Pub Date : 2019-09-01DOI: 10.1142/s2424913019990017
{"title":"Author index Volume 4 (2019)","authors":"","doi":"10.1142/s2424913019990017","DOIUrl":"https://doi.org/10.1142/s2424913019990017","url":null,"abstract":"","PeriodicalId":36070,"journal":{"name":"Journal of Micromechanics and Molecular Physics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49165527","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}
Pub Date : 2019-07-30DOI: 10.1142/S2424913019500012
O. Bachurina, R. Murzaev, D. Bachurin
A discrete breather (DB) is a spatially localized vibrational mode of large amplitude in a defect-free anharmonic lattice. Generally, zero-dimensional DB is considered to be localized in all [Formula: see text] directions of the [Formula: see text]-dimensional lattice. However, the question of existence of DBs localized in [Formula: see text]–[Formula: see text] directions and delocalized in other [Formula: see text] directions remains open. In the present paper, for the first time, the case of [Formula: see text] and [Formula: see text] is considered by constructing a two-dimensional (2D) DB in the fcc nickel lattice using molecular dynamics methods. In order to excite such DB, one of the delocalized vibrational modes of the triangular lattice was used (the (111) plane in fcc crystal is a triangular lattice). All simulations were carried out at zero temperature. The investigated 2D DB demonstrates hard-type nonlinearity, when its oscillation frequency increases with increasing amplitude. The oscillation frequencies of the DB are above the upper edge of the phonon spectrum for nickel, which is 10.3[Formula: see text]THz. The maximum DB lifetime is found to be 9.5[Formula: see text]ps. The obtained results expand our understanding of diversity of nonlinear spatially localized vibrational modes in nonlinear lattices.
{"title":"Molecular dynamics study of two-dimensional discrete breather in nickel","authors":"O. Bachurina, R. Murzaev, D. Bachurin","doi":"10.1142/S2424913019500012","DOIUrl":"https://doi.org/10.1142/S2424913019500012","url":null,"abstract":"A discrete breather (DB) is a spatially localized vibrational mode of large amplitude in a defect-free anharmonic lattice. Generally, zero-dimensional DB is considered to be localized in all [Formula: see text] directions of the [Formula: see text]-dimensional lattice. However, the question of existence of DBs localized in [Formula: see text]–[Formula: see text] directions and delocalized in other [Formula: see text] directions remains open. In the present paper, for the first time, the case of [Formula: see text] and [Formula: see text] is considered by constructing a two-dimensional (2D) DB in the fcc nickel lattice using molecular dynamics methods. In order to excite such DB, one of the delocalized vibrational modes of the triangular lattice was used (the (111) plane in fcc crystal is a triangular lattice). All simulations were carried out at zero temperature. The investigated 2D DB demonstrates hard-type nonlinearity, when its oscillation frequency increases with increasing amplitude. The oscillation frequencies of the DB are above the upper edge of the phonon spectrum for nickel, which is 10.3[Formula: see text]THz. The maximum DB lifetime is found to be 9.5[Formula: see text]ps. The obtained results expand our understanding of diversity of nonlinear spatially localized vibrational modes in nonlinear lattices.","PeriodicalId":36070,"journal":{"name":"Journal of Micromechanics and Molecular Physics","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1142/S2424913019500012","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41697001","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}
Pub Date : 2019-07-30DOI: 10.1142/S2424913019500036
Xiaoguang Guo, Chong-feng Chen, R. Kang, Zhuji Jin
The mechanical properties (hardness, elastic modulus) and subsurface damage of quartz glass at high temperature are studied by nanoindentation simulation based on molecular dynamics (MD). By heating the quartz crystal model to 3000[Formula: see text]K and annealing to 300[Formula: see text]K twice, the quartz glass model is prepared. According to the nanoindentation simulation results, the hardness of quartz glass decreases by 53.6% and the elastic modulus increases by 10.9% at 1500[Formula: see text]K compared to those at 300[Formula: see text]K. When the temperature rises from 300[Formula: see text]K to 1500[Formula: see text]K, the critical grinding depth of quartz glass increases from nanoscale to micron-scale. The investigation of subsurface damage shows that the damaged layer thickness decreases slightly with the increase of temperature. The damaged layer extends downward under the indenter at lower temperature and extends along the indenter at higher temperature.
