Fracture Simulation of Nanostructured Porous Polymers Using a Boundary Element Method With Fractional Heat Conduction and Pyrolysis Coupling

Transverse strength enhancement of carbon fiber reinforced polymer composites by means of magnetically aligned carbon nanotubes

Recently the boundary element method has been developed swiftly. The boundary element method is an efficient and accurate means for analysis of two dimensional elastic crack problems. This paper is concerned with the evaluation and the prediction of the stress intensity factor(SIF) for the crack emanating from the circular hole using boundary element method-neural network. The SIF of the crack emanating from the hole was calculated by using boundary element method. Neural network is used to evaluate and to predict SIF from the results of boundary element method. The organized neural network system (structure of four processing element) was learned with the accuracy 99%. The learned neural network system could be evaluated and predicted with the accuracy of 83.3% and 71.4% (in cases of SIF and virtual SIF). Thus the proposed boundary element method-neural network is very useful to estimate the SIF.

This study investigated magneto-thermoelastic interactions in rotating viscoelastic nanorods under moving heat sources, advancing the modeling of nanoscale systems. A key innovation was the adoption of Klein–Gordon-type nonlocal elasticity theory, which incorporated internal length and time scales to capture small-scale interactions effectively. Additionally, a fractional heat conduction model using two-parameter tempered-Caputo derivatives introduced memory effects and nonlocality, ensuring finite thermal wave speeds and overcoming the limitations of the classical Fourier model. The inclusion of the Kelvin–Voigt viscoelastic framework accounted for energy dissipation, enhancing the model’s accuracy. By integrating rotation, viscoelasticity, magnetic forces, and fractional heat conduction, the study developed a comprehensive nonlinear model of nanorod behavior. Numerical simulations demonstrated that fractional-order heat conduction and nonlocal elasticity significantly influenced the thermal and mechanical responses, reducing discrepancies in heat propagation predictions. These findings showed that the fractional and tempering parameters controlled thermal dissipation rates and thermal wave propagation velocity, ensuring physically realistic thermal responses. The incorporation of nonlocal length scale and time scale parameters enabled accurate representation of size-dependent behaviors, including stiffness reduction and stress redistribution in nanorods. These parameters also influenced memory effects affecting wave propagation and relaxation in viscoelastic materials.

To discuss the fractional order heat conduction based on Youssef’s model, a new mathematical model of a thermoelastic annular cylinder with variable thermal conductivity will be constructed in this work. The Moore–Gibson– Thompson theorem of generalized thermoelasticity will be considered and the governing equations will be derived in dimensionless forms. The Laplace transform technique will be used for a one-dimensional thermoelastic, isotropic, and homogeneous annular cylinder in which the interior surrounded surface is thermally shocked and there is an axial traction-free environment, while the outer surrounded surface has neither heat increment nor cubical deformation. The numerical results will be computed for the Laplace transform inversions by using Tzou’s iteration approach. The distributions of the cubical deformation, invariant average stress, axial stress, and temperature increment will be represented in figures to analyze and discuss. The results show that the fractional-order and variable thermal conductivity parameters have significant effects on all the studied functions. The physical behaviour of the thermal conductivity is closely aligned with the classification of thermal conductivity into weak, normal, and strong categories, which is essential.

