Nonlocal diffusion-elasticity based on nonlocal mass transfer and nonlocal elasticity and its application in shock-induced responses analysis

References

• S. L. Sobolev, “Rapid colloidal solidifications under local nonequilibrium diffusion conditions,” Phys. Lett. A, vol. 376, no. 47/48, pp. 3563–3566, 2012. DOI:10.1016/j.physleta.2012.10.031.
   Web of Science ®Google Scholar
• M. Asta et al., “Solidification microstructures and solid-state parallels: Recent developments, future directions,” Acta Mater., vol. 57, no. 4, pp. 941–971, 2009. DOI:10.1016/j.actamat.2008.10.020.
   Web of Science ®Google Scholar
• S. L. Sobolev, “On the transition from diffusion-limited to kinetic-limited regimes of alloy solidification,” Acta Mater., vol. 61, no. 20, pp. 7881–7888, 2013. DOI:10.1016/j.actamat.2013.09.027.
   Web of Science ®Google Scholar
• Y. Yang et al., “Atomistic simulations of nonequilibrium crystal-growth kinetics from alloy melts,” Phys. Rev. Lett., vol. 107, no.02, 2011.
   Google Scholar
• S. L. Sobolev, “Equations of transfer in nonlocal media,” Int. J. Heat Mass Transf., vol. 37, no. 14, pp. 2175–2182, 1994. DOI:10.1016/0017-9310(94)90319-0.
   Web of Science ®Google Scholar
• G. X. Wang and V. Prasad, “Microscale heat and mass transfer and non-equilibrium phase change in rapid solidification,” Mat. Sci. Eng. A Struct., vol. 292, no. 2, pp. 142–148, 2000. DOI:10.1016/S0921-5093(00)01003-0.
   Web of Science ®Google Scholar
• S. L. Sobolev, “Nonlocal diffusion models: Application to rapid solidification of binary mixtures,” Int. J. Heat Mass Transf, vol. 71, pp. 295–302, 2014. DOI:10.1016/j.ijheatmasstransfer.2013.12.048.
   Web of Science ®Google Scholar
• V. Etacheri, R. Marom, R. Elazari, G. Salitra, and D. Aurbach, “Challenges in the development of advanced Li-ion batteries: a review,” Energy Environ. Sci., vol. 4, no. 9, pp. 3243–3262, 2011. DOI:10.1039/c1ee01598b.
   Web of Science ®Google Scholar
• S. Goriparti, E. Miele, F. De Angelis, E. Di Fabrizio, R. P. Zaccaria, and C. Capiglia, “Review on recent progress of nanostructured anode materials for Li-ion batteries,” J. Power Sources, vol. 257, pp. 421–443, 2014. DOI:10.1016/j.jpowsour.2013.11.103.
   Web of Science ®Google Scholar
• Y. H. Liu and Y. F. Luo, “Search for an optimal rapid-charging pattern for Li-ion batteries using the Taguchi approach,” IEEE T. Ind. Electron., vol. 57, no. 12, pp. 3963–3971, 2016. DOI:10.1109/TIE.2009.2036020.
   Google Scholar
• S. Lee and J. Cho, “Critical requirements for rapid charging of rechargeable Al- and Li-Ion Batteries,” Angew. Chem. Int. Ed. Engl., vol. 54, no. 33, pp. 9452–9455, 2015. DOI:10.1002/anie.201504466.
   PubMed Web of Science ®Google Scholar
• F. Q. Yang, “Interaction between diffusion and chemical stresses,” Mat. Sci. Eng. A-Struct., vol. 409, no. 1-2, pp. 153–159, 2005. DOI:10.1016/j.msea.2005.05.117.
   Google Scholar
• S. Prussin, “Generation and distribution of dislocations by solute diffusion,” J. Appl. Phys., vol. 32, no. 10, pp. 1876, 1961. DOI:10.1063/1.1728256.
   Google Scholar
• A. Khanchehgardan, G. Rezazadeh, and R. Shabani, “Effect of mass diffusion on the damping ratio in micro-beam resonators,” Int. J. Solids Struct., vol. 51, no. 18, pp. 3147–3155, 2014. DOI:10.1016/j.ijsolstr.2014.05.009.
