Mathematical Modelling Reports

hr. J. So/i& Strucr. Vol. 23. No. 6, pp. 751-767. 1987

795

ANALYSIS OF A STRAIN SOFTENING CONSTITUTIVE MODEL

G. FRANTZISKONIS and C. S. DE~AI

Department of Civil Engineering and Engineering Mechanics, University of Arizona, Tucson, AZ 85721, U.S.A.

Abstract-The paper first examines the question of uniqueness of a basic yet simplified constitutive model with strain softening. It is shown that the constitutive equations lead to a unique solution for the case of rate-dependent as well as rate-independent formulation and its implementation in finite element analysis shows mesh size insensitivity in the hardening and softening regimes. Conditions for formation of narrow shear bands are developed and discussed. It is shown that as the damage accumulates the material approaches localization of deformation.

&I. scienr. Res. Vol. 44. No. l/2, pp. 1-7. 1987

MODELLING MUSHY REGIONS

A. B. CROWLEY

Mathematics and Ballistics Group, Royal Military College of Science, Shrivenham, Swindon, Wilts, England

J. R. OCKENDON

Mathematical Institute, 2429 St Giles, Oxford, England

Abstract-Two phase or mushy regions in which the phase boundary has a complicated morphology can exist in both pure and impure materials. In the former case, a macroscopic mathematical description can be given for the particular problem of melting by volumetric heating; no such procedure seems available for impure materials and this paper describes the reason for this. The principal mathematical difficulty is the analysis of the Stefan problem in the presence of a surface energy term.

Appl. s&W. Rex Vol. 44, No. i/2. pp. 2742, 1987

A MODEL OF A CASTING

S. C. FLUID and J. D. HUNT

Department of Metallurgy and Science of Materials, University of Oxford, Parks Road, Oxford, England

Abstract-A model of a casting is presented which describes the freezing of a mushy zone, growing with a dynamically calculated undercooling at the dendrite tips. Equiaxed grains are introduced ahead of a columnar front. The model resembles a combination of the Stefan and mushy zone problems.

Appl. scienr. Rex Vol. 44. No. l/2, pp. 4349. 1987

A MODEL FOR THE NUMERICAL COMPUTATION OF MICROSEGREGATION IN ALLOYS

A. J. W. OGILVY

Osprey Metals Ltd, Neath, South Wales

D. H. KIRKW~~D

Department of Metallurgy, University of Sheffield, Sheffield, England

Abstract-A development of the Brody-Flemings model for the prediction of dendritic microsegregation in alloys is proposed. The original model considered one-dimensional back diffusion into thickening