Object-Oriented Nonlinear Finite Element Programming: A Primer

A three dimensional finite element program is developed for the analysis of pavement systems. An explicit approach of the finite element analysis is adopted. This approach results in a vector formulation of the equation of motion. Large displacement is considered through the use of a co-rotational approach which considers small deformations and large rotations of the elements. For the convenience of application a two dimensional finite element program is also developed. An eight-node ¶metric solid element is used for the three dimensional analysis, and a four-node element for the two dimensional analysis. Loading conditions are verified for static ramp and step loadings, sinusoidal loadings, prescribed ground acceleration input, and pulse input. The material library is verified for linear elastic materials, elastic-plastic materials with h&es or Drucker-Prager criteria and assuming associated or non-associated flow rules, and a viscoelastic material of Maxwell type. Three hardening rules are implemented, namely the kinematical hardening, isotropic hardening, and the mixed type. Available analytical data and comparison studies by using ANSYS serve as the basis for the verification.

The principle of robot based incremental sheet metal forming is based on flexible shaping by means of a freely programmable path-synchronous movement of two tools, which are operated by two industrial robots. The final shape is produced by the incremental infeed of the forming tool in depth direction and its movement along the geometry’s contour in lateral direction. The main problem during the forming process is the influence on the dimensional accuracy resulting from the compliance of the involved machine structures and the springback effects of the workpiece. The project aims to predict these deviations caused by resiliences and to carry out a compensative path planning based on this prediction. Therefore a planning tool is implemented which compensates the robot’s compliance and the springback effects of the sheet metal. Finite element analysis using a material model developed at the Institute of Applied Mechanics (IFAM) [1] has been used for the simulation of the forming process. The finite strain constitutive model combines nonlinear kinematic and isotropic hardening and is derived in a thermodynamical setting. It is based on the multiplicative split of the deformation gradient in the context of hyperelasticity. The kinematic hardening component represents a continuum extension of the classical rheological model of Armstrong–Frederick kinematic hardening which is widely adopted as capable of representing the above metal hardening effects. The major problem of low-order finite elements used to simulate thin sheet structures, such as used for the experiments, is locking, a non-physical stiffening effect. Recent research focuses on the large deformation version of a new eight-node solid-shell finite element based on reduced integration with hourglass stabilization. In the solid-shell formulation developed at IFAM ([2], [3]) the enhanced assumed strain (EAS) concept as well as the assumed natural strain (ANS) concept are implemented to circumvent locking. These tools are very important to obtain a good correlation between experiment and simulation.

A peridynamic plastic model based on von Mises criteria with isotropic, kinematic and mixed hardenings under cyclic loading

Combined isotropic and kinematic hardening in phenomenological switching models for ferroelectric ceramics

This chapter shows, through the example of the addition of a plate and shell element to freeware FEM-object, an object-oriented (C++) finite element program, how object-oriented approaches, as opposed to procedural approaches, make finite element codes more compact, more modular, and versatile but mainly more easily expandable, in order to improve the continuity and the compatibility between software of research and industrial software. The fundamental traits of object-oriented programming are first briefly reviewed, and it is shown how such an approach simplifies the coding process. Then, the isotropic shell and orthotropic plate formulations used are given and the discretized equations developed. Finally, the necessary additions to the FEM-object code are reviewed. Numerical examples using the newly created plate membrane plate element are shown.

Effect of kinematic hardening on localized necking in substrate-supported metal layers

Constants and parameters of the damage accumulation model with isotropic and kinematic hardening for 25Cr1Mo1V steel

The authors have compiled some of the existing work to illustrate stress interpretation in finite element (FE) analysis and to show the errors in the calculation of stresses at nodes by some FE programs. Although the paper advises potential finite element users that not all FE programs offer the same accuracy, the examples and discussions in the paper indicate that some points are still misunderstood or could be mis- leading. No finite element program can replace the engineering judgement of an experienced engineer. Therefore any com- mercial FE program must not be used as a black box for structural analysis. Behind the finite element method, a lot of subtleties exist that every engineer using FE programs should understand. It is true that some dramatic failures of large structures, presumably designed with the aid of the FE method, occurred (Burnett 1987). Burnett wrote in his text- book the following comment which describes exactly what the discussers think about FE programs: One cannot simply pick up a user's manual to any commercial FE program and, lacking an understanding of basic FE concepts, expect to generate a solution to an engineering problem that is mean- ingful, reliable, and whose accuracy has been estimated and judged to be acceptable. Someone working on the problem must have this understanding, or else the project is likely to be a failure rather than a success. In the following, the main aspects treated in the paper are discussed.