{"title":"Study of mechanical properties and subsurface damage of quartz glass at high temperature based on MD simulation","authors":"Xiaoguang Guo, Chong-feng Chen, R. Kang, Zhuji Jin","doi":"10.1142/S2424913019500036","DOIUrl":"https://doi.org/10.1142/S2424913019500036","url":null,"abstract":"The mechanical properties (hardness, elastic modulus) and subsurface damage of quartz glass at high temperature are studied by nanoindentation simulation based on molecular dynamics (MD). By heating the quartz crystal model to 3000[Formula: see text]K and annealing to 300[Formula: see text]K twice, the quartz glass model is prepared. According to the nanoindentation simulation results, the hardness of quartz glass decreases by 53.6% and the elastic modulus increases by 10.9% at 1500[Formula: see text]K compared to those at 300[Formula: see text]K. When the temperature rises from 300[Formula: see text]K to 1500[Formula: see text]K, the critical grinding depth of quartz glass increases from nanoscale to micron-scale. The investigation of subsurface damage shows that the damaged layer thickness decreases slightly with the increase of temperature. The damaged layer extends downward under the indenter at lower temperature and extends along the indenter at higher temperature.","PeriodicalId":36070,"journal":{"name":"Journal of Micromechanics and Molecular Physics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1142/S2424913019500036","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44765519","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}
Pub Date : 2019-07-30DOI: 10.1142/S2424913019500024
I. Lobzenko
Properties of discrete breathers are discussed from two points of view: (I) the ab initio modeling in graphene and (II) classical molecular dynamics simulations in the ace-centered cubic (fcc) Ni. In the first (I) approach, the possibility of exciting breathers depends on the strain applied to the graphene sheet. The uniaxial strain leads to opening the gap in the phonon band and, therefore, the existence of breathers with frequencies within the gap. In the second (II) approach, the structure of fcc Ni supports breathers of another kind, which possess a hard nonlinearity type. It is shown that particular high frequency normal mode can be used to construct the breather by means of overlaying a spherically symmetrical function, the maximum of which coincides with the breather core. The approach of breathers excitation based on nonlinear normal modes is independent of the level of approximation. Even though breathers could be obtained both in classical and first-principles calculations, each case has advantages and shortcomings, that are compared in the present work.
{"title":"Discrete breathers modeling from first principles in graphene and in classical approximation in fcc Ni: Comparison","authors":"I. Lobzenko","doi":"10.1142/S2424913019500024","DOIUrl":"https://doi.org/10.1142/S2424913019500024","url":null,"abstract":"Properties of discrete breathers are discussed from two points of view: (I) the ab initio modeling in graphene and (II) classical molecular dynamics simulations in the ace-centered cubic (fcc) Ni. In the first (I) approach, the possibility of exciting breathers depends on the strain applied to the graphene sheet. The uniaxial strain leads to opening the gap in the phonon band and, therefore, the existence of breathers with frequencies within the gap. In the second (II) approach, the structure of fcc Ni supports breathers of another kind, which possess a hard nonlinearity type. It is shown that particular high frequency normal mode can be used to construct the breather by means of overlaying a spherically symmetrical function, the maximum of which coincides with the breather core. The approach of breathers excitation based on nonlinear normal modes is independent of the level of approximation. Even though breathers could be obtained both in classical and first-principles calculations, each case has advantages and shortcomings, that are compared in the present work.","PeriodicalId":36070,"journal":{"name":"Journal of Micromechanics and Molecular Physics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1142/S2424913019500024","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43569271","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}
Pub Date : 2019-07-01DOI: 10.1142/s2424913021420091
Junbo Wang, P. Yan, Leiting Dong, S. Atluri
In this study, analytical micromechanical models are developed for nanocomposites with both interface stretching and bending effects. First, the interior and exterior Eshelby tensors for a spherical nano-inclusion, with an interface defined by the Steigmann–Ogden (S–O) model, subjected to an arbitrary uniform eigenstrain are derived. Correspondingly, the stress/strain concentration tensors for a spherical nano-inhomogeneity subjected to arbitrary uniform far-field stress/strain loadings are also derived. Using the obtained concentration tensors, the effective bulk and shear moduli are derived by employing the dilute approximation and the Mori–Tanaka method, respectively, which can be used for both nano-composites and nano-porous materials. An equivalent interface curvature parameter reflecting the influence of the interface bending resistance is found, which can significantly simplify the complex expressions of the effective properties. In addition to size-dependency, the closed form expressions show that the effective bulk modulus is invariant to interface bending resistance parameters, in contrast to the effective shear modulus. We also put forward a characteristic interface curvature parameter, near which the effective shear modulus is affected significantly. Numerical results show that the effective shear moduli of nano-composites and nano-porous materials can be greatly improved by an appropriate surface modification. Finally, the derived effective modulus with the S–O interface model is provided in the supplemental MATLAB code, which can be easily executed, and used as a benchmark for semi-analytical solutions and numerical solutions in future studies.