MODELLING A COMPOSITE/CONCRETE T-BEAM USING A FINITE ELEMENT TECHNIQUE

Determination of stress intensity factors is a critical task in fracture mechanics, numerical methods such as the finite element and boundary element methods which have successful applications in various fields of engineering problems, encounter mesh-related difficulties in dealing with fracture mechanics problems, to overcome these difficulties, a number of meshless methods have been developed in recent years. In this paper the element free Galerkin method based on the linear elastic fracture mechanics is used to model the jointed rock medium under different types of loads. The stress intensity factors are calculated on the tips of the joints by using J-integral or M-integral methods. The visibility criterion and a cubic spline weight function are applied to model rock fractures. In addition, the Lagrange multipliers method is employed to enforce the boundary conditions. To verify the computational capability and accuracy of the method, some examples of jointed samples in mode I and mixed mode are considered and the stress intensity factors are determined. The results obtained from the EFGM models together with J-integral or M-integral, in comparison with analytical and finite element methods, show good accuracy. This study denotes that the element free Galerkin method can be used as a proper tool in rock fracture mechanics. Key words: Element free Galerkin method, stress intensity factors, jointed rock mass, J-integral, M-integral.Determination of stress intensity factors is a critical task in fracture mechanics, numerical methods such as the finite element and boundary element methods which have successful applications in various fields of engineering problems, encounter mesh-related difficulties in dealing with fracture mechanics problems, to overcome these difficulties, a number of meshless methods have been developed in recent years. In this paper the element free Galerkin method based on the linear elastic fracture mechanics is used to model the jointed rock medium under different types of loads. The stress intensity factors are calculated on the tips of the joints by using J-integral or M-integral methods. The visibility criterion and a cubic spline weight function are applied to model rock fractures. In addition, the Lagrange multipliers method is employed to enforce the boundary conditions. To verify the computational capability and accuracy of the method, some examples of jointed samples in mode I and mixed mode are considered and the stress intensity factors are determined. The results obtained from the EFGM models together with J-integral or M-integral, in comparison with analytical and finite element methods, show good accuracy. This study denotes that the element free Galerkin method can be used as a proper tool in rock fracture mechanics. Key words: Element free Galerkin method, stress intensity factors, jointed rock mass, J-integral, M-integral.

PurposeThe purpose of this paper is to present special nine‐node quadrilateral elements to discretize the un‐cracked boundary and the inclined surface crack in a transversely isotropic cuboid under a uniform vertical traction along its top and bottom surfaces by a three‐dimensional (3D) boundary element method (BEM) formulation. The mixed‐mode stress intensity factors (SIFs), KI, KII and KIII, are calculated.Design/methodology/approachA 3D dual‐BEM or single‐domain BEM is employed to solve the fracture problems in a linear anisotropic elastic cuboid. The transversely isotropic plane has an arbitrary orientation, and the crack surface is along an inclined plane. The mixed 3D SIFs are evaluated by using the asymptotical relation between the SIFs and the relative crack opening displacements.FindingsNumerical results show clearly the influence of the material and crack orientations on the mixed‐mode SIFs. For comparison, the mode‐I SIF when a horizontal rectangular crack is embedded entirely within the cuboid is calculated also. It is observed that the SIF values along the crack front are larger when the crack is closer to the surface of the cuboid than those when the crack is far away from the surface.Research limitations/implicationsThe FORTRAN program developed is limited to regular surface cracks which can be discretized by the quadrilateral shape function; it is not very efficient and suitable for irregular crack shapes.Practical implicationsThe evaluation of the 3D mixed‐mode SIFs in the transversely isotropic material may have direct practical applications. The SIFs have been used in engineering design to obtain the safety factor of the elastic structures.Originality/valueThis is the first time that the special nine‐node quadrilateral shape function has been applied to the boundary containing the crack mouth. The numerical method developed can be applied to the SIF calculation in a finite transversely isotropic cuboid within an inclined surface crack. The computational approach and the results of SIFs are of great value for the modeling and design of anisotropic elastic structures.

In the present article, a thermo-viscoelastic model is developed to investigate fractional single-phase lag heat conduction and the associated transient thermal mechanical behavior of a cracked viscoelastic material under a thermal shock. To avoid the negative temperature distribution around cracks, which violates the second law of thermodynamics, the time-fractional single-phase lag heat conduction is introduced to analyze the transient temperature field around the cracks. The Fourier and Laplace transforms, coupled with the singular integral equations, are employed to solve the governing partial differential equations numerically. Both the results of temperature field and stress intensity factors (SIFs) show that the fractional single-phase lag heat conduction model is more accurate and reasonable compared to the conventional hyperbolic heat conduction. A significant difference in transient fracture behavior exists between viscoelastic and elastic materials. A sharp pulse of the SIFs at the early stage is observed and should be consider carefully to meet the requirement of increased application of viscoelastic composites under thermal loading.