Comparison of isotropic hardening and kinematic hardening in thermoplasticity

The combination of kinematic and isotropic hardening models makes it possible to model the behaviour of cyclic elastic-plastic steel material, though the estimation of the hardening parameters and catching the influence of those parameters on the material response is a challenging task. In the current work, an approach for the numerical simulation of the low-cycle fatigue of AISI316L steel is presented using a finite element method to study the fatigue behaviour of the steel at different strain amplitudes and operating temperatures. Fully reversed uniaxial LCF tests are performed at different strain amplitudes and operating temperatures. Based on the LCF test experimental results, the non-linear isotropic and kinematic hardening parameters are estimated for numerical simulation. On comparing, the numerical simulation results were in very good agreement with those of the experimental ones. This presented method for the numerical simulation of the low-cycle fatigue on AISI316 stainless steel can be used for the approximate prediction of the fatigue life of the components under different cyclic loading amplitudes.

Loading-unloading behavior of a deformable sphere with a rigid flat under full stick contact condition is investigated for varying strain hardening. The study considers various tangent modulus using the finite element software ANSYS. Both the bilinear kinematic hardening and isotropic hardening models are considered. Numerical simulation reveals the qualitative similarity between kinematic and isotropic hardening regarding the variation of interfacial parameters during loading-unloading for various tangent modulus. It is found that the material with kinematic hardening dissipates more energy than the material with isotropic hardening during unloading. However for elastic perfectly plastic material, the loading-unloading behavior is insensitive to hardening model.

The present study provides a formulation of the creep constitutive equation which is descriptive of anisotropic creep hardening behavior. The basic structure of the model is based on the general framework of irreversible thermodynamics; we define a set of energy-conjugate state variables using the Helmholtz free energy function and the dissipation energy function. The prototypal model of the unified type accounts for combined isotropic and kinematic hardening, and it is applied to a description of anisotropic creep behavior. In order to enhance the predictive accurcy of prototypal evolution equations of the Bailey-Orowan type, we furthermore develop an auxiliary creep hardening rule in general form ; the concept of material memory is introduced where isotropic hardening is suppressed and kinematic hardening is promoted. It is shown that the auxiliary creep hardening rule is applicable to any model of the pure kinematic type. The proposed creep model, which is a combination of the prototypal model and the auxiliary rule, can well reproduce creep softening behavior under complete stress reversals, as in the ORNL creep model.

We present an ordinary state-based peridynamic model in 2D and 3D consistent with rate-independent J2 plasticity with associated flow rule. The new contribution is the capability of the elastoplastic law to describe isotropic, kinematic and mixed hardening. The hardening formulations follow those available in the literature for classical elastoplasticity. The comparison between the results obtained with the peridynamic model and those obtained with a commercial FEM software shows that the two approaches are in good agreement. The extent of the plastic regions and von Mises stress computed with the new model for 2D and 3D examples match well those obtained with FEM-based solutions using ANSYS.

This paper briefly describes the development of a finite layer element program for computing stresses and displacements resulting from nonlinear temperature gradients in continuous skew slab-girder bridges and deals with the experimental investigation of a two-span continuous skew bridge model with an intermediate stiffening beam. The temperature distribution through the depth of model, which constitutes the input of the finite element program, is obtained by solving the one-dimensional transient heat-flow equation. The experimental values of thermal stresses and deflections of bridge model are presented and compared with those obtained by the finite element program. An example of practical application of the program is also presented to illustrate the order of magnitude of thermal stresses expected in the two-span continuous skew bridge due to diurnal temperature variations.

The thermodynamic framework for continuum mechanics can be applied to model granular and porous materials. Broadly speaking, there exists two approaches: the French school approach and Ziegler’s approach. Despite the fact that they both have the same foundations, differences between them emerge regarding the way in which stored energy is accounted for. This is illustrated here by applying the two approaches to the classical Von Mises kinematic and isotropic hardening models. In Ziegler’s approach, the stored energy is solely used for the kinematic hardening, as opposed to the French school approach in which the stored energy is allowed in both cases of hardening. In spite of which modelling approach is taken, we will show how certain modifications to these theories have to be made in order to develop the classical modified Cam Clay model, which emphasises the difference between the classical and the thermodynamic formulations.