• Computers and Concrete
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• v.22 no.2
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• pp.227-237
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• 2018

Today, the modeling of concrete as a material within finite element simulations is predominantly done through nonlinear material models of concrete. In current sophisticated computational systems, there are a number of complex concrete material models which are based on theory of plasticity, damage mechanics, linear or nonlinear fracture mechanics or combinations of those theories. These models often include very complex constitutive relations which are suitable for the modeling of practically any continuum mechanics tasks. However, the usability of these models is very often limited by their parameters, whose values must be defined for the proper realization of appropriate constitutive relations. Determination of the material parameter values is very complicated in most material models. This is mainly due to the non-physical nature of most parameters, and also the large number of them that are frequently involved. In such cases, the designer cannot make practical use of the models without having to employ the complex inverse parameter identification process. In continuum mechanics, however, there are also constitutive relations that require the definition of a relatively small number of parameters which are predominantly of a physical nature and which describe the behavior of concrete very well within a particular task. This paper presents an example of such constitutive relations which have the potential for implementation and application in finite element systems. Specifically, constitutive relations for modeling the plane stress state of concrete are presented and subsequently tested and evaluated in this paper. The relations are based on the incremental theory of elastic strain-hardening plasticity in which a non-associated flow rule is used. The calculation result for the case of concrete under uniaxial compression is compared with the experimental data for the purpose of the validation of the constitutive relations used.

• Smart Structures and Systems
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• v.22 no.1
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• pp.105-120
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• 2018

In this paper, the nonlinear free and forced vibration responses of sandwich nano-beams with three various functionally graded (FG) patterns of reinforced carbon nanotubes (CNTs) face-sheets are investigated. The sandwich nano-beam is resting on nonlinear Visco-elastic foundation and is subjected to thermal and electrical loads. The nonlinear governing equations of motion are derived for an Euler-Bernoulli beam based on Hamilton principle and von Karman nonlinear relation. To analyze nonlinear vibration, Galerkin's decomposition technique is employed to convert the governing partial differential equation (PDE) to a nonlinear ordinary differential equation (ODE). Furthermore, the Multiple Times Scale (MTS) method is employed to find approximate solution for the nonlinear time, frequency and forced responses of the sandwich nano-beam. Comparison between results of this paper and previous published paper shows that our numerical results are in good agreement with literature. In addition, the nonlinear frequency, force response and nonlinear damping time response is carefully studied. The influences of important parameters such as nonlocal parameter, volume fraction of the CNTs, different patterns of CNTs, length scale parameter, Visco-Pasternak foundation parameter, applied voltage, longitudinal magnetic field and temperature change are investigated on the various responses. One can conclude that frequency of FG-AV pattern is greater than other used patterns.

• Proceedings of the KSME Conference
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• 2001.06a
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• pp.698-703
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• 2001

This paper is concerned with the nonlinear hyperelastic problem fur the incompressible characteristics of the rubber. Tension sensor is a strain gage type load cell element for a fence intrusion detection system and consists of the sensing part and the rubber housing. The analysis includes an elastic analysis and a hyperelastic analysis of a tension sensor for the deformed shape and variation of the maximum strain on the sensing part with respect to the vertical load. Numerical results show that the hyperelastic model is stiffer and less deformed than the elastic model. Comparing with the experimental test data, we know the hyperelastic model is the better approximation than the elastic model.

• Steel and Composite Structures
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• v.13 no.2
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• pp.157-169
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• 2012

Shell structures are very interesting from the design point of view and these are well recognized in the scientific literature. In this paper the analysis of the buckling loads and stability paths of a sandwich conical shell with unsymmetrical faces under combined load based on the assumptions of moderately large deflections (geometrically nonlinear theory) is considered and elastic-plastic properties of the material of the faces are taken into considerations. External load is assumed to be two-parametrical one and it is assumed that the shell deforms into the plastic range before buckling. Constitutive relations in the analysis are those of the Nadai-Hencky deformation theory of plasticity and Prandtl-Reuss plastic flow theory with the H-M-H (Huber-Mises-Hencky) yield condition. The governing stability equations are obtained by strain energy approach and Ritz method is used to solve the equations with the help of analytical-numerical methods using computer.

• Structural Engineering and Mechanics
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• v.7 no.4
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• pp.345-360
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• 1999

A general framework for the nonlinear geometric analysis of elastic space trusses is presented. Both total Lagrangian and finite incremental formulations are derived from the three key ingredients of statics, kinematics and constitutive law. Particular features of the general methodology include the preservation of static-kinematic duality through the concept of fictitious forces and deformations, and an exact description for arbitrarily large displacements, albeit small strain, that can be specialized to any order of geometrical nonlinearity. As for the numerical algorithm, we consider specifically the finite incremental case and suggest the use of a conventional, simple and flexible arc-length based method. Numerical examples are presented to illustrate and validate the accuracy of the approach.

