• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.9
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• pp.1562-1570
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• 2003

The prediction of the inelastic behavior of the structure is an essential part of reliability assessment procedure, because most of the failures are induced by the inelastic deformation, such as creep and plastic deformation. During decades, there has been much progress in understanding of the inelastic behavior of the materials and a lot of inelastic constitutive equations have been developed. The complexity of these constitutive equations generally requires a stable and accurate numerical method. The radial return mapping is one of the most robust integration scheme currently used. Nonlinear kinematic hardening model of Armstrong-Fredrick type has recovery term and the direction of kinematic hardening increment is not parallel to that of plastic strain increment. In this case, The conventional radial return mapping method cannot be applied directly. In this investigation, we expanded the radial return mapping method to consider the nonlinear kinematic hardening model and implemented this integration scheme into ABAQUS by means of UMAT subroutine. The solution of the non-linear system of algebraic equations arising from time discretization with the generalized midpoint rule is determined using Newton method and bisection method. Using dynamic yield condition derived from linearization of flow rule, the integration scheme for elastoplastic and viscoplastic constitutive model was unified. Several numerical examples are considered to demonstrate the efficiency and applicability of the present method.

• Structural Engineering and Mechanics
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• v.3 no.2
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• pp.185-192
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• 1995

A numerical algorithm for plane stress and shell elasto-plasticity is presented in this paper. The proposed strain decomposition (SD) algorithm is an elastic predictor/plastic corrector algorithm, and in the context of operator splitting, is a return mapping algorithm. However, it differs significantly from other return mapping algorithms in that only the necessary response functions are used without invoking their gradients, and the stress increment is updated only at the end of the time step. This makes the proposed SD algorithm more suitable for materials with complex yield surfaces and will guard against error accumulation during the time step. Comparative analyses of structural systems using the proposed strain decomposition (SD) algorithm and the iterative radial return (IRR) algorithm are presented. The results demonstrate the accuracy and usefulness of the proposed algorithm.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.6
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• pp.1455-1464
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• 1994

A new and efficient algorithm for the integration of the thermal-elasto-plastic constitutive equation is proposed. While it falls into the category of the return mapping method, the algorithm adopts the three point approximation of plastic corrector within one time increment step. The results of its application to a von Mises-type thermal-elasto-plastic model with combined hardening and temperature-dependent material properties show that the accurate iso-error maps are obtained for both angular and radial errors. The accuracy achieved is because the predicted stress increment in a single step calculation follows the exact value closely not only at the end of the step but also through the whole path. Also, the comparison of the computational time for the new and other algorithms shows that the new one is very efficient.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.29 no.6 s.237
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• pp.860-875
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• 2005

A new meshfree method for the analysis of elasto-plastic deformations is presented. The method is based on the proposed first-order least-squares formulation, to which the moving least-squares approximation is applied. The least-squares formulation for the classical elasto-plasticity and its extension to an incrementally objective formulation for finite deformations are proposed. In the formulation, the equilibrium equation and flow rule are enforced in least-squares sense, while the hardening law and loading/unloading condition are enforced exactly at each integration point. The closest point projection method for the integration of rate-form constitutive equation is inherently involved in the formulation, and thus the radial-return mapping algorithm is not performed explicitly. Also the penalty schemes for the enforcement of the boundary and frictional contact conditions are devised. The main benefit of the proposed method is that any structure of cells is not used during the whole process of analysis. Through some numerical examples of metal forming processes, the validity and effectiveness of the method are presented.