{"title":"Eshelby tensors and overall properties of nano-composites considering both interface stretching and bending effects","authors":"Junbo Wang, P. Yan, Leiting Dong, S. Atluri","doi":"10.1142/s2424913021420091","DOIUrl":"https://doi.org/10.1142/s2424913021420091","url":null,"abstract":"In this study, analytical micromechanical models are developed for nanocomposites with both interface stretching and bending effects. First, the interior and exterior Eshelby tensors for a spherical nano-inclusion, with an interface defined by the Steigmann–Ogden (S–O) model, subjected to an arbitrary uniform eigenstrain are derived. Correspondingly, the stress/strain concentration tensors for a spherical nano-inhomogeneity subjected to arbitrary uniform far-field stress/strain loadings are also derived. Using the obtained concentration tensors, the effective bulk and shear moduli are derived by employing the dilute approximation and the Mori–Tanaka method, respectively, which can be used for both nano-composites and nano-porous materials. An equivalent interface curvature parameter reflecting the influence of the interface bending resistance is found, which can significantly simplify the complex expressions of the effective properties. In addition to size-dependency, the closed form expressions show that the effective bulk modulus is invariant to interface bending resistance parameters, in contrast to the effective shear modulus. We also put forward a characteristic interface curvature parameter, near which the effective shear modulus is affected significantly. Numerical results show that the effective shear moduli of nano-composites and nano-porous materials can be greatly improved by an appropriate surface modification. Finally, the derived effective modulus with the S–O interface model is provided in the supplemental MATLAB code, which can be easily executed, and used as a benchmark for semi-analytical solutions and numerical solutions in future studies.","PeriodicalId":36070,"journal":{"name":"Journal of Micromechanics and Molecular Physics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43216822","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}
Pub Date : 2019-04-08DOI: 10.1142/S2424913018300013
Duanfeng Han, Yiheng Zhang, Qing Wang, W. Lu, Bin Jia
Peridynamics theory is a nonlocal meshless method that replaces differential equations with spatial integral equations, and has shown good applicability and reliability in the analysis of discontinuities. Further, with characteristics of clear physical meaning and simple and reliable numerical calculation, the bond-based peridynamics method has been widely applied in the field. However, this method describes the interaction between material points simply using a single elastic “spring”, and thus leads to a fixed Poisson’s ratio, relatively low computational efficiency and other inherent problems. As such, the goal of this review paper is to provide a summary of the various methods of bond-based peridynamics modeling, particularly those that have overcome the limitations of the Poisson’s ratio, considered the shear deformation and modeling of two-dimensional thin plates for bending and three-dimensional anisotropic composites, as well as explored coupling with finite element methods. This review will determine the advantages and disadvantages of such methods and serve as a starting point for researchers in the development of peridynamics theory.
{"title":"The review of the bond-based peridynamics modeling","authors":"Duanfeng Han, Yiheng Zhang, Qing Wang, W. Lu, Bin Jia","doi":"10.1142/S2424913018300013","DOIUrl":"https://doi.org/10.1142/S2424913018300013","url":null,"abstract":"Peridynamics theory is a nonlocal meshless method that replaces differential equations with spatial integral equations, and has shown good applicability and reliability in the analysis of discontinuities. Further, with characteristics of clear physical meaning and simple and reliable numerical calculation, the bond-based peridynamics method has been widely applied in the field. However, this method describes the interaction between material points simply using a single elastic “spring”, and thus leads to a fixed Poisson’s ratio, relatively low computational efficiency and other inherent problems. As such, the goal of this review paper is to provide a summary of the various methods of bond-based peridynamics modeling, particularly those that have overcome the limitations of the Poisson’s ratio, considered the shear deformation and modeling of two-dimensional thin plates for bending and three-dimensional anisotropic composites, as well as explored coupling with finite element methods. This review will determine the advantages and disadvantages of such methods and serve as a starting point for researchers in the development of peridynamics theory.","PeriodicalId":36070,"journal":{"name":"Journal of Micromechanics and Molecular Physics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1142/S2424913018300013","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41992669","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}
Pub Date : 2019-04-08DOI: 10.1142/S2424913018500054
A. Chetverikov, S. V. Dmitriev, E. Korznikova, K. Sergeev
Behavior of dissipative solitons and crowdions in the triangular lattice of interacting particles is studied by means of numerical simulations. Active properties of particles are determined by non-linear friction which slows down the rapid particles and accelerates slower ones. Local interaction between particles is determined by the modified Morse potential with established cut-off radius. It is shown that the excitation of crowdions in active lattice is possible for some definite values of parameters. Borderlines between crowdions and solitons excitation in a space of parameters and initial conditions are determined.
