J.St. Doltsinis

On the large strain inelastic analysis in natural formulation part I: Quasistatic problems

Abstract The paper first establishes for the large strain domain the transformation of the homogeneous, natural presentation of the strain and stress states to the standard formulation and vice versa. Possible definitions of natural strains appertaining to deformations composed of elastic and inelastic parts are discussed. Furthermore, the natural stress-strain relations are given based on total elastic and incremental plastic deformations. The results apply immediately to the description of simple finite elements which may serve, moreover, as subelements for the derivation of higher order finite elements. A solution algorithm is developed unifying the Newton technique with respect to the geometric nonlinearity and the normal iteration technique with respect to the material nonlinear behaviour. A number of numerical examples is presented such as the necking of a simple tension specimen, the extrusion of an aluminium billet and the heading of a steel bolt.

A primer on superplasticity in natural formulation

Abstract Manufacturing processes rely increasingly on superplastic properties of certain structural materials, such as titanium alloys, and gain significant importance, in particular, in the air- and spacecraft industry. This paper presents a computer-oriented review and analysis of superplastic deformation processes. The modelling of the material response subject to superplastic conditions is attacked first, and relies on recent experimental findings with respect to rate of deformation and grain-growth effects. Multiaxial constitutive relations are based on the homogeneous natural definition of stress and rate of deformation. Computational techniques developed within the framework of finite element discretisations account for the observance of the incompressibility constraint. Nonlinear solution methods for the velocity field are examined as well as the temporal approximation of the unsteady deformation process of superplastic forming. The numerical characteristics of the proposed techniques are demonstrated. A number of examples illustrating superplastic forming processes are investigated and compared, where possible, with experimental data. In this context unsteady contact with the die, frictional sliding, and the forming of an actual structural component are also examined.

Thermomechanical response of solids at high strains—Natural approach

Abstract The paper develops in pursuance of [4]the theoretical framework appertaining to coupled thermomechanical deformations of solids, subject to large as well as inelastic deformations. The essential feature of the analysis is a consistent natural formulation which encompasses also all thermodynamic aspects. On the other hand, it must be admitted that current concepts on mechanical constitutive assumptions [5, 6]are not sufficiently sophisticated to permit a precise generalisation for the purpose of incorporating thermomechanical effects and delivering a fully compatible theory of the coupled problem. Uniqueness and bifurcation of the solutions as well as stable postcritical deformation paths are also considered in this account. Furthermore, algorithms for the solution of the nonlinear algebraic equations representing the discretised problem and, in particular, quasi-Newton techniques are discussed. The paper concludes with a number of applications of technical relevance.

On the large strain inelastic analysis in natural formulation part II. Dynamic problems

Abstract The paper extends the considerations of part I concerning large strain inelastic phenomena into the dynamic domain. Using the homogeneous, natural presentation of the strain and stress states, the description of material behaviour is discussed on the basis of thermodynamics. Temperature generation due to the dissipation of mechanical work is included in the stress-strain relations, as well as temperature and rate sensitivity of the inelastic material characteristics. For the appropriate integration of the discretized equations of motion a general scheme is adopted which can be specialized in order to reproduce various explicit or implicit algorithms. Particular attention is paid to the evaluation of the resultants of the internal stresses and their time rates as required in the numerical procedure. Some solution methods are tested on the deformation history of a projectile striking a rigid wall. As further numerical examples the impact of a long rod and the heading of a steel bolt under dynamic loading are presented.

Elastoplastic and creep analysis with the ASKA program system

Abstract The objective of this article is a concise presentation of the extension of the general purpose program ASKA (Automatic System for Kinematic Analysis) to include material non-linearities such as plasticity and creep. A short derivation of the incremental stress-strain relations which form the basis of the iterative numerical procedure is given first, followed by a more detailed description of the relevant software package. An elastoplastic calculation of a pressure vessel as a typical application and suggestions for further developments conclude the article.

Ta πanta pei

Abstract The paper presents a survey of recent work on flow phenomena performed in the closing days of the traditional Institute for Statics and Dynamics of the University of Stuttgart. It serves as a swan song to the latter institution and as a clarion call initiating the work of the new Institute for Computer Applications. The paper develops, in particular, a rigorous natural methodology for the analysis of flow problems when described by the Navier-Stokes equations. The authors consider, apart from the continuous and the finite element formulations, also the solution of the associated large-scale nonlinear problems on present-day supercomputers. The theory is illustrated on a number of selected applications encompassing three-dimensional flow, thermally coupled phenomena, fluid-solid interaction and Stokesian motion for solid materials.

Numerical solution of transient nonlinear problems

Abstract The paper is concerned with computational aspects of nonlinear and transient finite element analysis. Particular emphasis is placed on the inelastic response behaviour of structures and continua, respectively, when exposed to quasistatic and dynamic environments. Several examples illustrate the application to different engineering disciplines such as thermal shock behaviour, explosive metal forming and wave propagation. The objective is twofold, (i) to demonstrate dominant features of explicit and implicit time-marching algorithms (linear and cubic Hermitean expansions with different weighting strategies) and (ii) to show the solution of relevant engineering problems. The paper is divided into three parts addressed to 1. 1. Computational strategies for nonlinear and transient analysis, 2. 2. Inelastic analysis of quasistatic motions, 3. 3. Dynamic analysis of inertial and wave propagation problems.

Natural finite element techniques for viscous fluid motion

Abstract The paper surveys recent work on fluid dynamics performed at the ISD, University of Stuttgart. It is in particular directed to a natural description of the flow phenomena and includes also a consideration of thermally coupled problems. The derivation of the relevant finite element equations when referred to natural quantities is outlined and examples of application are given. Also presented is a discussion on the associated modern developments in numerical solutions techniques.

Three-Dimensional Thermomechanical Analysis of Metal forming Processes

The analysis of metal forming processes requires consideration of the three-dimensional nature of the process involving a material undergoing substantial deformations under the action of the die. Significant thermal phenomena may be activated by both pronounced temperature differences and internal dissipation during the forming process. Furthermore, unsteady contact between material and die plays a significant role and involves frictional effects and heat transfer phenomena.

Extensions to the elastoplastic analysis with the aska program system

Abstract This article gives the theoretical background of the latest additions to the elastoplastic part of the general purpose program ASKA (Automatic System for Kinematic Analysis). Two independent topics are dealt with: a) material description concerning a combined isotropic kinematic hardening as well as a hydrostatic dependence of the yield condition and b) elastoplastic bending elements comprising a plate shell and a related stiffener. Two examples, one connected with a reinforced concrete plate and the other with soil mechanics (tunnel construction), illustrate the practical application.