• Advances in materials Research
• /
• v.13 no.2
• /
• pp.87-102
• /
• 2024

This paper is focused on the delamination analysis of a multilayered beam structure loaded in torsion under strain-path control. The beam under consideration has a rectangular cross-section. The layers of the beam are made of different viscoelastic materials which exhibit continuous inhomogeneity in longitudinal direction. Since the delamination is located inside the beam structure, the torsion moments in the two crack arms are obtained by modeling the beam as an internally static undetermined structure. The strain energy stored in the beam is analyzed in order to derive the strain energy release rate (SERR). Since the delamination is located inside the beam, the delamination has two tips. Thus, solutions of the SERR are obtained for both tips. The solutions are verified by analyzing the beam compliance. Delamination analysis with bending-torsion coupling is also performed. The solutions derived are timedependent due to two factors. First, the beam has viscoelastic behavior and, second, the angle of twist of the beam-free end induced by the external torsion moment changes with time according to a law that is fixed in advance.

• Coupled systems mechanics
• /
• v.13 no.2
• /
• pp.153-170
• /
• 2024

The problem considered in this theoretical paper is the delamination of a multilayered inhomogeneous beam structure that has viscoelastic behaviour under angle of twist, horizontal and vertical displacements which vary smoothly with time according to prescribed laws. The cross-section of the beam is a rectangle. The layers are made of different materials which are smoothly inhomogeneous along the length of the beam. The beam under consideration represents statically undetermined structure since it is clamped in its two ends. The problem of the strain energy release rate is solved. For this purpose, the strain energy stored in the beam structure is analyzed. In order to verify the solution obtained, the strain energy release rate is found also analyzing the time-dependent compliances of the beam under prescribed angle of twist and displacements. A parametric investigation is carried-out by applying the solution obtained. Special attention is paid to the effect of the parameters which control the variation of the angle of twist and the displacements with time on the strain energy release rate.

• Coupled systems mechanics
• /
• v.8 no.1
• /
• pp.1-17
• /
• 2019

The present paper deals with delamination fracture analyses of the multilayered functionally graded non-linear elastic Symmetric Split Beam (SSB) configurations. The material is functionally graded in both width and height directions in each layer. It is assumed that the material properties are distributed non-symmetrically with respect to the centroidal axes of the beam cross-section. Sine laws are used to describe the continuous variation of the material properties in the cross-sections of the layers. The delamination fracture is analyzed in terms of the strain energy release rate by considering the balance of the energy. A comparison with the J-integral is performed for verification. The solution derived is used for parametric analyses of the delamination fracture behavior of the multilayered functionally graded SSB in order to evaluate the effects of the sine gradients of the three material properties in the width and height directions of the layers and the location of the crack along the beam width on the strain energy release rate. The solution obtained is valid for two-dimensional functionally graded non-linear elastic SSB configurations which are made of an arbitrary number of lengthwise vertical layers. A delamination crack is located arbitrary between layers. Thus, the two crack arms have different widths. Besides, the layers have individual widths and material properties.

• Advances in materials Research
• /
• v.11 no.1
• /
• pp.41-57
• /
• 2022

This paper is focused on delamination analysis of a multilayered inhomogeneous viscoelastic beam subjected to linear creep under constant applied stress. The viscoelastic model that is used to treat the creep consists of consecutively connected units. Each unit consists of one spring and two dashpots. The number of units in the model is arbitrary. The modulus of elasticity of the spring in each unit changes with time. Besides, the modulii of elasticity and the coefficients of viscosity change continuously along the thickness, width and length in each layer since the material is continuously inhomogeneous in each layer of the beam. A time-dependent solution to the strain energy release rate for the delamination is derived. A time-dependent solution to the J-integral is derived too. A parametric analysis of the strain energy release rate is carried-out by applying the solution derived. The influence of various factors such as creep, material inhomogeneity, the change of the modulii of elasticity with time and the number of units in the viscoelastic model on the strain energy release rate are clarified.

• Geomechanics and Engineering
• /
• v.24 no.6
• /
• pp.545-557
• /
• 2021

Since the functionally graded materials (FGMs) are used extensively as thermal barriers in many of applications. Therefore, the current article focuses on studying and presenting dynamic responses of multilayer functionally graded (FG) deep beams placed in a thermal environment that is not addressed elsewhere. The material properties of each layer are proposed to be temperature-dependent and vary continuously through the height direction based on the Power-Law function. The deep layered beam is exposed to harmonic sinusoidal load and temperature rising. In the modelling of the multilayered FG deep beam, the two-dimensional (2D) plane stress continuum model is used. Equations of motion of deep composite beam with the associated boundary conditions are presented. In the frame of finite element method (FEM), the 2D twelve-node plane element is exploited to discretize the space domain through the length-thickness plane of the beam. In the solution of the dynamic problem, Newmark average acceleration method is used to solve the time domain incrementally. The developed procedure is verified and compared, and an excellent agreement is observed. In numerical examples, effects of graduation parameter, geometrical dimension and stacking sequence of layers on the time response of deep multilayer FG beams are investigated with temperature effects.

