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The purpose of this paper is to present a new effective integration method for cyclic plasticity models.

By defining an integrating factor and an augmented stress vector, the system of differential equations of the constitutive model is converted into a nonlinear dynamical system, which could be solved by an exponential map algorithm.

The numerical tests show the robustness and high efficiency of the proposed integration scheme.

The von‐Mises yield criterion in the regime of small deformation is assumed. In addition, the model obeys a general nonlinear kinematic hardening and an exponential isotropic hardening.

Integrating the constitutive equations in order to update the material state is one of the most important steps in a nonlinear finite element analysis. The accuracy of the integration method could directly influence the result of the elastoplastic analyses.

The paper deals with integrating the constitutive equations in a nonlinear finite element analysis. This subject could be interesting for the academy as well as industry. The proposed exponential‐based integration method is more efficient than the classical strategies.

The purpose of this paper is to introduce a computational time dependent modeling to investigate propagation of elastic-viscoplastic zones in the shock wave loaded circular plates.

Constitutive equations are implemented incrementally by the Von-Kármán finite deflection system which is coupled with a mixed strain hardening rule and physical-base viscoplastic models. Time integrations of the equations are done by the return mapping technique through the cutting-plane algorithm. An integrated solution is established by pseudo-spectral collocation methodology. The Chebyshev basis functions are utilized to evaluate the coefficients of displacement fields. Temporal terms are discretized by the Houbolt marching method. Spatial linearizations are accomplished by the quadratic extrapolation technique.

Results of the center point deflections, effective plastic strain and stress (dynamic flow stress) and temperature rise are compared for three features of the Von-Kármán system. Identifying time history of resultant stresses, propagations of the viscoplastic plastic zones are illustrated for two circumstances; with considering strain rate and hardening effects, and without them. Some of modeling and computation aspects are discussed, carefully. When the results are compared with experimental data of shock wave loadings and finite element simulations, good agreements between them are observed.

This computational approach makes coupling the structural equations with the physical descriptions of the high rate deformation through step-by-step spectral solution of the constitutive equations.

Presents a computational algorithm for the numerical integration of triaxial concrete plasticity formulations. The specific material formulation at hand is the so‐called extended leon model for concrete. It is based on the flow theory of plasticity which entails isotropic hardening as well as fracture energy‐based softening in addition to non‐associated plastic flow. The numerical algorithm resorts to implicit integration according to the backward Euler strategy that enforces plastic consistency according to the closes‐point‐projection method (generalized radial‐return strategy). Numerical simulations illustrate the overall performance of the proposed algorithm and the significant increase of the convergence rate when the algorithmic tangent is used in place of the continuum operator.

The finite element quasi‐static analysis of elastoplastic systems is studied by making use of a generalized variable approach for the spatial discretization and a generalized mid‐point rule for the time integration. Both the classical form of the constitutive law and the convex analysis formulation are presented. The relation between the mid‐point time integration and the extremal path theory is discussed. Extremal properties for the finite‐step solution are formulated.

This paper aims to provide a more rapid stress updating algorithm for von‐Mises plasticity with mixed‐hardening and to compare it with the previous works.

An augmented stress vector is defined. This can convert the original nonlinear differential equation system to a quasi‐linear one. Then the dynamical system can be solved with an exponential map approach in a semi‐implicit manner.

The presented stress updating algorithm gives very accurate results and it has a quadratic convergence rate.

Von‐Mises plasticity in a small strain regime is considered. Furthermore, the material is supposed to have linear hardening.

Stress updating is the heart of a nonlinear finite element analysis due to the large consumption of computation time. The efficiency and accuracy of the calculations of nonlinear finite element analysis are strongly influenced by the efficiency and accuracy of stress updating schemes.

The paper offers a new stress updating strategy based on exponential maps. This may be used as a routine in a nonlinear finite element analysis software to enhance its performance.

The purpose of this paper is to present an efficient return mapping algorithm for elastoplastic constitutive problems of ductile metals with an exact closed form solution of the local constitutive problem in the small strain regime. A Newton Raphson iterative method is adopted for the solution of the boundary value problem.

An efficient return mapping algorithm is illustrated which is based on an elastic predictor and a plastic corrector scheme resulting in an implicit and accurate numerical integration method. Nonlinear kinematic hardening rules and linear isotropic hardening rules are used to describe the components of the hardening variables. In the adopted algorithmic approach the solution of the local constitutive equations reduces to only one straightforward nonlinear scalar equation.

