Towards simulation of elasto-plastic deformation: An investigation

Can the deformation of a solid body during plastic flow be assumed to be similar to that of fluids? Here we investigate the possibility of using a modified Navier-Stokes equation as the governing differential equation by including elastic resistance. We adopt the microscopic point of view to explain the material behaviour by laying special emphasis on strain localisation and tension instabilities. A spring and damper model is constructed to obtain approximate simulation of the material behaviour. Based upon the understanding developed from simulating simple tests, we re-formulate the field equation using resistances to change in volume and shape. The new field equation reduces to the Navier-Stokes equation in the fluid limit and Cauchy’s equation in the solid limit. The viscosity and second viscosity of fluids are clearly defined. Bulk and shear modulii and solid damping determine the solid behaviour. Pressure disappears from the field equation and so there is no need to invoke the continuity equation. The four material parameters are determinable from simple measurments. This paper tries to capture the various steps of the investigation which lead to the final result     

Singular integral operators method for two-dimensional elasto-plastic stress analysis

The Singular Integral Operators Method is presented for the formulation of the two-dimensional elasto-plastic stress analysis. The formulation of the two-dimensional elasto-plastic problem is stated, by applying the fundamental solutions for an isotropic solid. The most interesting features of this method are the much smaller systems of equations and considerable reduction in the data required to run the elasto-plastic problem. An application is presented, to the determination of the stress field in the neighborhood of a circular hole under internal pressure in an infinite and isotropic solid. A second application is stated, to the determination of the plastic behaviour of a square block compressed by two opposite perfectly rough rigid punches in plane strain.     

Finite-element simulation of a new two-dissipative mechanisms model for bulk medium-density polyethylene

A two-dissipative mechanisms model, associating a Maxwell and an elastoplastic model in parallel, is discussed in order to account for the non-linear viscoelasticity of bulk medium-density polyethylene. On the one hand, the experimental determination of the constitutive equations coefficients is described from a tensile specimen machined from gas pipes. On the other hand, finite-element simulation of the stress relaxation experiment, proposed by Sweeney and Ward, is achieved, which yields a complete analysis of the dissipative mechanisms interaction during the test. The finite-element code built upon this modelling is finally used in a tentative simulation of a cyclic pressure test on a pipe specimen.     

Finite-element simulation of transient heat response in ultrasonic transducers

The application of the finite-element method to a transient heat response problem in electrostrictive ultrasonic transducers during their pulsed operation is described. The temperature and thermal stress distribution are of practical importance for the design of the ultrasonic transducers when they are operated at intense levels. Mechanical vibratory loss is responsible for heat in the elastic parts, while dielectric loss is responsible in the ferroelectric parts. A finite-element computer model is proposed for the temperature change evaluation in the transducers with time. Natural and forced cooling convection and heat radiation from the transducers' boundaries are included. Simulation is made for Langevin-type transducer models, for which comparison is made with experimental data.     

Finite-element simulation of firearm injury to the human cranium

An advanced physics-based simulation of firearms injury to the human cranium is presented, modeling by finite elements the collision of a firearm projectile into a human parietal bone. The space-discretized equations of motion are explicitly integrated in time with Newmark's time-stepping algorithm. The impact of the projectile on the skull, as well as the collisions between flying fragments, are controlled through a nonsmooth contact algorithm. Cohesive theories of fracture, in conjunction with adaptive remeshing, control the nucleation and the propagation of fractures. The progressive opening of fracture surfaces is governed by a thermodynamically irreversible cohesive law embedded into cohesive-interface elements. Numerical results compare well with forensic data of actual firearm wounds to human crania.     

A finite element method for elasto-plastic structures and contact problems by parametric quadratic programming

In this paper, the stiffness matrix of a contact element is introduced by means of a penalty function expression of the contact pressure and frictional force. The contact condition and the flow rule are expressed by the same form as in a non-associated plastic flow problem. A unified PQP (Parametric Quadratic Programming) model related to contact problems as well as to elasto-plastic structures is constructed. A series of PQP formulae for contact problems and elastic-plastic structures is derived in the text, and some numerical examples are illustrated as well.     

