The present work aims to investigate a penny-shaped crack problem in the interior of a homogeneous elastic material under axisymmetric torsion by a circular rigid inclusion embedded in the elastic medium. With the use of the Hankel integral transformation method, the mixed boundary value problem is reduced to a system of dual integral equations. The latter is converted into a regular system of Fredholm integral equations of the second kind which is then solved by quadrature rule. Numerical results for the displacement, stress and stress intensity factor are presented graphically in some particular cases of the problem.
{"title":"A mixed boundary value problem of a cracked elastic medium under torsion","authors":"B. Kebli, F. Madani","doi":"10.2298/tam200923010k","DOIUrl":"https://doi.org/10.2298/tam200923010k","url":null,"abstract":"The present work aims to investigate a penny-shaped crack problem in the interior of a homogeneous elastic material under axisymmetric torsion by a circular rigid inclusion embedded in the elastic medium. With the use of the Hankel integral transformation method, the mixed boundary value problem is reduced to a system of dual integral equations. The latter is converted into a regular system of Fredholm integral equations of the second kind which is then solved by quadrature rule. Numerical results for the displacement, stress and stress intensity factor are presented graphically in some particular cases of the problem.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":"65 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84439216","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
C. Reyes, L. Béjar, L. Pérez, C. Aguilar, C. J. Carranza, E. L. Carranza, I. Alfonso
The effect of space holder particles (SHP) fractal distribution on the porosity of aluminum foams manufactured by infiltration is studied in the present work. Physical models were used to estimate aluminum foam porosity, simulating SHP distribution for bimodal mixtures with different particle sizes and relative quantities. Results of these models were compared with mathematical models and the results obtained for experimental aluminum foams manufactured using a 332 Al-alloy base material and NaCl grains as SHP. Experimental foam structural characterization was carried out using image analysis to obtain porosity, density, wall thickness and fractal dimension, while mechanical characterization focused on the compressive Young modulus. Results show that it was possible to manufacture foams with different fractal porosities and a wide variety of unit cells, reaching a maximum of ? 68%. It was also found that pore wall thicknesses significantly decreased with the increase in the fine particles fraction. Besides, all the models presented a peak with a maximum porosity, whose values increased and shifted to low fine particles fraction with the increase in the sizes ratio. This behavior was also observed for the experimental foams with low particle size ratio. Nevertheless, for higher size ratios porosity showed an irregular behavior attributed to the mixing process.
{"title":"Use of the fractal dimension for porosity modification in aluminum foams manufactured using space holder particles","authors":"C. Reyes, L. Béjar, L. Pérez, C. Aguilar, C. J. Carranza, E. L. Carranza, I. Alfonso","doi":"10.2298/TAM210129005R","DOIUrl":"https://doi.org/10.2298/TAM210129005R","url":null,"abstract":"The effect of space holder particles (SHP) fractal distribution on the porosity of aluminum foams manufactured by infiltration is studied in the present work. Physical models were used to estimate aluminum foam porosity, simulating SHP distribution for bimodal mixtures with different particle sizes and relative quantities. Results of these models were compared with mathematical models and the results obtained for experimental aluminum foams manufactured using a 332 Al-alloy base material and NaCl grains as SHP. Experimental foam structural characterization was carried out using image analysis to obtain porosity, density, wall thickness and fractal dimension, while mechanical characterization focused on the compressive Young modulus. Results show that it was possible to manufacture foams with different fractal porosities and a wide variety of unit cells, reaching a maximum of ? 68%. It was also found that pore wall thicknesses significantly decreased with the increase in the fine particles fraction. Besides, all the models presented a peak with a maximum porosity, whose values increased and shifted to low fine particles fraction with the increase in the sizes ratio. This behavior was also observed for the experimental foams with low particle size ratio. Nevertheless, for higher size ratios porosity showed an irregular behavior attributed to the mixing process.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":"39 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85810572","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The paper describes the flow of a suspension which is a mixture of two phases: liquid and solid granules. The continuum model with microstructure is introduced, which involves two independent kinematic quantities: the velocity vector and the micro-rotation vector. The physical analogy is based on the movement of the suspension between two coaxial cylinders. The inner cylinder is stationary and the outer one rotates with constant angular velocity. This physical analogy enabled a mathematical model in a form of two coupled differential equations with variable coefficients. The aim of the paper is to present the numerical aspect of the solution for this complex mathematical model. It is assumed that the solid granules are identically oriented and that under the influence of the fluid they move translationally or rotate around the symmetry axis but the direction of their symmetry axes does not change. The solution was obtained by the ordinary finite difference method, and then the corresponding sets of points (nodes) were routed by interpolation graphics.
