SUMMARYRate plasticity equations for the case of Drucker-Prager's model in small strain regime are considered. By defining an augmented stress vector, the formulations convert the original problem into a quasi-linear differential equation system. Two new exponential mapping schemes for integrating model equations are proposed. In addition, two traditional schemes for solving the dynamical system in an explicit manner are discussed. The two semi-implicit schemes developed pose higher accuracy and better convergency. Error contours are provided for all four methods to display the accuracy of each scheme. In order to compare the results, these contours for the classical one-step backward Euler integration method are also displayed. Accuracy and efficiency along with the rate of convergency of the existing and the proposed methods are examined by numerical examples.

Article information:To cite this document: M. Rezaiee-Pajand Cyrus Nasirai, (2007),"Accurate integration scheme for von-Mises plasticity with mixedhardening based on exponential maps", Engineering Computations, Vol. 24 Iss 6 pp. 608 -635 Permanent link to this document: http://dx.If you would like to write for this, or any other Emerald publication, then please use our Emerald for Authors service information about how to choose which publication to write for and submission guidelines are available for all. Please visit www.emeraldinsight.com/authors for more information. About Emerald www.emeraldinsight.comEmerald is a global publisher linking research and practice to the benefit of society. The company manages a portfolio of more than 290 journals and over 2,350 books and book series volumes, as well as providing an extensive range of online products and additional customer resources and services.Emerald is both COUNTER 4 and TRANSFER compliant. The organization is a partner of the Committee on Publication Ethics (COPE) and also works with Portico and the LOCKSS initiative for digital archive preservation. AbstractPurpose -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. Design/methodology/approach -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. Findings -The presented stress updating algorithm gives very accurate results and it has a quadratic convergence rate. Research limitations/implications -Von-Mises plasticity in a small strain regime is considered. Furthermore, the material is supposed to have linear hardening. Practical implications -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. Originality/value -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 von-Mises plasticity model, in the small strain regime, along with a class of multicomponent nonlinear kinematic hardening rules is considered. The material is assumed to be stabilized after several load cycles and therefore, isotropic hardening will not be accounted for. Application of exponential-based methods in integrating plasticity equations is provided, which is based on defining an augmented stress vector and using exponential maps to solve a system of quasi-linear differential equations. The solutions obtained by this new technique give very accurate updated stress values that are consistent with the yield surface. The classical forward Euler method is reformulated in details and applied to the multicomponent form of the nonlinear kinematic hardening in order to provide a comparison for the suggested technique. Moreover, a consistent tangent operator for the exponential-based integration strategy and also for the classical forward Euler algorithm is presented. In order to show the robustness and performance of the proposed formulation, an extensive numerical investigation is carried out.

Abstract-Locking Compression Plates (LCP) are useful fixation devices for tibia and other human long bones. Orthopedists use LCPs with various numbers of holes to fix bone fractures [1] . Not all of holes on plates are often used with Screws so various screw positioning is possible in operations. In this research, a 3D model of tibia is created with the exact geometry of the real bone by using CT scan images of the human right leg .It was materialized by MIMIX and developed in ABAQUS software. This was done considering whole bone material including bone marrow and cancellous bone that have been mostly ignored in previous researches [2] . The model is mechanically validated and verified in comparison with response and behavior of previous cadaveric bone studies [3] .Comparing the stress and stiffness in various positioning of screws on a stainless steel 11 holes LCP used for fixating tibia with a medial transverse fracture in various treatments and finding the optimized screw omission, was the purpose of this paper which can help orthopedists to choose the suitable cases of screws positioning of fixation devices.