• Structural Engineering and Mechanics
• /
• v.63 no.4
• /
• pp.481-495
• /
• 2017

The present article examines the static response of multilayered magneto-electro-elastic (MEE) beam in thermal environment through finite element (FE) methods. On the basis of the minimum total potential energy principle and the coupled constitutive equations of MEE material, the FE equilibrium equations of cantilever MEE beam is derived. Maxwell's equations are considered to establish the relation between electric field and electric potential; magnetic field and magnetic potential. A simple condensation approach is employed to solve the global FE equilibrium equations. Further, numerical evaluations are made to examine the influence of different in-plane and through-thickness temperature distributions on the multiphysics response of MEE beam. A parametric study is performed to evaluate the effect of stacking sequence and different temperature profiles on the direct and derived quantities of MEE beam. It is believed that the results presented in this article serve as a benchmark for accurate design and analysis of the MEE smart structures in thermal applications.

• Interaction and multiscale mechanics
• /
• v.5 no.4
• /
• pp.369-383
• /
• 2012

In this paper, soil-structure interaction analysis has been presented for beams resting on multilayered geosynthetic-reinforced granular fill-soft soil system. The soft soil and geosynthetic reinforcements are idealized as nonlinear springs and elastic membranes, respectively. The governing differential equations are solved by finite difference technique and the results are presented in non-dimensional form. It is observed from the study that use of geosynthetic reinforcement is not very effective for maximum settlement reduction in case of very rigid beam. Similarly the reinforcements are not effective for shear force reduction if the granular fill has very high shear modulus value. However, multilayered reinforced system is very effective for bending moment and differential settlement reduction.

• Journal of the Korean Vacuum Society
• /
• v.12 no.S1
• /
• pp.7-9
• /
• 2003

Solid-state reactions in Ni/Si multilayered films (MLF) with an overall stoichiometry of $Ni_2Si$, NiSi and $NiSi_2$, induced by ion-beam mixing (IBM) and thermal annealing, were studied by using spectroscopic ellipsometry and magneto-optical spectroscopy as well as x-ray diffraction (XRD). The mixing was performed with Ar+ ions of an energy of 80 keV and a dose of $1.5 x\times10^{16}$ $Ar^+$/$\textrm{cm}^2$. It was shown that the IBM induces structural changes in the Ni/Si MLF, which cannot be detected by XRD but are confidently recognized by the optical method. A thermal annealing at 673 K of the Ni/Si MLF with an overall stoichiometry of NiSi and $NiSi_2$ causes formation of the first η -NiSi phase. The first trace for $NiSi_2$ phase on the background of NiSi one was detected by XRD after an annealing at 1073 K while, according to the optical results, $NiSi_2$ turns out be the dominant phase for the annealed Ni/Si MLF with an overall stoichiometry of $NiSi_2$.

• Coupled systems mechanics
• /
• v.12 no.4
• /
• pp.297-313
• /
• 2023

This paper deals with delamination analysis of non-linear viscoelastic multilayered beam subjected to bending in the plane of the layers. For this purpose, first, a non-linear viscoelastic model is presented. In order to take into account the non-linear viscoelastic behaviour, a non-linear spring and a non-linear dashpot are assembled in series with a linear spring connected in parallel to a linear dashpot. The behaviours of the non-linear spring and dashpot are described by applying non-linear stress-strain and stress-rate of strain relationships, respectively. The constitutive law of the model is derived. Due to the non-linear spring and dashpot, the constitutive law is non-linear. This law is used for describing the time-dependent mechanical behaviour of the beam under consideration. The material properties involved in the constitutive law vary along the beam length due to the continuous material inhomogeneity of the layers. Solution of the strain energy release rate for the delamination is obtained by analyzing the balance of the energy with considering of the non-linear viscoelastic behaviour. The strain energy release rate is found also by using the complementary strain energy for verification. A parametric study is carried-out by using the solution obtained. The solutions derived and the results obtained help to understand the time-dependent delamination of non-linear viscoelastic beams under loading in the plane of layers.

• Structural Engineering and Mechanics
• /
• v.42 no.5
• /
• pp.729-745
• /
• 2012

This study presents dynamic analysis of laminated beams traversed by moving loads using a multilayered beam element based on the first-order shear deformation theory. The present element consists of N layers with different thickness and material property, and has (3N + 7) degrees of freedom corresponding three axial, four transversal, and 3N rotational displacements. Delamination and interfacial slip are not allowed. Comparisons with analytical and/or numerical results available in literature for some illustrative examples are made. Numerical results for natural frequencies, deflections and stresses of laminated beams are given to explain the effect of load speed, lamina layup, and boundary conditions.