{"title":"Micropolar fluid between two coaxial cylinders (numerical approach)","authors":"Duško R. Salemović, A. Dedić, B. Jovanovic","doi":"10.2298/tam210823012s","DOIUrl":"https://doi.org/10.2298/tam210823012s","url":null,"abstract":"The paper describes the flow of a suspension which is a mixture of two phases: liquid and solid granules. The continuum model with microstructure is introduced, which involves two independent kinematic quantities: the velocity vector and the micro-rotation vector. The physical analogy is based on the movement of the suspension between two coaxial cylinders. The inner cylinder is stationary and the outer one rotates with constant angular velocity. This physical analogy enabled a mathematical model in a form of two coupled differential equations with variable coefficients. The aim of the paper is to present the numerical aspect of the solution for this complex mathematical model. It is assumed that the solid granules are identically oriented and that under the influence of the fluid they move translationally or rotate around the symmetry axis but the direction of their symmetry axes does not change. The solution was obtained by the ordinary finite difference method, and then the corresponding sets of points (nodes) were routed by interpolation graphics.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":"25 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83675754","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper deals with solution methods for singularly perturbed delay differential equations having delay on the convection and reaction terms. The considered problem exhibits an exponential boundary layer on the left or right side of the domain. The terms with the delay are treated using Taylor?s series approximation and the resulting singularly perturbed boundary value problem is solved using a specially designed exponentially finite difference method. The stability of the scheme is analysed and investigated using a comparison principle and solution bound. The formulated scheme converges uniformly with linear order of convergence. The theoretical findings are validated using three numerical test examples.
{"title":"Fitted numerical scheme for singularly perturbed convection-diffusion reaction problems involving delays","authors":"M. Woldaregay, W. Aniley, G. Duressa","doi":"10.2298/tam201208006w","DOIUrl":"https://doi.org/10.2298/tam201208006w","url":null,"abstract":"This paper deals with solution methods for singularly perturbed delay differential equations having delay on the convection and reaction terms. The considered problem exhibits an exponential boundary layer on the left or right side of the domain. The terms with the delay are treated using Taylor?s series approximation and the resulting singularly perturbed boundary value problem is solved using a specially designed exponentially finite difference method. The stability of the scheme is analysed and investigated using a comparison principle and solution bound. The formulated scheme converges uniformly with linear order of convergence. The theoretical findings are validated using three numerical test examples.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":"177 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79901838","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Minh‐Quan Thai, Sy-Tuan Nguyen, Thanh-Sang Nguyen, Phu-Son Mai
This paper aims to model the effect of different shapes of inclusions on the homogenized viscoelastic properties of composite materials made of a viscoelastic matrix and inclusion particles. The viscoelastic behavior of the matrix phase is modeled by the Generalized Maxwell rheology. The effective properties are firstly derived by combining the homogenization theory of elasticity and the correspondence principle. Then, the effective rheological properties in time space are explicitly derived without using the complex inverse Laplace?Carson transformation (LC). Closed-form solutions for the effective bulk and shear rheological viscoelastic properties, the relaxation and creep moduli as well as the Poisson ratio are obtained for the isotropic case with random orientation distribution and different shapes of inclusions: spherical, oblate and elongate inclusions. The developed approach is validated against the exact solutions obtained by the classical inverse LC method. It is observed that the homogenized viscoelastic moduli are highly sensitive to different shapes of inclusions.
{"title":"Analytical solutions for the effective viscoelastic properties of composite materials with different shapes of inclusions","authors":"Minh‐Quan Thai, Sy-Tuan Nguyen, Thanh-Sang Nguyen, Phu-Son Mai","doi":"10.2298/TAM200806004T","DOIUrl":"https://doi.org/10.2298/TAM200806004T","url":null,"abstract":"This paper aims to model the effect of different shapes of inclusions on the homogenized viscoelastic properties of composite materials made of a viscoelastic matrix and inclusion particles. The viscoelastic behavior of the matrix phase is modeled by the Generalized Maxwell rheology. The effective properties are firstly derived by combining the homogenization theory of elasticity and the correspondence principle. Then, the effective rheological properties in time space are explicitly derived without using the complex inverse Laplace?Carson transformation (LC). Closed-form solutions for the effective bulk and shear rheological viscoelastic properties, the relaxation and creep moduli as well as the Poisson ratio are obtained for the isotropic case with random orientation distribution and different shapes of inclusions: spherical, oblate and elongate inclusions. The developed approach is validated against the exact solutions obtained by the classical inverse LC method. It is observed that the homogenized viscoelastic moduli are highly sensitive to different shapes of inclusions.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":"107 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77410205","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In 1913 A. D. Bilimovich observed that rheonomic constraints which are linear and homogeneous in generalized velocities are ideal. As a typical example, he considered rheonomic nonholonomic deformation of the Euler equations whose scleronomic version is equivalent to the nonholonomic Suslov system. For the Bilimovich system, equations of motion are reduced to quadrature, which is discussed in rheonomic and scleronomic cases.
