Numerical solutions for elastic‐plastic problems

Mitchell, G. P.; Owen, D. R. J.

doi:10.1108/eb023746

Cited by 37 publications

(6 citation statements)

References 10 publications

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“…corresponding to yielding and damage conditions, the following non-linear system of equations is obtained The algorithm is summarized in Table 1. Some recent publications [16][17][18][19] pointed out the advantage of using a consistent stiffness matrix when solving elastoplastic problems. It has been proved that the quadratic rate of convergence of an incremental solution based on a Newton-Raphson procedure can only be ensured if the tangent modulus is derived in a way consistent with the constitutive integration algorithm.…”

Section: Algorithm For the Numerical Implementation Of The Plastic-damaged Modelmentioning

confidence: 99%

Coupled plastic-damaged model

Luccioni

Oller

Danesi

1996

Computer Methods in Applied Mechanics and Engineering

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Section: Algorithm For the Numerical Implementation Of The Plastic-damaged Modelmentioning

confidence: 99%

Coupled plastic-damaged model

Luccioni

Oller

Danesi

1996

Computer Methods in Applied Mechanics and Engineering

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“…and the index (i) denotes the ith iteration of the procedure.The fourth order tensor C dev *ep is the deviatoric part of the consistent elasto-plastic moduli, which Solution of large strain elastoplastic problems 155 are derived by appropriate linearizing of the expression in parentheses of the constitutive equation ( 8) (Mitchell and Owen, 1988;Nagtegaal, 1982).…”

Section: The Mixed Solution Proceduresmentioning

confidence: 99%

On a mixed approach to the finite element solution of large strain elastoplastic problems

Rojc

1998

Engineering Computations

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A mixed approach to large strain elastoplastic problems is presented in a somewhat different way to that usually used within the context of the additive split of the rate of deformation tensor into an elastic and plastic part. A non‐linear extended mixed variational equation, in which the Jacobian of the deformation gradient and the pressure part of the stress tensor appear as additional independent variables, is introduced. This equation is then linearized in the accordance with the Newton‐Raphson method to obtain the system of linear equations which represent the basis of the mixed finite element procedure. For the case of a bilinear isoparametric interpolation of the displacement field, and for piece‐wise constant pressure and Jacobian, simplified expressions, differing from similar expressions corresponding to mixed finite element implementations, are obtained. The effectiveness of the proposed mixed approach is demonstrated by means of two examples.

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“…Now, we choose the principal axes of the strain rate tensor to coincide with the local {, q-co-ordinate system of an element, This choice is permissible, since under planar deformations 8, and f are both invariant. For the Mohr-Coulomb yield function resembling plastic potential (3), equation (10) then specialises as The normal strain rates within the element are obtained by standard differentiation as:…”

Section: Some Basic Notions From Soil and Rock Plasticitymentioning

confidence: 99%

Some observations on element performance in isochoric and dilatant plastic flow

Borst

Groen

1995

Numerical Meth Engineering

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SUMMARYThe performance of finite elements is scrutinized in isochoric and dilatant/contractant plastic flow. Standard displacement based elements, uniformly and selectively integrated elements, and elements with augmented strain rate fields are considered in plane-strain, axisymmetric and three-dimensional configurations with particular reference to the kinematic constraint imposed by dilatant/contractant plastic flow. It turns out that findings for isochoric deformations do not necessarily carry over to cases with plastic dilatancy or contraction. For the elements with augmented strain rate fields the danger of spurious mechanisms in ideal plasticity is brought out. A particular strategy which augments only the normal strain rates at the expense of a lesser improvement for the bending behaviour does not suffer from the possibility of spurious modes, while preserving the ability to accommodate dilatant/contractant plastic flow. Illustrative examples on planestrain, axisymmetry and three-dimensional structures are included which support the above findings.

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Numerical solutions for elastic‐plastic problems

Cited by 37 publications

References 10 publications

Coupled plastic-damaged model

Coupled plastic-damaged model

On a mixed approach to the finite element solution of large strain elastoplastic problems

Some observations on element performance in isochoric and dilatant plastic flow

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