Journal ArticleDOI
Development of a method for integrating time‐dependent constitutive equations with large, small or negative strain rate sensitivity
T. G. Tanaka,A. K. Miller +1 more
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In this article, a unified numerical method to integrate stiff time-dependent constitutive equations has been developed, which is a stable, non-iterative and self-correcting solution procedure which works successfully over a wide range in strain rate sensitivity.Abstract:
A unified numerical method to integrate stiff time-dependent constitutive equations has been developed. This method is a stable, non-iterative and self-correcting solution procedure which works successfully over a wide range in strain rate sensitivity. Time steps are automatically controlled during integration to achieve a user-specified accuracy. This method is implemented in the program package NONSS whose dual purpose is examination of the behaviour of unified constitutive models by themselves (‘one-element behaviour’) as well as providing a computationally efficient subroutine for utilizing such models with existing finite element programs for non-linear structural and metal forming analyses. \n \nThis paper first reviews the relation between the numerical characteristic of constitutive equations and the choice of integration methods. Then the paper presents the derivation of the governing basic equations in the new method, and also derives a special algorithm which permits large integration steps within the negative strain rate sensitivity (‘serrated yielding’) regime. Examples of the program's performance are given, including plasticity at high and low temperatures, cyclic deformation and multiaxial straining.read more
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Nonlinear mechanical response of high density polyethylene. Part II: Uniaxial constitutive modeling
Chuntao Zhang,Ian D. Moore +1 more
TL;DR: In this paper, two uniaxial constitutive models are constructed based on the experimental data presented in Part I, based on which a nonlinear viscoelastic (NVE) model is formulated using the mechanical analogy consisting of one independent spring and six Kelvin elements in series.
Journal ArticleDOI
An implicit time-integration procedure for a set of internal variable constitutive equations for isotropic elasto-viscoplasticity
A.M. Lush,G. Weber,Lallit Anand +2 more
TL;DR: In this paper, a fully implicit, Euler backward time-integration procedure for a set of internal variable constitutive equations for isothermal, isotropic elasto-viscoplasticity with isothermal hardening is presented.
Journal ArticleDOI
ALSPEN-A mathematical model for thermal stresses in direct chill casting of aluminum billets
Hallvard G. Ejær,Asbjørn Mo +1 more
TL;DR: In this paper, the authors present the mathematical model ALSPEN, in which the thermally induced strains and stresses which develop during direct chill (DC) semicontinuous casting of aluminum billets are calculated by a finite-element method.
Journal ArticleDOI
Unified Constitutive Equations of Foam Materials
TL;DR: In this article, a unified constitutive equation with the effect of compression strain rate, tension strain, and shear strain for foam materials with very low Poisson's ratio has been developed.
References
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Book
Numerical methods for engineering application
TL;DR: A short review of linear algebra can be found in this article, where the authors consider the following problems: I. Initial Value Problems. II. Boundary value problems. III. Interpolation.
Journal ArticleDOI
An Inelastic Constitutive Model for Monotonic, Cyclic, and Creep Deformation: Part I—Equations Development and Analytical Procedures
Journal ArticleDOI
On the Structure of Stress-Strain Relations for Time-Dependent Plastic Deformation in Metals
TL;DR: In this paper, a general kinematical relation is developed between the macroscopic inelastic strain tensor and microstructural slip displacements, as modeled either by continuum shearing on crystallographic planes of individual grains or by the motion of discrete dislocation lines.
Journal ArticleDOI
Numerical stability in quasi‐static elasto/visco‐plasticity
TL;DR: In this article, the numerical stability of simple marching schemes used in elasto/visco-plasticity is investigated and a theoretical stability criterion based on the identification of the numerical process with the integration of a nonlinear, first order, system of ordinary differential equations is derived.
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