Engineering topics

Reed, K. W.

Publications and source records attributed to Reed, K. W..

6 records

NASA NTRS1985

Constitutive modeling and computational implementation for finite strain plasticity

This paper describes a simple alternate approach to the difficult problem of modeling material behavior. Starting from a general representation for a rate-tpe constitutive equation, it is shown by example how sets of test data may be used to derive restrictions on the scalar functions appearing in the representation. It is not possible to determine these functions from experimental data, but the aforementioned restrictions serve as a guide in their eventual definition. The implications are examined for hypo-elastic, isotropically hardening plastic, and kinematically hardening plastic materials. A simple model for the evolution of the 'back-stress,' in a kinematic-hardening plasticity theory, that is entirely analogous to a hypoelastic stress-strain relation is postulated and examined in detail in modeling finitely plastic tension-torsion test. The implementation of rate-type material models in finite element algorithms is also discussed.

Reed, K. W.↗

NASA NTRS1984

Hybrid stress finite elements for large deformations of inelastic solids

A new hybrid stress finite element algorithm, based on a generalization of Fraeijs de Veubeke's complementary energy principle is presented. Analyses of large quasistatic deformation of inelastic solids (hypoelastic, plastic, viscoplastic) are within its capability. Principle variables in the formulation are the nominal stress rate and spin. A brief account is given of the boundary value problem in these variables, and the 'equivalent' variational principle. The finite element equation, along with initial positions and stresses, comprise an initial value problem. Factors affecting the choice of time integration schemes are discussed. Results found by application of the new algorithm are compared to those obtained by a velocity based finite element algorithm.

Reed, K. W.↗

NASA NTRS1983

Analyses of large quasistatic deformations of inelastic bodies by a new hybrid-stress finite element algorithm - Applications

A new hybrid-stress finite element algorithm suitable for analyzing large quasistatic deformations of inelastic solids is presented and its feasibility and performance are demonstrated with examples. The algorithm provides extremely accurate bifurcation analysis which is stable with respect to variation in the finite element mesh, so long as the same type of element is used in every mesh. When the mesh element is varied, the result changes in a predictable manner. The method does not necessarily lead to an upper or lower bound for the critical load. An explicit forward gradient scheme is used to improve stability and is shown to be useful also for elongation-dominated deformations. The application of the method to the onset of necking in plane extension and to deformation and stress in plane extension of an elasticoviscous fluid with an array of cylindrical voids is given in detail.

Reed, K. W.↗

NASA NTRS1983

Analyses of large quasistatic deformations of inelastic bodies by a new hybrid-stress finite element algorithm

A new hybrid-stress finite element algorithm, suitable for analyses of large, quasistatic, inelastic deformations, is presented. The algorithm is base upon a generalization of de Veubeke's complementary energy principle. The principal variables in the formulation are the nominal stress rate and spin, and thg resulting finite element equations are discrete versions of the equations of compatibility and angular momentum balance. The algorithm produces true rates, time derivatives, as opposed to 'increments'. There results a complete separation of the boundary value problem (for stress rate and velocity) and the initial value problem (for total stress and deformation); hence, their numerical treatments are essentially independent. After a fairly comprehensive discussion of the numerical treatment of the boundary value problem, we launch into a detailed examination of the numerical treatment of the initial value problem, covering the topics of efficiency, stability and objectivity. The paper is closed with a set of examples, finite homogeneous deformation problems, which serve to bring out important aspects of the algorithm.

Reed, K. W.↗

NASA NTRS1983

Stress and Fracture Analyses Under Elastic-plastic and Creep Conditions: Some Basic Developments and Computational Approaches

A new hybrid-stress finite element algorith, suitable for analyses of large quasi-static deformations of inelastic solids, is presented. Principal variables in the formulation are the nominal stress-rate and spin. A such, a consistent reformulation of the constitutive equation is necessary, and is discussed. The finite element equations give rise to an initial value problem. Time integration has been accomplished by Euler and Runge-Kutta schemes and the superior accuracy of the higher order schemes is noted. In the course of integration of stress in time, it has been demonstrated that classical schemes such as Euler's and Runge-Kutta may lead to strong frame-dependence. As a remedy, modified integration schemes are proposed and the potential of the new schemes for suppressing frame dependence of numerically integrated stress is demonstrated. The topic of the development of valid creep fracture criteria is also addressed.

Reed, K. W.↗

NASA NTRS1983

Inelastic stress analyses at finite deformation through complementary energy approaches

A new hybrid-stress finite element algorithm, suitable for analyses of large, quasistatic, inelastic deformations, is presented. The algorithm is based upon a generalization of de Veubeke's (1972) complementary energy principle. The principal variables in the formulation are the nominal stress rate and spin, and the resulting finite element equations are discrete versions of the equations of compatibility and angular momentum balance. The algorithm produces true rates, time derivatives, as opposed to 'increments'. There results a boundary value problem (for stress rate and velocity) and an initial value problem (for total stress and deformation). A discussion of the numerical treatment of the boundary value problem is followed by a detailed examination of the numerical treatment of the initial value problem, covering the topics of efficiency, stability, and objectivity. The paper is closed with a set of examples, finite homogeneous deformation problems, which serve to bring out important aspects of the algorithm.

Atluri, S. N.↗