The presented algorithmic scheme naturally leads to a particularly simple form of the nonlinear scalar equation which ultimately scales down to an algebraic (polynomial) equation with a single variable. The straightforwardness of the present approach allows to find the analytical solution of the algebraic equation in a closed form. Further, the consistent tangent operator is derived as associated with the proposed algorithmic scheme and it is shown that the proposed computational procedure ensures a quadratic rate of asymptotic convergence when used with a Newton Raphson iterative method for the global solution procedure.

In the present approach the solution of the algebraic nonlinear equation is found in a closed form and accordingly no iterative method is required to solve the problem of the local constitutive equations. The computational procedure ensures a quadratic rate of asymptotic convergence for the global solution procedure typical of computationally efficient solution schemes. In the paper it is shown that the proposed algorithmic scheme provides an efficient and robust computational solution procedure for elastoplasticity boundary value problems. Numerical examples and computational results are reported which illustrate the effectiveness and robustness of the adopted integration algorithm for the finite element analysis of elastoplastic structures also under elaborate loading conditions.

Gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view. The range of applications of FEMs in this area is wide and cannot be presented in a single paper; therefore aims to give the reader an encyclopaedic view on the subject. The bibliography at the end of the paper contains 2,025 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1992‐1995.

The purpose of this paper is to clarify the effect of material hardening model and lump-pass method on the thermal-elastic-plastic (TEP) finite element (FE) simulation of residual stress induced by multi-pass welding of materials with cyclic plasticity.

Nickel-base alloy and stainless steel, which are used in J-type weld for manufacturing the nuclear reactor pressure head, can easily harden during multi-pass welding. The J-weld welding experiment is carried out and the temperature cycle and residual stress are measured to validate the TEP simulation. Thermal-mechanical sequence coupling method is employed to get the welding residual stress. The lumped-pass model and pass-by-pass FE model are built and two materials hardening models, kinematic hardening model and mixed hardening model, are adopted during the simulations. The effects of material hardening models and lumped-pass method on the residual stress in J-weld are distinguished.

Based on the kinematic hardening model, the stresses simulated with the lumped-pass FE model are almost consistent with those obtained by the pass-by-pass FE model; while with the mixed hardening material model, the lumped-pass method has great effect on the simulated stress.

A computation with mixed isotropic-kinematic material seems not to be the appropriate solution when using the lumped-pass method to save the computation time.

In the simulation of multi-pass welding residual stress involved in materials with cyclic plasticity, the material hardening model should be carefully considered. The kinematic hardening model with lump-pass FE model can be used to get better simulation results with less computation time. The results give a direction for welding residual stress simulation for the large structure such as the reactor pressure vessel.

In this paper, quasi‐Tresca yield surfaces are reviewed. In order to do elasto‐plastic analysis, a new yield criterion is presented. The proposed yield surface can be used in nonlinear three‐dimensional analysis of structures. Function of the yield surface is presented in principal stress space and also Cartesian one. A computer program has been developed for nonlinear analysis in C++. Numerical examples have been solved by the proposed yield surface and good results have been obtained.

The purpose of this paper is to present eight local elasto‐plastic beam element formulations incorporated into the corotational framework for two‐noded three‐dimensional beams. These formulations capture the warping torsional effects of open cross‐sections and are suitable for the analysis of the nonlinear buckling and post‐buckling of thin‐walled frames with generic cross‐sections. The paper highlights the similarities and discrepancies between the different local element formulations. The primary goal of this study is to compare all the local element formulations in terms of accuracy, efficiency and CPU‐running time.

The definition of the corotational framework for a two‐noded three‐dimensional beam element is presented, based upon the works of Battini .The definitions of the local element kinematics and displacements shape functions are developed based on both Timoshenko and Bernoulli assumptions, and considering low‐order as well as higher‐order terms in the second‐order approximation of the Green‐Lagrange strains. Element forces interpolations and generalized stress resultant vectors are then presented for both mixed‐based Timoshenko and Bernoulli formulations. Subsequently, the local internal force vector and tangent stiffness matrix are derived using the principle of virtual work for displacement‐based elements and the two‐field Hellinger‐Reissner assumed stress variational principle for mixed‐based formulations, respectively. A full comparison and assessment of the different local element models are performed by means of several numerical examples.

In this study, it is shown that the higher order elements are more accurate than the low‐order ones, and that the use of the higher order mixed‐based Bernoulli element seems to require the least number of FEs to accurately model the structural behavior, and therefore allows some reduction of the CPU time compared to the other converged solutions; where a larger number of elements are needed to efficiently discretize the structure.

The paper reports computation times for each model in order to assess their relative efficiency. The effect of the numbers of Gauss points along the element length and within the cross‐section are also investigated.