Numerical solution of two-dimensional viscoplasticity problem with Perzyna model based on zonal free element method

Metals at high temperatures are sensitive to strain rate effects and exhibit viscoplastic behavior. The Perzyna model is one of the most widely used ones to study rate-dependent plasticity. This paper presents the details of calibration of Perzyna model parameters of an austenitic stainless steel from tension tests and calibration of Chaboche and Voce model parameters from low-cycle fatigue test at 1000 K. Tests are conducted in an INSTRON 8862 electromechanical UTM. Perzyna model parameters are validated by comparing tension test results with finite element simulations using ANSYS (Version 16.0) software. Sensitivity of Perzyna model parameters on viscoplastic behavior is investigated for monotonic as well as cyclic loading situations. Perzyna model is combined with the Chaboche–Voce cyclic plasticity model for investigating cyclic loading. Finally, viscoplastic cyclic stress analysis of a double-walled rocket engine thrust chamber is carried out using a combination of Perzyna, Chaboche and Voce models and its cyclic life evaluated.

Analysis of nonlinear thermo-viscoelastic–viscoplastic contacts

SUMMARY Non-associated flow rule is essential when the popular Mohr–Coulomb model is used to model nonlinear behavior of soil. The global tangent stiffness matrix in nonlinear finite element analysis becomes nonsymmetric when this non-associated flow rule is applied. Efficient solution of this large-scale nonsymmetric linear system is of practical importance. The standard Krylov solver for a non-symmetric solver is Bi-CGSTAB. The Induced Dimension Reduction [IDR(s)] solver was proposed in the scientific computing literature relatively recently. Numerical studies of a drained strip footing problem on homogenous soil layer show that IDR(s=6) is more efficient than Bi-CGSTAB when the preconditioner is the incomplete factorization with zero fill-in of global stiffness matrix Kep (ILU(0)-Kep). Iteration time is reduced by 40% by using IDR(s=6) with ILU(0)-Kep. To further reduce computational cost, the global stiffness matrix Kep is divided into two parts. The first part is the linear elastic stiffness matrix Ke, which is formed only once at the beginning of solution step. The second part is a low-rank matrix Δ, which is re-formed at each Newton–Raphson iteration. Numerical studies show that IDR(s=6) with this ILU(0)-Ke preconditioner is more time effective than IDR(s=6) with ILU(0)-Kep when the percentage of yielded Gauss points in the mesh is less than 15%. The total computation time is reduced by 60% when all the recommended optimizing methods are used. Copyright © 2013 John Wiley & Sons, Ltd.

Load identification for viscoplastic materials with some unknown material parameters

On the basis of the moving least-squares (MLS) approximation, the complex variable element-free Galerkin (CVEFG) method for two-dimensional elastic large deformation problems, such as large displacement and large rotation, is presented in this paper. The advantage of the CVMLS approximation is that the trial function of a two-dimensional problem is formed with one-dimensional basis function. Then the CVMLS approximation is applied to solve two-dimensional large deformation problems. The Galerkin weak form is employed to obtain the discretized system equation, the penalty method is used to apply the essential boundary conditions. And then the complex variable element-free Galerkin (CVEFG) method for two-dimensional large deformation problems based on the total lagrange formulation is formed, the corresponding formulae are obtained, and the Newton-Raphson iteration is used in the numerical implementation. Three numerical examples are given to show that this method in this paper is effective for elastic large deformation problems.

A combined viscoelastic–viscoplastic behavior of particle reinforced composites

ANALYSIS OF AXISYMMETRIC BORE-TYPE FOUNDATION IN RESPECT OF PLASTIC DEFORMATION/AŠIAI SIMETRINIO GRĘŽININIO PAMATO ANALIZĖ ĮVERTINANT PLASTINES DEFORMACIJAS

Even with recent supercomputers having a large memory, Navier-Stokes simulations for vortical flows do not provide satisfactory results because of the lack of grid resolution to accurately simulate the strength of separation vortices. To overcome this problem, a zonal method is proposed to increase the number of grid points locally. Interface scheme which is critical for an efficient and stable zonal method is based on the Fortified Navier-Stokes concept. Application to both two-dimensional conical and three-dimensional delta wing problems indicates this simple zonal method can improve the accuracy of vortical flow simulations.

This paper presents a novel Petrov-Galerkin free element method (PGPZ-FREM) based on a combination of the strong form free element method (FREM), sub-domain mapping technique, and Petrov-Galerkin method for analyzing piezoelectric structures. This is a brand new numerical method that combines the ideas of isogeometric method and meshless method. Similar to the isogeometric method, the computational domain is divided into a lot of patchs or subdomains firstly. In each subdomain, local collocation Lagrangian elements are generated according to the location of the nodes. Additionally, the Heaviside step function is selected as the weight function to simplify the calculations. By constructing equations point by point, a set of linear algebraic equations is established to solve the piezoelectric problem. Finally, the accuracy and stability of the piezoelectric zonal Petrov-Galerkin free element method are verified by numerical examples, including a symmetric piezoelectric block, a piezoelectric tuning fork, a dual-material MFC sensor, and the wing skin pressure sensing system. • A novel Petrov-Galerkin zonal free element method is proposed. • The transformation and relationship of differentials in different configurations are derived. • Complex piezoelectric examples are analyzed and verified.