{"title":"Dissipative solitons and crowdions in triangular lattice of active particles","authors":"A. Chetverikov, S. V. Dmitriev, E. Korznikova, K. Sergeev","doi":"10.1142/S2424913018500054","DOIUrl":"https://doi.org/10.1142/S2424913018500054","url":null,"abstract":"Behavior of dissipative solitons and crowdions in the triangular lattice of interacting particles is studied by means of numerical simulations. Active properties of particles are determined by non-linear friction which slows down the rapid particles and accelerates slower ones. Local interaction between particles is determined by the modified Morse potential with established cut-off radius. It is shown that the excitation of crowdions in active lattice is possible for some definite values of parameters. Borderlines between crowdions and solitons excitation in a space of parameters and initial conditions are determined.","PeriodicalId":36070,"journal":{"name":"Journal of Micromechanics and Molecular Physics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1142/S2424913018500054","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43319911","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}
Pub Date : 2019-04-08DOI: 10.1142/S2424913018500066
Ying Song, Haicheng Yu, Zhuang Kang
Ice-structure interaction is currently one of the hot topics in engineering fields and has not been addressed. Traditional numerical methods derived from classical continuum mechanics have difficulties in solving such discontinuous problems of ice fragmentations. In the present paper, a non-ordinary state-based peridynamics formulation is presented to simulate the behavior of the ice under impact loads applied by a rigid ball. Ice is assumed as a viscoelastic-plastic material and simulated by the modified Drucker–Prager plasticity model. The failure criterion of ice is defined based on fracture toughness. A continuous contact algorithm is adopted to detect the contact between the rigid ball and ice particles. It is shown that numerical results are in good agreement with experimental data from open-literatures, and the non-ordinary state-based peridynamics model can capture the detail fragmentation features of ice under impact loads.
{"title":"Numerical study on ice fragmentation by impact based on non-ordinary state-based peridynamics","authors":"Ying Song, Haicheng Yu, Zhuang Kang","doi":"10.1142/S2424913018500066","DOIUrl":"https://doi.org/10.1142/S2424913018500066","url":null,"abstract":"Ice-structure interaction is currently one of the hot topics in engineering fields and has not been addressed. Traditional numerical methods derived from classical continuum mechanics have difficulties in solving such discontinuous problems of ice fragmentations. In the present paper, a non-ordinary state-based peridynamics formulation is presented to simulate the behavior of the ice under impact loads applied by a rigid ball. Ice is assumed as a viscoelastic-plastic material and simulated by the modified Drucker–Prager plasticity model. The failure criterion of ice is defined based on fracture toughness. A continuous contact algorithm is adopted to detect the contact between the rigid ball and ice particles. It is shown that numerical results are in good agreement with experimental data from open-literatures, and the non-ordinary state-based peridynamics model can capture the detail fragmentation features of ice under impact loads.","PeriodicalId":36070,"journal":{"name":"Journal of Micromechanics and Molecular Physics","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1142/S2424913018500066","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"63853573","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}
Pub Date : 2018-09-01DOI: 10.1142/S242491301840009X
A. Ask, S. Forest, B. Appolaire, K. Ammar
This paper discusses a coupled mechanics–phase-field model that can predict microstructure evolution in metallic polycrystals and in particular evolution of lattice orientation due to either deformation or grain boundary migration. The modeling framework relies on the link between lattice curvature and geometrically necessary dislocations and connects a micropolar or Cosserat theory with an orientation phase-field model. Some focus is placed on the underlying theory and in particular the theory of dislocations within a continuum single crystal plasticity setting. The model is finally applied to the triple junction problem for which there is an analytic solution if the grain boundary energies are known. The attention is drawn on the evolution of skew–symmetric stresses inside the grain boundary during migration.
