• Steel and Composite Structures
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• v.27 no.2
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• pp.201-216
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• 2018

In this paper, three-dimensional (3D) elasticity theory in conjunction with nonlocal strain gradient theory (NSGT) is developed for mechanical analysis of anisotropic nanoparticles. The present model incorporates two scale coefficients to examine the mechanical characteristics much accurately. All the elastic constants are considered and assumed to be the functions of (r, ${\theta}$, ${\varphi}$), so all kind of anisotropic structures can be modeled. Moreover, all types of functionally graded spherical structures can be investigated. To justify our model, our results for the radial vibration of spherical nanoparticles are compared with experimental results available in the literature and great agreement is achieved. Next, several examples of the radial vibration and wave propagation in spherical nanoparticles including nonlocal strain gradient parameters are presented for more than 10 different anisotropic nanoparticles. From the best knowledge of authors, it is the first time that 3D elasticity theory and NSGT are used together with no approximation to derive the governing equations in the spherical coordinate. Moreover, up to now, the NSGT has not been used for spherical anisotropic nanoparticles. It is also the first time that all the 36 elastic constants as functions of (r, ${\theta}$, ${\varphi}$) are considered for anisotropic and functionally graded nanostructures including size effects. According to the lack of any common approximations in the displacement field or in elastic constant, present theory can be assumed as a benchmark for future works.

• 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.

• Elastomers and Composites
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• v.42 no.3
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• pp.168-176
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• 2007

When the rubber vulcanizates reinforced with carbon black or silica are subjected to cyclic loading from its virgin state, the stress required on reloading is less than that on the initial loading. This stress softening phenomenon is referred to as the Mullins effect. The strain energy function of rubber vulcanizates was investigated using theory of pseudo-elasticity incorporated damage parameter that Ogden and Roxburgh have proposed to describe the damage-induced stress softening effect in rubber-like solids. The quasi-static cyclic loading test was performed using the NR-SBR vulcanizates reinforced with carbon black, and then the effect of a damage parameter to stress-strain curve in reloading and subsequent reloading paths was studied. The strain energy function of the rubber vulcanizates with a different filler content was also evaluated.

• Smart Structures and Systems
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• v.30 no.3
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• pp.221-237
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• 2022

This paper is concerned with nonlinear modeling and efficient numerical simulation of electrostrictive materials and structures. Two types of such materials are considered: relaxor ferroelectric ceramics and electrostrictive polymers. For ceramics, a geometrically linear formulation is developed, whereas polymers are studied in a geometrically nonlinear regime. In the paper, we focus on constitutive modeling first. For the reversible constitutive response under consideration, we introduce the augmented Helmholtz free energy, which is composed of a purely elastic part, a dielectric part and an augmentation term. For the elastic part, we involve an additive decomposition of the strain tensor into an elastic strain and an electrostrictive eigenstrain, which depends on the polarization of the material. In the geometrically nonlinear case, a corresponding multiplicative decomposition of the deformation gradient tensor replaces the additive strain decomposition used in the geometrically linear formulation. For the dielectric part, we first introduce the internal energy, to which a Legendre transformation is applied to compute the free energy. The augmentation term accounts for the contribution from vacuum to the energy. In our formulation, the augmented free energy depends not only on the strain and the electric field, but also on the polarization and an internal polarization; the latter two are internal variables. With the constitutive framework established, a Finite Element implementation is briefly discussed. We use high-order elements for the discretization of the independent variables, which include also the internal variables and, in case the material is assumed incompressible, the hydrostatic pressure, which is introduced as a Lagrange multiplier. The elements are implemented in the open source code Netgen/NGSolve. Finally, example problems are solved for both, relaxor ferroelectric ceramics and electrostrictive polymers. We focus on thin plate-type structures to show the efficiency of the numerical scheme and its applicability to thin electrostrictive structures.

• Journal of the Korean GEO-environmental Society
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• v.12 no.5
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• pp.59-63
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• 2011

Ground dynamic parameter such as shear elastic modulus and damping ratio is a very important variable in design of ground-structure with repeated load and dynamic load. Shear elastic modulus and damping ratio on small strain below linear limit strain is constant regardless of strain. Shear elastic modulus as the maximum shear elastic modulus and damping ratio as the minimum damping ratio were considered. As a lot of experiment related to the maximum shear elastic modulus, which is in dynamic deformation characteristics, have been conducted, many factors including voiding ratio, over consolidation ratio(OCR), confining pressure, geology time, PI, and the number of load cycle affect to dynamic soil characteristic. However, the research of ground dynamic characteristic improved with grout is absent such as underground continuous wall construction, deep mixing method, umbrella arch method. In order to investigate the dynamic soil characteristics improved with grout, in this study, resonant column tests were performed with changing water content(20%, 25%, 30%) and injection ratio of grout(5%, 10%, 15%), cure time(7th day, 28th day) As a result, shear elastic modulus and damping ratio, which are ground dynamic parameter, are affected by the injection ratio of milk grout, cure time and water content.

