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A numerical study on the stretching of a Newtonian fluid filament is analysed. Stretching is performed between two retracting plates, moving under constant extension rate. A semi‐implicit Taylor‐Galerkin/pressure‐correction finite element formulation is employed on variable‐structure triangular meshes. Stability and accuracy of the scheme is maintained up to large Hencky‐strain levels. A non‐uniform radius profile, minimum at the filament mid‐plane, is observed along the filament‐length at all times. We have found maintenance of a suitable mesh aspect‐ratio around the mid‐plane region (maximum stretch zone) to restrict early filament break‐up and consequently solution divergence. As such, true transient flow evolution is traced and the numerical results bear close agreement with the literature.

A new and explicit form of the elastic strain-energy function for modeling large strain elastic responses of soft solids is constructed based on Hencky's logarithmic strain tensor.

Well-designed invariants of the Hencky strain are introduced for characterizing deformation modes and, furthermore, a new interpolating technique is proposed for combining piecewise splines into a single smooth function.

With this new form and this new technique, objectives in three respects may be achieved for the first time.

First, no adjustable parameters need to be treated. Second, large strain responses for three benchmark modes are derivable in a decoupled sense without involving strongly nonlinear coupling effects. Finally, large strain data may be automatically and accurately matched for three benchmark modes, including uniaxial, equi-biaxial and plane-strain extension. Numerical examples are presented and compared with usual approaches.

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..

A direct and unified approach is proposed toward simultaneously simulating large strain elastic behaviors of gellan gels with different gellan polymer concentrations. The purpose of this paper is to construct an elastic potential with certain parameters of direct physical meanings, based on well-designed invariants of Hencky’s logarithmic strain.

For each given value of the concentration, the values of the parameters incorporated may be determined in the sense of achieving accurate agreement with large strain uniaxial extension and compression data. By means of a new interpolating technique, each parameter as a function of the concentration is then obtained from a given set of parameter values for certain concentration values.

Then, the effects of gellan polymer concentrations on large strain elastic behaviors of gellan gels are studied in demonstrating how each parameter relies on the concentration. Plane-strain (simple shear) responses are also presented for gellan gels with different polymer concentrations.

A direct, unified approach was proposed toward achieving a simultaneous simulation of large elastic strain behaviors of gellan gels for different gellan polymer concentrations. Each parameter incorporated in the proposed elastic potential will be derived as a function of the polymer concentration in an explicit form, in the very sense of simultaneously simulating large strain data for different concentrations.

A finite strain measure and a Hookean type finite hyperelastic model based on it were introduced by H. Hencky (1928, 1929) about seventy‐five years ago. About tweenty‐five years later, an objective Eulerian equation of rate form was established by C. Truesdell (1952, 1955) for a rate type extension of Hooke’s law to finite deformations. Originating from these, a history is constantly extending and a tradition is continuing to develop in constitutive modeling of elastic and inelastic behaviour at finite deformations. In a short story consisting of five parts, we would like to relate selected episodes and events in some relevant aspects. Our main objective is to disclose unexpected, perhaps interesting, intrinsic relationships between these independent creations by two great masters and to expound how and why these relationships play essential roles in understanding and clarifying fundamental issues in Eulerian rate theories of finite elastoplasticity

THE work described in this paper is part of a programme concerned with the plastic, creep, and relaxation properties of metals under complex stress systems at elevated temperatures.which is being carried out in the Engineering Division of the N.P.L. It comprises data on the criterion of departure from elastic behaviour, of a low carbon steel over the temperature range 20–550 deg. C, and of an aluminium alloy over the temperature range 20–200 deg. C, and the creep properties under complex stress systems of the low carbon steel at 350 deg. C, and of the aluminium alloy at 150 and 200 deg. C.

A new approach is proposed toward accurately matching any given realistic hardening and softening data from uniaxial tensile test up to failure and moreover, toward bypassing usual tedious implicit trial-and-error iterative procedures in identifying numerous unknown parameters.

Finite strain response features of metals with realistic hardening-to-softening transition effects up to eventual failure are studied for the first time based on the self-consistent elastoplastic J₂-flow model with the logarithmic stress rate. As contrasted with usual approximate and incomplete treatments merely considering certain particular types of hardening effects such as power type hardening, here a novel and explicit approach is proposed to obtain a complete form of the plastic-work-dependent yield strength over the whole hardening and softening range.

A new multi-axial evolution equation for both hardening and softening effects is established in an explicit form. Complete results for the purpose of model validation and prediction are presented for the finite strain responses of monotonic uniaxial stretching up to failure.

New finite strain elastoplastic equations are established with a new history-dependent variable equivalently in place of the usual plastic work. With these equations, a unified and accurate simulation of both gardening and softening effects up to failure is achieved for the first time in an explicit sense without involving usual tedious implicit trial-and-error iterative procedures.

The purpose of this study is to show how gradual strength degradation of metal beams under cyclic bending up to fatigue failure is simulated based on a new elastoplasticity model free of any yield criterion.

A new approach is proposed toward accurately and explicitly prescribing evolution of non-uniform stress distribution on beam cross-section under cyclic bending and, as such, gradual degradation of the bending strength can be directly determined.

Explicit results for the bending response in a whole cyclic process up to fatigue failure are obtained and the fatigue characteristic curve is for the first time simulated directly between the curvature amplitude and the cycle number to failure.

First, explicit and accurate determination of the non-uniform stress distribution on beam cross-section is achieved with asymptotic softening effects. Second, degradation of the bending strength can be directly deduced cycle by cycle. Finally, the relationship between the bending moment and the curvature is calculated using new and efficient numerical algorithms, thus bypassing usual time-consuming calculations with finite element procedures. Numerical results are presented and in good agreement with experimental data.

DURING the last few years a programme of creep tests under general stress systems at high temperatures has been carried out at the N.P.L., using four metallic alloys which were chosen as being representative of basic groups of materials used in practice in machinery operating at high temperatures. This work, it was hoped, would fulfil, at least partly, the great need for experimental data in this field, as opposed to the comparative abundance of theoretical work available, and also enable a critical examination of the merits of this theoretical work to be made. The materials chosen in order of examination were a cast 0–17 per cent carbon steel, an aluminium alloy (R.R. 59), a magnesium alloy (containing 2 per cent aluminium), and a nickel‐chromium alloy (Nimonic 75). Each material was tested at temperatures lying within the normal working range of the material in question. Thus the 0–17 per cent carbon steel was tested at 350, 450 and 550 dcg. C. (662, 842 and 1,022 deg. F.), the aluminium alloy at 150 and 200 deg. C. (302 and 392 dcg. F.), the magnesium alloy at 20 and 50 deg. C. (68 and 122 dcg. F.), and the nickel‐chromium alloy at 550 and 650 dcg. C. (1,022 and 1,202 deg. F.).

This paper aims to present a direct analysis to demonstrate why markedly different tensile and compressive behaviors of concretes could not be simulated with the Drucker–Prager yield criterion.

This study proposed an extended form of the latter for establishing a new elastoplasticity model with evolving yield strengths.

Explicit closed-form solutions to non-symmetric tensile and compressive responses of uniaxial specimens at finite strain are for the first time obtained from hardening to softening.

With such exact solutions, the yield strengths in tension and compression can be explicitly prescribed by uniaxial tensile and compressive stress-strain functions. Then, the latter two are further provided in explicit forms toward accurately simulating tensile and compressive behaviors. Numerical examples are supplied for meso-scale heterogeneous concrete (MSHC) and high-performance concrete (HPC), etc. Model predictions are in good agreement with test data.