Dynamic response of a cracked thermopiezoelectric strip under thermoelectric loading using fractional heat conduction

A comparative study of the boundary and finite element methods for the Helmholtz equation in two dimensions

In many structures, cracks may appear during manufacturing process or in service. Stress intensity factor is used in fracture mechanics to more accurately predict the stress state (stress intensity) near the tip of the crack caused by remote load or residual stresses. In this work a rectangular plate with central hole & two cracks emanating from his hole is analyzed for remote tensile loading. Stress Intensity Factor is determined for this configuration using finite element based software ANSYS. This value is compared with the one obtained by analytical method. Then hole as a stress reducing feature is studied. The effect of hole location, hole size on the stress intensity factor is studied. Feasibility of pressurized hole as a stress reducing feature is studied for the best hole location & size obtained earlier. Further variation in the pressure was done to study effect of pressurized hole. Fracture Mechanics is the field of mechanics concerned with the study of the propagation of cracks in materials. It uses methods of analytical solid mechanics to calculate the driving force on a crack and those of experimental solid mechanics to characterize the material resistance to fracture. Stress intensity factor, K, is used in fracture mechanics to more accurately predict the stress state (stress intensity) near the tip of the crack caused by remote load or residual stresses. It is theoretical construct applicable to a homogeneous elastic material and is useful for providing failure criteria for brittle materials. The stress intensity factor remains finite and provides a basis for determining the critical load. If the value of SIF is less than the toughness of the material, the structure is safe. If SIF value is more than the toughness of material, the structure fails. Typical Stress Intensity Factor Reduction Techniques used by earlier researchers are: Strip or patch repair method, Artificial crack closure by crack filling, Welding repair, Hole drilling. In this work, finite element analysis of a cracked plate is done. Initially a hole is used as a stress reducing feature. Then the effect of pressure applied in this hole is studied. II. LITERATURE REVIEW Miloud Souiyah, Abdulnaser Alshoaibi. et al (1) considered a rectangular plate with crack starting from a circular hole and double edge notched plate. Both geometries were in tensile loading and under mode-I conditions. In this paper a displacement extrapolation technique was employed particularly to predict the crack propagations direction and to calculate SIFs and validated with the relevant numerical and analytical results obtained by other researcher. Xiangqiao Yan (2) studied the stress intensity factors (SIFs) of cracks emanating from a rhombus hole in a rectangular plate subjected to internal pressure by means of the displacement discontinuity method with crack-tip elements (a boundary element method) proposed by the author. Moreover, an empirical formula of the SIFs of the crack problem was presented and examined. It was found that the empirical formula is very accurate for evaluating the SIFs of the crack problem. Junping Pu (3) studied a Boundary value problem of a plate with crack and defect such as the circular and/or elliptical holes. This kind of problem was suitable for solving by boundary element method with its higher precision. The sub-region method was used in this work. A center cracked plate subjected to remote tensile and shear loading was studied numerically. Levend Parnas and Omer G. Bilir (4) calculated Stress Intensity Factor by experimental procedures using strain gages. In this method, cracks were opened at the tip of crack starter slot on the standard compact tension test specimens by using Electrical Discharge Machining (EDM) and Wiring Discharge Machining (WDM). Strain gage data from the crack tip region were used to calculate stress intensity factors. But the values obtained were on lower side. This was partly due to unavoidable deformations in the adhesives used to fasten the strain gages to the specimen. This might be also due to the use of the relatively long strain gages, local yielding and three-dimensional effects and limited regions for strain gauge.

Critical study of existing solutions for a penny-shaped interface crack, comparing with a new boundary element solution allowing for frictionless contact

This paper is concerned with the stress intensity factors (SIFs) of a rectangular plate with symmetric edge cracks and edge half-circular-hole cracks in tension (see Figs. 1 and 2) by using the displacement discontinuity method with crack-tip elements (a boundary element method) proposed recently by the author. It is found that the boundary element method is simple, yet accurate for calculating the SIFs of complex crack problems not only in infinite plate [1] but also in finite plate [2]. Specifically, detail solutions of the SIFs of the two plane elastic crack problems are given, which can reveal the effect of H/W on the SIFs. By comparing the calculated SIFs of the symmetric edge half-circular-hole cracks (Fig. 2) with those of the symmetric edge cracks (Fig. 1); in addition, a shielding effect of the half-circular hole on the SIFs of the symmetric edge half-circular-hole cracks are discussed in detail.

Effect of heat addition on the electrogasdynamic flow and thermodynamic cycle efficiency

Transient thermal and physiological responses from air-conditioned room to semi-outdoor space in the tropics