Boris Štok

NICE-An explicit numerical scheme for efficient integration of nonlinear constitutive equations

The paper presents a simple but efficient new numerical scheme for the integration of nonlinear constitutive equations. Although it can be used for the integration of a system of algebraic and differential equations in general, the scheme is primarily developed for use with the direct solution methods for solving boundary value problems, e.g. explicit dynamic analysis in ABAQUS/Explicit. In the developed explicit scheme, where no iteration is required, the implementation simplicity of the forward-Euler scheme and the accuracy of the backward-Euler scheme are successfully combined. The properties of the proposed NICE scheme, which was also implemented into ABAQUS/Explicit via User Material Subroutine (VUMAT) interface platform, are compared with the properties of the classical forward-Euler scheme and backward-Euler scheme. For this purpose two highly nonlinear examples, with the von Mises and GTN material model considered, have been studied. The accuracy of the new scheme is demonstrated to be at least of the same level as experienced by the backward-Euler scheme, if we compare them on the condition of the same CPU time consumption. Besides, the simplicity of the NICE scheme, which is due to implementation similarity with the classical forward-Euler scheme, is its great Advantage.

Parallel computing with load balancing on heterogeneous distributed systems

In the present work, the parallelization of the solution of a system of linear equations, in the framework of finite element computational analyses, is dealt with. As the substructuring method is used, the basic idea refers to a way of decomposing the considered spatial domain, discretized by the finite elements, into a finite set of non-overlapping subdomains, each assigned to an individual processor and computationally analysed in parallel. Considering the fact that Personal Computers and Work Stations are still the most frequently used computers, a parallel computational platform can be built by connecting the available computers into a computer network. The incorporated computers being usually of different computational power and memory size, the efficiency of parallel computations on such a heterogeneous distributed system depends mainly on proper load balance. To cope the balance problem, an algorithm for the efficient load balance for structured and free 2D quadrilateral finite element meshes based on the rearrangement of elements among respective subdomains, has been developed.

TOOL DESIGN OPTIMIZATION IN EXTRUSION PROCESSES

Abstract Tool design optimization in steady-state extrusion processes, based on the finite element discretization and non-linear mathematical programming techniques, is considered in this paper. In order to perform the optimization the die geometry is adequately parameterized, according to the polynomial representation. By imposing real technological and geometry constraints the optimal tool design is effected by extremizing the actual optimization objectives. In particular, the minimization of the forming energy consumption and the maximization of the possible area reduction are considered. The results, obtained numerically by assuming the Lagrange incremental elastic–plastic finite element formulation in modelling the material flow and the considered optimization approach, are compared to the known theoretical solutions, in cases where such solutions are available. It is demonstrated that the discussed approach is quite effective.

Earing Prediction in Cup Drawing using the BBC2008 Yield Criterion

The paper deals with constitutive modelling of highly anisotropic sheet metals. It presents FEM based earing predictions in cup drawing simulation of highly anisotropic aluminium alloys where more than four ears occur. For that purpose the BBC2008 yield criterion, which is a plane‐stress yield criterion formulated in the form of a finite series, is used. Thus defined criterion can be expanded to retain more or less terms, depending on the amount of given experimental data. In order to use the model in sheet metal forming simulations we have implemented it in a general purpose finite element code ABAQUS/Explicit via VUMAT subroutine, considering alternatively eight or sixteen parameters (8p and 16p version). For the integration of the constitutive model the explicit NICE (Next Increment Corrects Error) integration scheme has been used. Due to the scheme effectiveness the CPU time consumption for a simulation is comparable to the time consumption of built‐in constitutive models. Two aluminium alloys, namely...

Impact Of Elastic Modulus Degradation On Springback In Sheet Metal Forming

Strain recovery after removal of forming loads, commonly defined as springback, is of great concern in sheet metal forming, in particular with regard to proper prediction of the final shape of the part. To control the problem a lot of work has been done, either by minimizing the springback on the material side or by increasing the estimation precision in corresponding process simulations. Unfortunately, by currently available software springback still cannot be adequately predicted, because most analyses of springback are using linear, isotropic and constant Young’s modulus and Poisson’s ratio. But, as it was measured and reported, none of it is true. The aim of this work is to propose an upgraded mechanical model which takes evolution of damage and related orthotropic stiffness degradation into account. Damage is considered by inclusion of ellipsoidal cavities, and their influence on the stiffness degradation is taken in accordance with the Mori‐Tanaka theory, adopting the GTN model for plastic flow. In ...