Impact-damage visualization in CFRP by resistive heating: Development of a new detection method for indentations caused by impact loads

Rapid and automatic inspection of composite aircraft after every flight would reduce the safety factor and allow for more flights. Although, an electrical resistance change method (ERCM) has been proposed, there are many problems with its practical application. In this study, a new diagnostic method, impact-damage visualization, was developed. Indentation damage increases fiber-fiber contact at the interlaminar interface and electrical conductivity. Consequently, electrical current applied to the material will concentrate around the damaged area, and lead to selective and intense resistive heating. This temperature increase can be observed by thermography or detected as a change in electrical resistance caused by the temperature difference. The proposed method had sufficient reliability and sensitivity for practical application as a damage inspection method.     

A new multiscale computational method for elasto-plastic analysis of heterogeneous materials

A new multiscale computational method is developed for the elasto-plastic analysis of heterogeneous continuum materials with both periodic and random microstructures. In the method, the multiscale base functions which can efficiently capture the small-scale features of elements are constructed numerically and employed to establish the relationship between the macroscopic and microscopic variables. Thus, the detailed microscopic stress fields within the elements can be obtained easily. For the construction of the numerical base functions, several different kinds of boundary conditions are introduced and their influences are investigated. In this context, a two-scale computational modeling with successive iteration scheme is proposed. The new method could be implemented conveniently and adopted to the general problems without scale separation and periodicity assumptions. Extensive numerical experiments are carried out and the results are compared with the direct FEM. It is shown that the method developed provides excellent precision of the nonlinear response for the heterogeneous materials. Moreover, the computational cost is reduced dramatically.     

Finite-element simulation of wave propagation in periodic piezoelectric SAW structures

Many surface acoustic wave (SAW) devices consist of quasiperiodic structures that are designed by successive repetition of a base cell. The precise numerical simulation of such devices, including all physical effects, is currently beyond the capacity of high-end computation. Therefore, we have to restrict the numerical analysis to the periodic substructure. By using the finite-element method (FEM), this can be done by introducing periodic boundary conditions (PBCs) at special artificial boundaries. To be able to describe the complete dispersion behavior of waves, including damping effects, the PBC has to be able to model each mode that can be excited within the periodic structure. Therefore, the condition used for the PBCs must hold for each phase and amplitude difference existing at periodic boundaries. Based on the Floquet theorem, our two newly developed PBC algorithms allow the calculation of both, the phase and the amplitude coefficients of the wave. In the first part of this paper we describe the basic theory of the PBCs. Based on the FEM, we develop two different methods that deliver the same results but have totally different numerical properties and, therefore, allow the use of problem-adapted solvers. Further on, we show how to compute the charge distribution of periodic SAW structures with the aid of the new PBCs. In the second part, we compare the measured and simulated dispersion behavior of waves propagating on periodic SAW structures for two different piezoelectric substrates. Then we compare measured and simulated input admittances of structures similar to SAW resonators.     

Application of method of fundamental solutions for elasto-plastic torsion of prismatic rods

In this paper torsion of prismatic bars considering elastic-plastic material behavior is studied. Based on the Saint-Venant displacement assumption and deformation theory of plasticity for stress-strain relation the boundary value non-linear problem for stress function is formulated. The purpose of our paper is application of method fundamental solution (MFS) and radial basic function (RBF) for solution of this problem. The non-linear torsion problem in plastic region is solved by means of the Picard iteration. Proposed algorithm is based on solution of the linear Poisson equation on each iteration steps.     

Adaptive reproducing kernel particle method using gradient indicator for elasto-plastic deformation

An adaptive meshless method based on the multi-scale Reproducing Kernel Particle Method (RKPM) for analysis of nonlinear elasto-plastic deformation is proposed in this research. In the proposed method, the equivalent strain, stress, and the second invariant of the Cauchy–Green deformation tensor are decomposed into two scale components, viz., high- and low-scale components by deriving them from the multi-scale decomposed displacement. Through combining the high-scale components of strain and the stress update algorithm, the equivalent stress is decomposed into two scale components. An adaptive algorithm is proposed to locate the high gradient region and enrich the nodes in the region to improve the computational accuracy of RKPM. Using the algorithm, the high-scale components of strain and stress and the second invariant of the Cauchy–Green deformation tensor are normalized and used as criteria to implement the adaptive analysis. To verify the validity of the proposed adaptive meshless method in nonlinear elasto-plastic deformation, four case studies are calculated by the multi-scale RKPM. The patch test results show that the used multi-scale RKPM is reliable in analysis of the regular and irregular nodal distribution. The results of other three cases show that the proposed adaptive algorithm can not only locate the high gradient region well, but also improve the computational accuracy in analysis of the nonlinear elasto-plastic deformation.     