{"title":"On rheonomic nonholonomic deformations of the Euler equations proposed by Bilimovich","authors":"A. Borisov, A. Tsiganov","doi":"10.2298/TAM200120009B","DOIUrl":"https://doi.org/10.2298/TAM200120009B","url":null,"abstract":"In 1913 A. D. Bilimovich observed that rheonomic constraints which are linear and homogeneous in generalized velocities are ideal. As a typical example, he considered rheonomic nonholonomic deformation of the Euler equations whose scleronomic version is equivalent to the nonholonomic Suslov system. For the Bilimovich system, equations of motion are reduced to quadrature, which is discussed in rheonomic and scleronomic cases.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":"13 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2020-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83642041","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Fracture of welded joints has been an important research and industrial topic for a long time, having in mind the key role of welded joints in ensuring the safe operation and integrity of welded structures. This work contains an overview of application of micromechanical models to ductile fracture of welded joints. The main benefit of these models, in comparison with the classical fracture mechanics approach, is consideration of the local quantities (stress and strain) in prediction of damage development. The damage is quantified through the value of the damage parameter, which is typically related to the void nucleation, growth and coalescence for ductile fracture of metallic materials, i.e. the description of the material can be related to the actual material behaviour during fracture. Most of the presented studies, including those published by the present authors, are performed on steel as the base material, and the rest deal with aluminium alloys.
{"title":"An overview of application of micromechanical models in ductile fracture analysis of welded joints","authors":"M. Rakin, B. Medjo, N. Gubeljak, A. Sedmak","doi":"10.2298/tam200117004r","DOIUrl":"https://doi.org/10.2298/tam200117004r","url":null,"abstract":"Fracture of welded joints has been an important research and industrial topic for a long time, having in mind the key role of welded joints in ensuring the safe operation and integrity of welded structures. This work contains an overview of application of micromechanical models to ductile fracture of welded joints. The main benefit of these models, in comparison with the classical fracture mechanics approach, is consideration of the local quantities (stress and strain) in prediction of damage development. The damage is quantified through the value of the damage parameter, which is typically related to the void nucleation, growth and coalescence for ductile fracture of metallic materials, i.e. the description of the material can be related to the actual material behaviour during fracture. Most of the presented studies, including those published by the present authors, are performed on steel as the base material, and the rest deal with aluminium alloys.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":"56 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91253100","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
. Being a common phenomenon in failure mechanism, fretting fatigue has emerged as one of the major concerns in recent years both in research and industrial applications. In the present study, the effect of notch and fretting on bending fatigue has been examined by FEM analysis. Based on the available and validated FEM model, analyses have been carried out on single point fretting with a double notch and double point fretting with a single notch respectively. Along the predefined paths through the edge, thickness and notch, fatigue behavior and stress-strain distribution have been studied. It has been found that stress and strain distribution is uniformly spaced for constant fretting loads with a variable concentric load whereas variable fretting loads yield almost two times results. Stress and strain singularity is found for transverse loading when highly stressed. Peak stress was found on the stress distribution path for fretting action for the combined fretting and notch pres-ence. Fatigue life was influenced more drastically by variable fretting loads than variable concentric loadings only in case of tension. Dual action of fretting with notches was found more detrimental than the single action of double fretting/notching.