About finite element sensitivity analysis of elastoplastic systems at large strains

Abstract Influence of a discontinuous nature of the elastoplastic systems response at large strain onto their sensitivity with respect to a design parameter is considered in the paper. It is discussed in the framework of the finite element modelling using the direct differentiation method for the sensitivity response calculation. Elastoplastic behaviour is formulated on the additive approach of the rate of deformation tensor and a hypoelastic characterization of the elastic response. It is shown that the computed sensitivity response of the system’s FE models can experience steep jumps on its overall path. This fact is confirmed by some examples.

NICE h : a higher-order explicit numerical scheme for integration of constitutive models in plasticity

The article introduces, as a result of further development of the first-order scheme NICE, a simple and efficient higher-order explicit numerical scheme for the integration of a system of ordinary differential equations which is constrained by an algebraic condition (DAE). The scheme is based on the truncated Taylor expansion of the constraint equation with order h of the scheme being determined by the highest exponent in the truncated Taylor series. The integration scheme thus conceived will be named NICEh, considering both principal premises of its construction. In conjunction with a direct solution technique used to solve the boundary value problem, the NICEh scheme is very convenient for integrating constitutive models in plasticity. The plasticity models are defined mostly by a system of algebraic and differential equations in which the yield criterion represents the constraint condition. To study the properties of the new integration scheme, which, like the forward-Euler scheme, is characterised by its implementation simplicity due to the explicitness of its formulations, a damage constitutive model (Gurson–Tvergaard–Needleman model) is considered. The general opinion that the implicit backward-Euler scheme is much more accurate than the thus-far known explicit schemes is challenged by the introduction of the NICEh scheme. The accuracy of the higher-order explicit scheme in the studied cases is significantly higher than the accuracy of the classical backward-Euler scheme, if we compare them under the condition of a similar CPU time consumption.

Computer aided identification of the moisture transport parameters in spruce wood

Summary An inverse identification method for characterization of wood sorptive properties is presented. The method relies on a computer simulation of a real experiment, in our case a desorption experiment, where spruce heartwood samples were dried from 27% to 8% moisture content. Three samples, distinguished by the respective moisture flow pattern through the specimen, were investigated. A computer aided material characterization using the so-called inverse problem identification method was performed on the measurements. The solution of the specified inverse problem enabled us to estimate the moisture diffusion coefficients of wood and to determine the moisture content field in the sample simultaneously. The method is first verified on two simple cases of uniaxial moisture flow, and then is used to characterize the diffusion coefficients on a biaxial moisture flow sample. In the latter case some salient features of the proposed method are exhibited.

Optimization of single and multistep wire drawing processes with respect to minimization of the forming energy

Optimization of single and multistep wire drawing processes, based on the finite element analysis and nonlinear mathematical programming techniques, is considered. Since the investigated problem involves the optimal selection of the extrusion die angles and the correspondent reduction rate sequence, it can be considered as one belonging to a class of optimum shape design problems. Characteristic to the considered problem is that the domain boundary, the shape of which is to be optimized, is subject to the shape dependent forming loads. The minimization of the objective function, which is related to the process energy consumption, is sought by taking several technological and geometrical constraints into account. The numerically evaluated examples demonstrate that by using the proposed optimization technique not only a substantial cost reduction, but also a considerable improvement in the homogeneity of plastic deformation through the cross-section of the drawn wire can be achieved.

How to tackle the compatibility constraints in a computational solution of frictional contact problem

Abstract A computational strategy for an effective solution of a multibody contact problem with friction in the mechanics of deformable bodies is considered. Due to the coupling of quantities appertaining to the material points at the common contact boundary and due to imposing of additional constraints regarding the stress-displacement compatibility in the contact area, the primary set of the nonrelated one body system equations that is obtained according to the assumption of the nonconnected multibody system, is additionally augmented when a contact problem is considered. Due to the incorporated nonlinearities the analysis of contact problems requires a proper treatment of the history of the applied load. Therefore, to allow the external load to be applied in small finite steps the solution is traced in an incremental way, with the magnitude of the load increment being monitored by the contact compatibility. Namely, a reliable tracing of the contact compatibility variation along the application of the external load is achieved by introducing only one change of the contact status in each load increment. However, to fulfill all compatibility and contact constraints the incremental solution technique has to be additionally implemented by an iterative procedure within each increment, thus providing a means for satisfactory fulfilment of the contact compatibility.