Summary The natural neighbour Galerkin method is tailored to solve boundary value problems of the couple-stress elasticity to model the size dependent behaviour of materials. This method is based on the displacement-based Galerkin approach, and the calculation of the global stiffness matrix is performed using gradient smoothing technique combined with the non-Sibsonian partition of unity approximation scheme. This method possesses the following properties: the complex C1-continuous approximation scheme is avoided without using either Lagrange multipliers or penalty parameters; no domain integrals involved in the assembly of the global stiffness matrix; and the imposition of essential boundary conditions is straightforward. The validity and accuracy of this method are investigated through numerical examples. The results show that strong size effects can be captured by the numerical method when the length of deformation field and the characteristic length of the material are comparable, and good agreements with analytical solutions are obtained.

Chapter 15 - Two-Dimensional Problems

Quasistatic and implicit time integration schemes are typically employed to alleviate the stringent time step restrictions imposed by their explicit counterparts. However, both quasistatic and implicit methods are subject to hidden time step restrictions associated with both the prevention of element inversion and the effects of discontinuous contact forces. Furthermore, although fast iterative solvers typically require a symmetric positive definite global stiffness matrix, a number of factors can lead to indefiniteness such as large jumps in boundary conditions, heavy compression, etc. We present a novel quasistatic algorithm that alleviates geometric and material indefiniteness allowing one to use fast conjugate gradient solvers during Newton-Raphson iteration. Additionally, we robustly compute smooth elastic forces in the presence of highly deformed, inverted elements alleviating artificial time step restrictions typically required to prevent such states. Finally, we propose a novel strategy for treating both collision and self-collision in this context.

This work specifically examines the analysis of building blocks structures that experience finite displacements. The analysis was conducted with incremental sequential techniques. The Newton-Raphson iteration approach is used to load structural stages that have the ability to either soften or harden. A modified Newton-Raphson iteration technique is employed for loading stages in which the determinant of the global stiffness matrix is near 0 or negative, as observed in the snap-through scenario. The advanced computer language Fortran is used for structural analysis. To ensure the program's integrity, SAP (structural analysis program) is used for verification. The software is then used in several structural systems case studies. To accomplish this, the authors compare the axial stiffness of panels and jack elements as well as the height-to-span ratios of various structures. The structural responses were modelled using stiffening, snap-through, and softening load-displacement curves.

A finite‐element computer program consists of four basic modules, namely, computation of element stiffness matrices, assembly of the global stiffness matrix, solution of the system of linear simultaneous equations, and calculation of stresses. Vector algorithms consisting of direct vector Fortran code and the Engineering and Scientific Subroutine Library (ESSL) routines are presented for these modules. Numerical investigations were conducted using the IBM 3090–600E VF computer.For element stiffness matrix calculation, using a vector length equal to the number of elements produced speed‐up in the range of 3·2 to 3·7 over the corresponding scalar code. The vectorized global element stiffness matrix assembly was accomplished with the help of an INDEX array and the ESSL routine DAXPYI that resulted in the speed‐up of 2·6 to 4·3. The ESSL routines DPBF and DPBS gave speed‐up of 7·7 to 53·6 over a scalar Gaussian solver. The scalar‐to‐vector speed‐up for the stress calculation ranges from 2·2 to 5·33. The speed‐up of the totally vectorized program over the scalar program is from 7·4 to 51·9.As would be expected, the equation solution takes up the most computational effort in a finite‐element analysis. For the models we analysed the equation solution consumed 93 per cent to almost 100 per cent of the total CPU time in the scalar computations. Vectorizing the equation solver only reduces the percentage of its share to the range of 63 per cent to 88 per cent. In a totally vectorized program, the share of the equation solver effort is 85 per cent to 97 per cent. For the models analysed, the additional speed‐up accomplished by vectorizing the whole program over the one with a vectorized equation solver only was from 10 per cent to 40 per cent.

The preconditioned conjugate gradient method with aggregation multilevel preconditioning is employed for solution of large-scale finite element linear static and natural vibration problems. The aggregation approach, proposed by Prof. V.E.Bulgakov, is applied to create the aggregation multilevel preconditioning. Formulation of the restriction-prolongation operators and preparation of the coarse level matrix is based on clear mechanical interpretation. Application of the element-by-element (EBE) procedure makes evaluation of the coarse level matrix almost as fast as the assembly of the global stiffness matrix. Use of the shift improves properties of the aggregation multilevel preconditioning for solution of natural vibration problems. The PCG algorithm with acceleration by shifts is developed further on. Next, the implicit approach to solution of the additional equation set with the preconditioning ”shifted” respectively is applied. There is a correlational relationship between the well-known inverse iteration procedure with the shift and the PCG method accelerated by shifts. Efficiency of the approach proposed is illustrated by large-scale examples. These methods are incorporated in the Robot Millennium software (RoboBAT Software Company, Krakow, Poland, http://robot-structures.com/us/).KeywordsCoarse LevelPreconditioned Conjugate GradientRigid LinkInverse IterationPreconditioned Conjugate Gradient MethodThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.