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Publication date: 1 February 2006

Dragan D. Milasinovic

The paper deals with the rheological‐dynamical analogy in which the three‐dimensional stress‐strain relations are defined under cyclic variation of stress for Hencky’s total…

136

Abstract

The paper deals with the rheological‐dynamical analogy in which the three‐dimensional stress‐strain relations are defined under cyclic variation of stress for Hencky’s total strain theory. In many practical visco‐elasto‐plastic problems, like as multiaxial fatigue under loading at constant stress amplitude and constant stress ratio, the load‐carrying members are subjected to proportional loading. The classical Hencky’s theory has the advantage of mathematical convenience but its disadvantage is that the deformations predicted for the volume element are independent of the loading path. The existing formulations of the constitutive models for metals are mainly based on the Prandtl‐Reuss incremental theory of elasto‐plasticity, slip theory of plasticity or continuum damage mechanics. They have been shown capable of reproducing satisfactorily most experimental results available for metallic specimens. However, from the theoretical viewpoint little has been said about how these formulations relate to realistic predicting many different inelastic and time dependent problems of two‐ or threedimensional solids, such as fatigue, discontinuous plastic deformation etc. In this paper, fundamentally new aspect of isochronous constitutive relations for Hencky’s theory, which are dependent of the each loading path, is achieved by systematically introducing RDA concept into the continuum framework. Specific inelastic and fatigue formulation of triaxial state of stress is developed and discussed within the new theoretical tool and related to von Mises plasticity..

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Multidiscipline Modeling in Materials and Structures, vol. 2 no. 2
Type: Research Article
ISSN: 1573-6105

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Article
Publication date: 1 January 2006

Dragan D. Milasinovic

This paper is concerned with a new proposal regarding the analysis of visco‐elastoplasticity and fatigue and is based on rheological‐dynamical theory. Due to the analogy between…

104

Abstract

This paper is concerned with a new proposal regarding the analysis of visco‐elastoplasticity and fatigue and is based on rheological‐dynamical theory. Due to the analogy between rheological model and dynamical model with viscous damping, it becomes obvious that inelastic response of members is essentially a dynamical problem. An analytical rheological‐dynamical viscoelasto‐ plastic solution of one‐dimensional longitudinal continuous vibration under loading and solution for the stress relaxation as unloading have been developed and used to obtain the fatigue limit of thin long bars. Rheologic behavior of the bar can be characterized by one parameter, like in a single‐degree‐of‐freedom spring mass system. In all inelastic strains time rate effects are always present to some degree. Whether or not their exclusion has a significant influence on the prediction of the material fatigue behavior depends upon several factors like: maximum absolute stress in the cycle, coefficient of asymmetry of cycle, creep coefficient, slope of the strain hardening portion of the stress‐strain curve, relative frequency and uniaxial yield stress. This paper provides description of dynamic magnification factor, relaxation of stress, stress concentration and the fatigue limit of thin long symmetrical bars.

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Multidiscipline Modeling in Materials and Structures, vol. 2 no. 1
Type: Research Article
ISSN: 1573-6105

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Article
Publication date: 1 January 1987

Miodrag Sekulovi and Dragan Milašinovi

An analysis of the plate and folded plate structures is carried out, taking into account the geometrical non‐linearities and the effects of creep, using the finite strip method…

78

Abstract

An analysis of the plate and folded plate structures is carried out, taking into account the geometrical non‐linearities and the effects of creep, using the finite strip method. An assumption is made that only small deformations and large displacements and rotations exist. Creep of concrete has an important influence on some structures and cannot be neglected in such analysis, especially when geometrical non‐linearities are taken into account. The stiffness matrices (classical and geometrical) and the vector of equivalent nodal loading for the finite strips are obtained using the variation approach. The interpolation functions used are multiples of polynomial and trigonometric functions. Numerical examples showing the theoretical considerations are presented.

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Engineering Computations, vol. 4 no. 1
Type: Research Article
ISSN: 0264-4401

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