixed Kinematic Methodsmentioning

confidence: 99%

Section: The Mixed Kinematic Methodsmentioning

confidence: 99%

Numerical limit analysis and plasticity criterion of a porous Coulomb material with elliptic cylindrical voids

Pastor¹,

Pastor²,

Kondo³

2015

Comptes Rendus. Mécanique

View full text Add to dashboard Cite

show abstract

“…Most of the early implementations of FELA relied on linear programming optimisation techniques, which required the yield function to be linearised. [7][8][9][10][11] More recent FELA implementations have tended to use nonlinear programming [12][13][14][15][16][17] or conic programming [18][19][20][21][22][23] optimisation techniques. These allow a range of smooth and nonsmooth yield functions to be treated natively, without linearisation.…”

Section: Background To Sequential Limit Analysismentioning

confidence: 99%

Modelling large plastic deformations of cohesive soils using sequential limit analysis

Kong

Martin

Byrne

2017

Num Anal Meth Geomechanics

View full text Add to dashboard Cite

Summary This paper introduces sequential limit analysis (SLA) as a method for modelling large plastic deformations of purely cohesive materials such as undrained clay. The method involves solving a series of consecutive small‐deformation plastic collapse problems using finite element limit analysis, thus ensuring high levels of accuracy, efficiency, and robustness. The techniques needed to develop an SLA implementation for two‐dimensional (plane strain) problems are described in detail, including model geometry updating routines, treatment of rigid bodies, interfaces and boundaries, and periodic remeshing and interpolation of field variables. A simple total stress‐based constitutive model is used to account for strain softening and strain rate effects. Extensive verifications and validations are performed using analytical solutions and physical model test results, comparing both collapse loads and failure mechanisms, to demonstrate the effectiveness of the SLA approach. Additional solution quality checks on the bracketing discrepancy between lower‐bound and upper‐bound limit analysis solutions, and on the incompressibility of the rigid‐plastic material, are also presented.

show abstract

“…The virtual power principle (VPP) states that the stress tensor fields σ and the load vector Q are in equilibrium if, for any KA u , the equation is fulfilled. The mixed formulation of and can be modified as

\begin{matrix} leftalign \\ rightalign-odd & align-even max_{Q, σ, σ'} F = Q \cdot q_{d} & rightalign-label (12.i) \end{matrix}

\begin{matrix} leftalign \\ rightalign-odd s.t. & align-even \int_{V} σ : d d V + \int_{S_{disc}} MathClass-open(σ' \cdot n MathClass-close) \cdot MathClass-open[u MathClass-close] d S = Q \cdot q MathClass-open(u MathClass-close) \forall KA u, & rightalign-label (12.ii) \end{matrix}

\begin{matrix} leftalign \\ rightalign-odd & align-even f MathClass-open(σ MathClass-close) ⩽ 0, f MathClass-open(σ' MathClass-close) ⩽ 0, & rightalign-label (12.iii) \end{matrix}

where σ is the stress tensor inside the 3D finite elements and σ ′ the stress tensor specific to the discontinuity surfaces.…”

Section: Theoretical Tools Of the Studymentioning

confidence: 99%

3D‐FEM formulations of limit analysis methods for porous pressure‐sensitive materials

Pastor¹,

Kondo

Pastor

2013

Numerical Meth Engineering

View full text Add to dashboard Cite

SUMMARYThe first purpose of this paper is the numerical formulation of the three general limit analysis methods for problems involving pressure‐sensitive materials, that is, the static, classic, and mixed kinematic methods applied to problems with Drucker–Prager, Mises–Schleicher, or Green materials. In each case, quadratic or rotated quadratic cone programming is considered to solve the final optimization problems, leading to original and efficient numerical formulations. As a second purpose, the resulting codes are applied to non‐classic 3D problems, that is, the Gurson‐like hollow sphere problem with these materials as matrices. To this end are first presented the 3D finite element implementations of the static and kinematic classic methods of limit analysis together with a mixed method formulated to give also a purely kinematic result. Discontinuous stress and velocity fields are included in the analysis. The static and the two kinematic approaches are compared afterwards in the hydrostatic loading case whose exact solution is known for the three cases of matrix. Then, the static and the mixed approaches are used to assess the available approximate criteria for porous Drucker–Prager, Mises–Schleicher, and Green materials. Copyright © 2013 John Wiley & Sons, Ltd.

show abstract

Mixed method and convex optimization for limit analysis of homogeneous Gurson materials: a kinematical approach

Cited by 45 publications

References 12 publications

Numerical limit analysis and plasticity criterion of a porous Coulomb material with elliptic cylindrical voids

Numerical limit analysis and plasticity criterion of a porous Coulomb material with elliptic cylindrical voids

Modelling large plastic deformations of cohesive soils using sequential limit analysis

3D‐FEM formulations of limit analysis methods for porous pressure‐sensitive materials

Contact Info

Product

Resources

About