   Web of Science ®Google Scholar
• T. D. Le, D. Lasseux, X. P. Nguyen, G. Vignoles, N. Mano, and A. Kuhn, “Multi-scale modeling of diffusion and electrochemical reactions in porous micro-electrodes,” Chem. Eng. Sci., vol. 173, pp. 153–167, 2017. DOI:10.1016/j.ces.2017.07.039.
   Web of Science ®Google Scholar
• F. Q. Yang, “Diffusion-induced bending of viscoelastic beams,” Int. J. Mech. Sci., vol. 131, pp. 137–145, 2017. DOI:10.1016/j.ijmecsci.2017.06.055.
   Web of Science ®Google Scholar
• Y. H. Suo and S. P. Shen, “Dynamical theoretical model and variational principles for coupled temperature–diffusion–mechanics,” Acta Mech., vol. 223, no. 1, pp. 29–41, 2012. DOI:10.1007/s00707-011-0545-4.
   Web of Science ®Google Scholar
• Z. B. Kuang, “Energy and entropy equations in coupled nonequilibrium thermal mechanical diffusive chemical heterogeneous system,” Sci. Bull., vol. 60, no. 10, pp. 952–957, 2015. DOI:10.1007/s11434-015-0784-1.
   Web of Science ®Google Scholar
• Y. H. Suo and S. P. Shen, “Analytical solution for one-dimensional coupled non-Fick diffusion mechanics,” Arch. Appl. Mech., vol. 83, no. 3, pp. 397–411, 2013. DOI:10.1007/s00419-012-0687-4.
   Web of Science ®Google Scholar
• S. A. Hosseini, M. H. Abolbashari, and S. M. Hosseini, “Shock-induced molar concentration wave propagation and coupled non-Fick diffusion-elasticity analysis using an analytical method,” Acta Mech., vol. 225, no. 12, pp. 3591–3599, 2014. DOI:10.1007/s00707-014-1161-x.
   Web of Science ®Google Scholar
• S. M. Hosseini, J. Sladek, and V. Sladek, “Application of meshless local integral equations to two-dimensional analysis of coupled non-Fick diffusion-elasticity,” Eng. Anal. Bound. Elem., vol. 37, no. 3, pp. 603–615, 2013. DOI:10.1016/j.enganabound.2013.01.010.
   Web of Science ®Google Scholar
• S. M. Hosseini, “Shock-induced two dimensional coupled non-Fickian diffusion-elasticity analysis using meshless generalized finite difference (GFD) method,’ Eng Anal Bound Elem., vol. 61, pp. 232–240, 2015. DOI:10.1016/j.enganabound.2015.07.019.
   Web of Science ®Google Scholar
• A. C. Eringen, Nonlocal Continuum Field Theories, Springer-Verlag, New York, 2002.
   Google Scholar
• S. Govindjee and J. L. Sackman, “On the use of continuum mechanics to estimate the properties of nanotubes,” Solid State Commun., vol. 110, no. 4, pp. 227–230, 1999. DOI:10.1016/S0038-1098(98)00626-7.
   Web of Science ®Google Scholar
• A. C. Eringen, “On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves,” J. Appl. Phys., vol. 54, no. 9, pp. 4703–4710, 1983. DOI:10.1063/1.332803.
   Web of Science ®Google Scholar
• M. Z. Nejad, A. Hadi, and A. Rastgoo, “Buckling analysis of arbitrary two-directional functionally graded Euler-Bernoulli nano-beams based on nonlocal elasticity theory,” Int. J. Eng. Sci., vol. 103, pp. 1–10, 2016. DOI:10.1016/j.ijengsci.2016.03.001.
   Web of Science ®Google Scholar
• F. Ebrahimi and M. Karimiasl, “Nonlocal and surface effects on the buckling behavior of flexoelectric sandwich nanobeams,” Mech. Adv. Mater. Struct., vol. 25, no. 11, pp. 943–952, 2018. DOI:10.1080/15376494.2017.1329468.