Finite-element simulation of tack welds in girth welding of a pipe-flange joint

Summary Welding deformations play an important role in sealing capabilities and service life of welded pipe-flange joints. A numerical procedure for modeling of tack welds in girth butt-welding of such joints is of vital importance for the prediction of transverse shrinkage and flange face deformation, which is directly related to the joint sealing capability. This paper presents a 3-D finite element simulation of a pipe-flange joint to describe the numerical procedure for modeling of tack welds in circumferential joints. Sequentially coupled nonlinear transient thermo-mechanical analysis is performed to simulate Metal Inert Gas (MIG) welding. Single pass butt weld geometry with single “V” for 100 mm nominal diameter pipe with same sized weld neck type ANSI flange of class no. 300 is used. Temperature dependent material properties are used and deposition of filler metal is obtained by element birth and death feature. The peak temperature of the tack during the butt-welding of the tacked model is concluded a key parameter for numerical prediction of deformations, whereas tack temperature has negligible effect on the residual stresses.     

Phase transformations in materials studied by micro-Raman spectroscopy of indentations

 Phase transformations occurring in materials under high pressures are important for a wide range of problems in materials science and solid-state physics. Most of the results in this area have been obtained using various sophisticated high-pressure cells. We studied solid-state phase transformations and amorphisation under high non-hydrostatic pressures in very simple experiments using a combination of hardness indentation tests with micro-Raman spectroscopy. Amorphisation of diamond, that did not occur under hydrostatic loading, has been observed. Shearing and distortion of cubic diamond structure above 100 GPa resulted not only in its amorphisation, but also in the formation of threefold coordinated carbon. A carbon film that was squeezed between a SiC substrate and diamond indenter lost its graphitic structure and produced a Raman band typical of diamond-like carbon (DLC). Even for such a well-studied material as Si, principally new data have been obtained. High spatial resolution of the method allowed us to show that the Raman spectrum that was previously ascribed to a metastable Si-III phase originates from two different high-pressure phases of Si. Up to five different phases of Si were found within a single impression. Studies of reversible transformations that occur upon unloading or heating of samples by the laser beam have also been carried out. Amorphisation and/or phase transformations have been observed for some other materials, such as SiC, quartz, Ge, GaAs and other. The combination of indentation tests with micro-Raman spectroscopy provides a powerful and fast tool for in-situ and ex-situ monitoring of pressure-induced phase transformations in materials. Received: 2 January 1997 / Accepted: March 1997     

A simple and efficient solution method for the limit elasto-plastic analysis of plane frames

A solution method for the first order step-by-step limit analysis of plane frames is presented. The formulation of the governing equations is based on the plastic node method and takes into account stress reversals and any type of yield conditions. The solution of the governing equilibrium equations in each step is obtained with the preconditioned conjugate gradient method. Special attention is paid to the fact that the overall stiffness matrix changes gradually with the successive formation of plastic nodes. A number of test problems have been performed which show the usefulness of the present approach. The results also reveal the superiority of this technique, in both storage requirements and computing time, with respect to efficient methods of solution.     

A novel model for determining tensile properties and hardness of steels by spherical indentations

An energy-based spherical indentation (ESI) model according to equivalent energy principle is developed to determine the stress–strain relation, tensile strength and hardness of steels. Several parameters in the model are determined with finite element analysis (FEA). For a wide range of homogeneous and isotropic materials in power stress–strain law, a large number of FEA calculations are carried out to verify the ESI model. Results show that both the forward-predicted load-depth relations and the reverse-predicted stress–strain relations from the model agree well with the results from FEA. For 12 steels, the tensile properties, Rockwell and Brinell hardness predicted by the ESI model are close to the standard testing results.     

Calibrator for studying electromagnetic flowmeters by a simulation method

A simulation method is considered for checking electromagnetic flowmeters without using a magnetic field transducer.Translated from Izmeritelnaya Tekhnika, No. 12, pp. 45–47, December, 2004.This revised version was published online in April 2005 with a corrected cover date.     

Finite-element method for power losses calculation in longrectangular conductors located in transverse harmonic magneticfield

A method is presented for calculation of the Joule power losses in a long linear isotropic nonferromagnetic rectangular conductor located in a harmonic transverse magnetic field that is situated in a homogeneous environment. The method links two others: the method of finite elements (for the internal region) and the separation of variables method (for the external region). On the basis of the obtained relationships, numerical calculations were performed, and plots of Joule power losses for the rectangular conductors were made