Bree’s cylinder was used to show different material behaviors under constant mechanical and cyclic thermal gradient loadings. Bree showed different behaviors with the help of a diagram known by his name as Bree’s diagram. In this research, the problem was reconsidered without his simplified hypothesis. The used material model is NONLINEAR kinematic HARDENING. The two dimensional problem and the Poisson’s effect were considered. In order to obtain the Bree’s diagram, return mapping algorithm was used. The results showed that the one dimensional model of Bree is conservative and the bi-dimensional Bree’s diagram does not correspond to the complete model.

A type of NONLINEARity in vibrational engineering systems emerges when the restoring force is a NONLINEAR function of displacement. The derivative of this function is known as stiffness. If the stiffness increases by increasing the value of displacement from the equilibrium position, then the system is known as HARDENING type oscillator and if the stiffness decreases by increasing the value of displacement, then the system is known as softening type oscillator. The restoring force as a NONLINEAR polynomial function of order three, can describe a wide variety of practical NONLINEAR situations by proper choosing of constant multipliers. In this paper, a spring-mass system is considered by the restoring force of the introduced type. Choosing suitable values for a, b and n, a HARDENING and softening type oscillators are constructed and related equations of motion are introduced as second order NONLINEAR differential equations. The equations are solved directly, using the Adomian’s decomposition method (ADM). In another approach, the equations are converted to a system of first order differential equations and then solved using the same method. Results show that the ADM gives accurate results in both approaches, beside it shows that converting the equation to a system of equations of lower order, tends to give more accurate solutions when ADM is applied.

The composition of several different materials is often used in structural components in order to optimize the responses of structures subjected to severe thermal and mechanical loads. Functionally graded materials (FGMs) are suitable to achieve this purpose in the case of pressure vessels. On the other hand these structures usually sustain cyclic loadings resulting in ratcheting and shakedown behavior. In this study the NONLINEAR kinematic HARDENING theories are used to evaluate the cyclic loading behavior of a thick walled FGM Cylinder under internal pressure. The power law volume fraction distribution of materials, geometry and mechanical load are assumed to be axisymmetric. The finite element method combined with a multi-layered approach is used to model the structure by ABAQUS software. The response of structure under cyclic loadings is considered. Fredrick & Armstrong NONLINEAR kinematic HARDENING theories based on different type of back stress numbers are used to predict the ratcheting and shakedown behavior of the structure. The effects of variation of materials distribution on cyclic behavior are also studied. The achieved results show that using functionally graded material leads to a more flexible design so that cyclic rupture can be improved by selecting a suitable material distribution profiles.

In this paper, the cyclic NONLINEAR behavior of a brace element has been modeled. A brace element is modeled as two elastic beam-column segments, which are connected to each other via a plastic hinge. The far ends of the element are hinged. By a suitable combination of the isotropic and kinematical HARDENING rules of plasticity, the NONLINEAR axial force-displacement relation for a beam element has been derived. So, the strain HARDENING, strain softening, tangential modulus of elasticity and Bauschinger effects are taken into account. This model shows good agreement with experimental results that have been reported in other research works.

In this paper, a corotational constitutive model for rigid plastic isotropic and kinematic HARDENING materials obeying von Mises yield criterion is introduced. This constitutive model relates the corotational rate of the back stress tensor to the corotational rate of the logarithmic strain tensor. It is illustrated that use of Jaumann and Zaremba corotational rates in the constitutive model yields the same results for a given problem. Applying the proposed constitutive model to the simple shear problem, the effects of NONLINEAR isotropic and kinematic HARDENINGs on the stress components are studied.

Transient thermal field in laser surface HARDENING treatment of medium carbon steel was analyzed by employing both three-dimensional analytical model and finite element model. In finite element model the laser beam was considered as a moving plane heat flux to establish the temperature rise distribution in the work-piece, while in analytical model laser beam was considered as an internal heat source. The numerical results were compared with the analytical results. In laser heat treatment of steel some methods are used to produce a wider and nearly uniform average irradiance profile. It may be achieved by rotating the beam optically, thereby producing an overlapping spiral track, or by dithering the beam (rocking the lens or mirror) perpendicular to the track, thus producing a zigzag pattern. In this paper, these models are used to cover the two mentioned patterns for laser HARDENING with Gaussian distribution, and to compare the results with the hardened region of bimodal and uniform distribution. The results show that dithering beam and rotating beam are useful for obtaining a uniform heat intensity distribution, if the parameters of dithering beam or rotating beam are properly chosen with the aid of these models. The diffusion process being a time dependent phenomenon, an interaction time of 15 ms was taken as a basis to determine the hardened region.

In this research, the strain HARDENING behavior of dual phase steel containing 0.11% C 1.30% Mn is studied, using the tensile tests. The empirical relationshipa=k(e°+e)n , which has been suggested by several investigators for strain HARDENING behavior, is conformed. It is also shown that dual phase steels with up to 50% martensite have two stages of strain HARDENING and by increasing martensite over than 50% there is only one stage of this process. Finally it was observed that increasing martensite volume fraction results in decreasing strain HARDENING exponent (n) and increasing strain HARDENING coefficient (k).