• Journal of Pharmaceutical Investigation
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• v.36 no.1
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• pp.31-38
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• 2006

Using a Rheometries Dynamic Analyzer (RDA II), the dynamic viscoelastic properties of a semi-solid ointment base (vaseline) in large amplitude oscillatory shear flow fields were measured over a temperature range of $25{\sim}45^{\circ}C$ and the linear viscoelastic behavior in small amplitude oscillatory shear flow fields was investigated over a wide range of angular frequencies. In this article, the nonlinear viscoelastic behavior was reported from the experimentally obtained data and the effect of temperature on this behavior was discussed in detail. In addition, the angular frequency and temperature dependencies of a linear viscoelastic behavior were explained. Finally, the applicability of a time-temperature superposition principle originally developed for polymeric materials was examined using a shift factor. Main results obtained from this study can be summarized as follows : (1) At very small strain amplitude region, vaseline shows a linear viscoelastic behavior independent of the imposed deformation magnitudes. Above a critical strain amplitude $({\gamma}_{0}=0.1{\sim}0.2%)$, however, vaseline exhibits a nonlinear viscoelastic behavior ; indicating that both the storage modulus and dynamic viscosity are sharply decreased with increasing deformation magnitude. (2) In large amplitude oscillatory shear flow fields, an elastic behavior (storage modulus) has a stronger strain amplitude dependence and begins to show a nonlinear behavior at a smaller strain amplitude region than does a viscous behavior (dynamic viscosity). (3) In small amplitude oscillatory shear flow fields, the storage modulus as well as the loss modulus are continuously increased as an increase in angular frequency and an elastic nature is always superior to a viscous behavior over a wide range of angular frequencies. (4) A time-temperature superposition principle can successfully be applicable to vaseline. This finding allows us to estimate the dynamic viscoelastic behavior of vaseline over an extraordinarily extended range (11 decades) of angular frequencies inaccessible from the experimentally measured range (4 decades).

• Journal of the Korean Society of Hazard Mitigation
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• v.9 no.2
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• pp.11-15
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• 2009

This paper is concerned with the elastic buckling of thin-walled arches that are subjected to uniform bending. Nonlinear strain-displacement relations with the initial curvature are substituted into the second variation of the total potential energy to obtain the energy equation including initial curvature effects. The approximation for initial curvature effects that the bending normal strain distribution is linear across the cross section is applied consistently in the derivation process. The closed form solution is obtained for flexural-torsional buckling of arches under uniform bending and, it is compared with the previous theoretical results.

• Aerospace Engineering and Technology
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• v.9 no.2
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• pp.73-79
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• 2010

In this study, the equivalent elastic modulus of flexible textile composites was predicted by nonlinear finite element analysis. The analysis was carried out considering the material nonlinearity of fiber tows and the geometrical nonlinearity during large deformation using commercial analysis software, ABAQUS. To account for the geometrical nonlinearity due to the large shear deformation of fiber tows, a user defined material algorithm was developed and inserted in ABAQUS. In results, nonlinear stress-strain curve for the flexible textile composites under uni-axial tension was predicted from which effective elastic modulus was obtained and compared to the test result. The effective elastic moduli were calculated for the various finite element models with different waviness ratio of fiber tow.

• Steel and Composite Structures
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• v.14 no.1
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• pp.1-20
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• 2013

This paper presents the formulation for a novel force-based 1-D compound-element that captures both material and second order P-${\Delta}$ nonlinearities in steel frames. At the nodal points, the element is attached to nonlinear rotational and a translational springs which represent the flexural and axial stiffness of the connections respectively. By decomposing the total strain in the material as well as the generalised displacements of the flexible connections to their elastic and inelastic components, a secant solution strategy based on a direct iterative scheme is introduced and the corresponding solution strategy is outlined. The strain and slope of the deformed element are assumed to be small; however the equilibrium equations are satisfied for the deformed element taking account of P-${\Delta}$ effects. The formulation accuracy and efficiency is verified by some numerical examples on the nonlinear static, cyclic and dynamic analysis of steel frames.

• Geomechanics and Engineering
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• v.8 no.3
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• pp.323-359
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• 2015

This paper presents an elasto-plastic model for determination of the ground response curve of a circular underwater tunnel excavated in elastic-strain softening rock mass compatible with a nonlinear Hoek-Brown yield criterion. The finite difference method (FDM) was used to propose a new solution to calculate pore water pressure, stress, and strain distributions on periphery of circular tunnels in axisymmetric and plain strain conditions. In the proposed solution, a modified non-radial flow pattern, for the hydraulic analysis, is utilized. To evaluate the effect of gravitational loads and variations of pore water pressure, the equations concerning different directions around the tunnel (crown, wall, and floor) are derived. Regarding the strain-softening behavior of the rock mass, the stepwise method is executed for the plastic zone in which parameters of strength, dilatancy, stresses, strains, and deformation are different from their elasto-plastic boundary values as compared to the tunnel boundary values. Besides, the analytical equations are developed for the elastic zone. The accuracy and application of the proposed method is demonstrated by a number of examples. The results present the effects of seepage body forces, gravitational loads and dilatancy angle on ground response curve appropriately.