{"title":"Investigation of the combined effect of notch and fretting on bending fatigue","authors":"Quazi Md. Zobaer Shah, A. Kowser, M. Chowdhury","doi":"10.2298/tam191019002z","DOIUrl":"https://doi.org/10.2298/tam191019002z","url":null,"abstract":". Being a common phenomenon in failure mechanism, fretting fatigue has emerged as one of the major concerns in recent years both in research and industrial applications. In the present study, the effect of notch and fretting on bending fatigue has been examined by FEM analysis. Based on the available and validated FEM model, analyses have been carried out on single point fretting with a double notch and double point fretting with a single notch respectively. Along the predefined paths through the edge, thickness and notch, fatigue behavior and stress-strain distribution have been studied. It has been found that stress and strain distribution is uniformly spaced for constant fretting loads with a variable concentric load whereas variable fretting loads yield almost two times results. Stress and strain singularity is found for transverse loading when highly stressed. Peak stress was found on the stress distribution path for fretting action for the combined fretting and notch pres-ence. Fatigue life was influenced more drastically by variable fretting loads than variable concentric loadings only in case of tension. Dual action of fretting with notches was found more detrimental than the single action of double fretting/notching.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":"30 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82796320","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The classical wave equation is generalized within the framework of fractional calculus in order to account for the memory and non-local effects that might be material features. Both effects are included in the constitutive equation, while the equation of motion of the deformable body and strain are left unchanged. Memory effects in viscoelastic materials are modeled through the distributed-order fractional constitutive equation that generalizes all linear models having differentiation orders up to order one. The microlocal approach in analyzing singularity propagation is utilized in the case of viscoelastic material described by the fractional Zener model, as well as in the case of two non-local models: non-local Hookean and fractional Eringen.
{"title":"Hereditariness and non-locality in wave propagation modeling","authors":"D. Zorica","doi":"10.2298/tam200116005z","DOIUrl":"https://doi.org/10.2298/tam200116005z","url":null,"abstract":"The classical wave equation is generalized within the framework of fractional calculus in order to account for the memory and non-local effects that might be material features. Both effects are included in the constitutive equation, while the equation of motion of the deformable body and strain are left unchanged. Memory effects in viscoelastic materials are modeled through the distributed-order fractional constitutive equation that generalizes all linear models having differentiation orders up to order one. The microlocal approach in analyzing singularity propagation is utilized in the case of viscoelastic material described by the fractional Zener model, as well as in the case of two non-local models: non-local Hookean and fractional Eringen.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":"67 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83590059","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Milan Cajić, Danilo Karličić, Stepa Paunović, S. Adhikari
Research on phononic and acoustic materials and structures emerged in the recent decade as a result of switching from theoretical physics to applications in various engineering fields. Periodicity is the main characteristic of the phononic medium stemming from periodic material phases, geometry or the boundary condition with wave propagation properties analysed through frequency band structure. To obtain these characteristics, the generalized Bloch theorem is usually applied to obtain the dispersion relations of viscously damped resonant metamaterials. Here we develop a novel analytical approach to analyse the fractionally damped model of phononic crystals and acoustic metamaterials introduced through the fractional-order Kelvin–Voigt and Maxwell damping models. In the numerical study, the results obtained using the proposed models are compared against the elastic cases of the phononic crystal and locally resonant acoustic metamaterial, where significant differences in dispersion curves are identified. We show that the fractional-order Maxwell model is more suitable for describing the dissipation effect throughout the spectrum due to the possibility of fitting both, the order of fractional derivative and the damping parameter.
{"title":"A fractional calculus approach to metadamping in phononic crystals and acoustic metamaterials","authors":"Milan Cajić, Danilo Karličić, Stepa Paunović, S. Adhikari","doi":"10.2298/tam200117003c","DOIUrl":"https://doi.org/10.2298/tam200117003c","url":null,"abstract":"Research on phononic and acoustic materials and structures emerged in the recent decade as a result of switching from theoretical physics to applications in various engineering fields. Periodicity is the main characteristic of the phononic medium stemming from periodic material phases, geometry or the boundary condition with wave propagation properties analysed through frequency band structure. To obtain these characteristics, the generalized Bloch theorem is usually applied to obtain the dispersion relations of viscously damped resonant metamaterials. Here we develop a novel analytical approach to analyse the fractionally damped model of phononic crystals and acoustic metamaterials introduced through the fractional-order Kelvin–Voigt and Maxwell damping models. In the numerical study, the results obtained using the proposed models are compared against the elastic cases of the phononic crystal and locally resonant acoustic metamaterial, where significant differences in dispersion curves are identified. We show that the fractional-order Maxwell model is more suitable for describing the dissipation effect throughout the spectrum due to the possibility of fitting both, the order of fractional derivative and the damping parameter.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":"1 1","pages":"81-97"},"PeriodicalIF":0.7,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88386244","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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