   Web of Science ®Google Scholar
• F. Ebrahimi and M. R. Barati, “Scale-dependent effects on wave propagation in magnetically affected single/double-layered compositionally graded nanosize beams,” Wave Random Complex, vol. 28, no. 2, pp. 326–342, 2018. DOI:10.1080/17455030.2017.1346331.
   Google Scholar
• C. L. Li, H. L. Guo, and X. G. Tian, “Shock-induced thermal wave propagation and response analysis of a viscoelastic thin plate under transient heating loads,” Wave Random Complex, vol. 28, no. 2, pp. 270–286, 2018. DOI:10.1080/17455030.2017.1341670.
   Google Scholar
• H. Khetir, M. B. Bouiadjra, M. S. A. Houari, A. Tounsi, and S. R. Mahmoud, “A new nonlocal trigonometric shear deformation theory for thermal buckling analysis of embedded nanosize FG plates,” Struct. Eng. Mech., vol. 64, pp. 391–402, 2017.
   Web of Science ®Google Scholar
• A. Mouffoki, E. A. A. Bedia, M. S. A. Houari, and A. Tounsi, ‘Vibration analysis of nonlocal advanced nanobeams in hygro-thermal environment using a new two-unknown trigonometric shear deformation beam theory,” Smart Struct. Syst., vol. 20, pp. 369–383, 2017.
   Web of Science ®Google Scholar
• C. L. Li, H. L. Guo, and X. G. Tian, “A size-dependent generalized thermoelastic diffusion theory and its application,” J. Therm. Stress, vol. 40, no. 5, pp. 603–626, 2017. DOI:10.1080/01495739.2017.1300786.
   Web of Science ®Google Scholar
• C. L. Li, H. L. Guo, and X. G. Tian, “Size-dependent effect on thermo-electro mechanical responses of heated nano-sized piezoelectric plate,” Wave Random Complex, pp. 1–19, 2018. DOI:10.1080/17455030.2018.1450539.
   Google Scholar
• C. W. Lim, G. Zhang, and J. N. Reddy, “A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation,” J. Mech. Phys. Solids, vol. 78, pp. 298–313, 2015. DOI:10.1016/j.jmps.2015.02.001.
   Web of Science ®Google Scholar
• L. Li and Y. J. Hu, “Buckling analysis of size-dependent nonlinear beams based on a nonlocal strain gradient theory,” Int. J. Eng. Sci., vol. 97, pp. 84–94, 2015. DOI:10.1016/j.ijengsci.2015.08.013.
   Web of Science ®Google Scholar
• F. Ebrahimi and M. R. Barati, “Longitudinal varying elastic foundation effects on vibration behavior of axially graded nanobeams via nonlocal strain gradient elasticity theory,” Mech. Adv. Mater. Struct., vol. 25, no. 11, pp. 953–963, 2018. DOI:10.1080/15376494.2017.1329467.
   Web of Science ®Google Scholar
• B. Karami, D. Shahsavari, D, and M. Janghorban, “Wave propagation analysis in functionally graded (FG) nanoplates under in-plane magnetic field based on nonlocal strain gradient theory and four variable refined plate theory,” Mech. Adv. Mater. Struct., vol. 25, no. 12, pp. 1047–1057, 2018. DOI:10.1080/15376494.2017.1323143.
   Web of Science ®Google Scholar
• S. L. Sobolev, “Diffusion-stress coupling in liquid phase during rapid solidification of binary mixtures,” Phys. Lett. A, vol. 378, no. 5-6, pp. 475–479, 2014. DOI:10.1016/j.physleta.2013.12.031.
   Web of Science ®Google Scholar
• Y. J. Lu, P. L. Zhang, F. H. Wang, K. Zhang, and X. Zhao, “Reaction-diffusion-stress coupling model for Li-ion batteries: The role of surface effects on electrochemical performance,” Electrochim. Acta, vol. 274, pp. 359–369, 2018. DOI:10.1016/j.electacta.2018.04.105.
   Web of Science ®Google Scholar
• L. Brancik, “Programs for fast numerical inversion of Laplace Transforms in MATLAB Language Environment,” Proc. Seventh Prague Conference MATLAB, vol. 99, pp. 27–39, 1999.
   Google Scholar