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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 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.

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 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..

This paper aims to develop a simple and efficient shell element for large strains hyper‐elastic analyses.

Based on the classical MITC4 shell element formulation a 3D shell element with finite strain kinematics is developed. The new quadrilateral shell element has five dof per node and two global dof to model the thickness stretching. The shell element is implemented for hyperelastic material models and the application of different hyperelastic constitutive relations is discussed.

The results obtained considering three of the hyperelastic material models available in the literature are quite different when the developed strains are relatively high; this indicates that, for analyzing actual engineering examples, experimental data should be used to decide on the most suitable constitutive relation.

The 3D version of the MITC4 element was developed.