• KIEE International Transactions on Electrophysics and Applications
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• v.4C no.2
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• pp.51-54
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• 2004

In this paper, the thermal and mechanical properties of elastic epoxy for the application of high voltage products were investigated. Glass transition temperature (Tg) of elastic epoxies cannot be found from room temperature to 20$0^{\circ}C$ by DSC (Differential Scanning Calorimetry). Weight reduction occurred at 285$^{\circ}C$ and 451$^{\circ}C$ according to a thermogravimeter. The first temperature was affected by addictives and the second by epoxies characteristic. Maximum tensile strain showed 28.3kgf/$\textrm{cm}^2$/$\textrm{cm}^2$ at 20% of mechanical stress in addictives 35 (phr). The SEM (Scanning electron microscope) micrograph of the fracture surface observed void and tearing of elastic epoxy at addictives 35 (phr). On the other side, the SEM micrograph of the rigid epoxy showed a broken trace.

• Journal of the Earthquake Engineering Society of Korea
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• v.3 no.4
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• pp.95-100
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• 1999

Dynamic measurements are used rather sparingly to determine the elastic modull of rock cores and modulus values are not much utilized in design practice. The reason seems to result from the general perception that values obtained by dynamic measurement are much higher (about 10 times) than those determined statically. This paper presents results from dynamic and static tests on rock cores. The findings are: 1) elastic modull can be consistently determined by laboratory seismic testing. 2) nonlinear deformation characteristics of rock cores was tentatively proposed with variation in elastic modulus with strain.

• Structural Engineering and Mechanics
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• v.60 no.4
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• pp.615-631
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• 2016

In this paper, an analytical method for the Post-buckling response of cylindrical shells with spiral stiffeners surrounded by an elastic medium subjected to external pressure is presented. The proposed model is based on two parameters elastic foundation Winkler and Pasternak. The material properties of the shell and stiffeners are assumed to be continuously graded in the thickness direction. According to the Von Karman nonlinear equations and the classical plate theory of shells, strain-displacement relations are obtained. The smeared stiffeners technique and Galerkin method is used to solve the nonlinear problem. To valid the formulations, comparisons are made with the available solutions for nonlinear static buckling of stiffened homogeneous and un-stiffened FGM cylindrical shells. The obtained results show the elastic foundation Winkler on the response of buckling is more effective than the elastic foundation Pasternak. Also the ceramic shells buckling strength higher than the metal shells and minimum critical buckling load is occurred, when both of the stiffeners have angle of thirty degrees.

• Steel and Composite Structures
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• v.27 no.2
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• pp.177-184
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• 2018

This study contributes to evaluate multiphase topology optimization design of plate-like structures on elastic foundations by using classic plate theory. Multi-material optimal topology and shape are produced as an alternative to provide reasonable material assignments based on stress distributions. Multi-material topology optimization problem is solved through an alternative active-phase algorithm with Gauss-Seidel version as an optimization model of optimality criteria. Stiffness and adjoint sensitivity formulations linked to thin plate potential strain energy are derived in terms of multiphase design variables and Winkler-Pasternak parameters considering elastic foundation to apply to the current topology optimization. Numerical examples verify efficiency and diversity of the present topology optimization method of elastic thin plates depending on multiple materials and Winkler-Pasternak parameters with the same amount of volume fraction and total structural volume.

• Structural Engineering and Mechanics
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• v.78 no.3
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• pp.281-296
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• 2021

This article analyzed the modulus degradation of concrete subjected to multi-level compressive cyclic loading. The evolution of secant elastic modulus is investigated based on measurements from top loading platen and LVDT in the middle part of concrete. The difference value of the two secant elastic moduli is reduced when close to failure and could be used as a fatigue failure precursor. The fatigue hardening is observed for concrete during cyclic loading. When the maximum stress is smaller the fatigue hardening is more obvious. The slight increase of maximum stress will lead to the "periodic hardening". The tangent elastic modulus shows a specific "bowknot" shape during cyclic loading, which can characterize the hysteresis of stress-strain and is influenced by the cyclic loading stresses. The deterioration of secant elastic modulus acts a similar role with respect to the P-wave speed during cyclic loading, can both characterize the degradation of the concrete properties.