{"title":"Cosserat crystal plasticity with dislocation-driven grain boundary migration","authors":"A. Ask, S. Forest, B. Appolaire, K. Ammar","doi":"10.1142/S242491301840009X","DOIUrl":"https://doi.org/10.1142/S242491301840009X","url":null,"abstract":"This paper discusses a coupled mechanics–phase-field model that can predict microstructure evolution in metallic polycrystals and in particular evolution of lattice orientation due to either deformation or grain boundary migration. The modeling framework relies on the link between lattice curvature and geometrically necessary dislocations and connects a micropolar or Cosserat theory with an orientation phase-field model. Some focus is placed on the underlying theory and in particular the theory of dislocations within a continuum single crystal plasticity setting. The model is finally applied to the triple junction problem for which there is an analytic solution if the grain boundary energies are known. The attention is drawn on the evolution of skew–symmetric stresses inside the grain boundary during migration.","PeriodicalId":36070,"journal":{"name":"Journal of Micromechanics and Molecular Physics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1142/S242491301840009X","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49305929","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}
Pub Date : 2018-09-01DOI: 10.1142/S242491301840012X
M. Lazar, E. Agiasofitou
In this work, we derive the [Formula: see text]-, [Formula: see text]- and [Formula: see text]-integrals of body charges and point charges in electrostatics, and the [Formula: see text]-, [Formula: see text]- and [Formula: see text]-integrals of body forces and point forces in elasticity and we investigate their physical interpretation. Electrostatics is considered as field theory of an electrostatic scalar potential [Formula: see text] (scalar field theory) and elasticity as field theory of a displacement vector [Formula: see text] (vector field theory). One of the basic quantities appearing in the [Formula: see text]-, [Formula: see text]- and [Formula: see text]-integrals is the electrostatic Maxwell–Minkowski stress tensor in electrostatics and the Eshelby stress tensor in elasticity. Among others, it is shown that the [Formula: see text]-integral of body charges in electrostatics represents the electrostatic part of the Lorentz force, and the [Formula: see text]-integral of body forces in elasticity represents the Cherepanov force. The [Formula: see text]-integral between two-point sources (charges or forces) equals half the electrostatic interaction energy in electrostatics and half the elastic interaction energy in elasticity between these two-point sources. The [Formula: see text]-integral represents the configurational vector moment or torque between two body or point sources (charges or forces). Interesting mathematical and physical features are revealed through the connection of the [Formula: see text]-, [Formula: see text]- and [Formula: see text]-integrals with their corresponding infinitesimal generators in both theories. Several important outcomes arise from the comparison between the examined concepts in electrostatics and elasticity. Differences and similarities, that provide a deeper insight into the [Formula: see text]-, [Formula: see text]- and [Formula: see text]-integrals and the related quantities to them, are pointed out and discussed. The presented results show that the [Formula: see text]-, [Formula: see text]- and [Formula: see text]-integrals are fundamental concepts which can be applied in any field theory.
{"title":"The J-, M- and L-integrals of body charges and body forces: Maxwell meets Eshelby","authors":"M. Lazar, E. Agiasofitou","doi":"10.1142/S242491301840012X","DOIUrl":"https://doi.org/10.1142/S242491301840012X","url":null,"abstract":"In this work, we derive the [Formula: see text]-, [Formula: see text]- and [Formula: see text]-integrals of body charges and point charges in electrostatics, and the [Formula: see text]-, [Formula: see text]- and [Formula: see text]-integrals of body forces and point forces in elasticity and we investigate their physical interpretation. Electrostatics is considered as field theory of an electrostatic scalar potential [Formula: see text] (scalar field theory) and elasticity as field theory of a displacement vector [Formula: see text] (vector field theory). One of the basic quantities appearing in the [Formula: see text]-, [Formula: see text]- and [Formula: see text]-integrals is the electrostatic Maxwell–Minkowski stress tensor in electrostatics and the Eshelby stress tensor in elasticity. Among others, it is shown that the [Formula: see text]-integral of body charges in electrostatics represents the electrostatic part of the Lorentz force, and the [Formula: see text]-integral of body forces in elasticity represents the Cherepanov force. The [Formula: see text]-integral between two-point sources (charges or forces) equals half the electrostatic interaction energy in electrostatics and half the elastic interaction energy in elasticity between these two-point sources. The [Formula: see text]-integral represents the configurational vector moment or torque between two body or point sources (charges or forces). Interesting mathematical and physical features are revealed through the connection of the [Formula: see text]-, [Formula: see text]- and [Formula: see text]-integrals with their corresponding infinitesimal generators in both theories. Several important outcomes arise from the comparison between the examined concepts in electrostatics and elasticity. Differences and similarities, that provide a deeper insight into the [Formula: see text]-, [Formula: see text]- and [Formula: see text]-integrals and the related quantities to them, are pointed out and discussed. The presented results show that the [Formula: see text]-, [Formula: see text]- and [Formula: see text]-integrals are fundamental concepts which can be applied in any field theory.","PeriodicalId":36070,"journal":{"name":"Journal of Micromechanics and Molecular Physics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1142/S242491301840012X","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48588897","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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