Implicit non-ordinary state-based peridynamics model for linear piezoelectricity

References

• H. S. Kim, J.-H. Kim, and J. Kim, A review of piezoelectric energy harvesting based on vibration, Int. J. Precis. Eng. Manuf., vol. 12, no. 6, pp. 1129–1141, 2011. DOI: 10.1007/s12541-011-0151-3.
   Web of Science ®Google Scholar
• N. Sezer, and M. Koç, A comprehensive review on the state-of-the-art of piezoelectric energy harvesting, Nano Energy., vol. 80, pp. 105567, 2021. DOI: 10.1016/j.nanoen.2020.105567.
   Web of Science ®Google Scholar
• F. S. Vieira, and A. L. Araújo, Optimization and modelling methodologies for electro-viscoelastic sandwich design for noise reduction, Compos. Struct., vol. 235, pp. 111778, 2020. DOI: 10.1016/j.compstruct.2019.111778.
   Web of Science ®Google Scholar
• F. S. Vieira, and A. L. Araújo, Implementation of a pid controller in ansys[copyright] for noise reduction applications, Mech. Adv. Mater. Struct., vol. 28, no. 15, pp. 1579–1587, 2021. DOI: 10.1080/15376494.2019.1690721.
   Web of Science ®Google Scholar
• A. L. Araújo, and J. F. A. Madeira, Multiobjective optimization solutions for noise reduction in composite sandwich panels using active control, Compos. Struct., vol. 247, pp. 112440, 2020. DOI: 10.1016/j.compstruct.2020.112440.
   Web of Science ®Google Scholar
• A. L. Araújo, and J. F. A. Madeira, Optimal passive shunted damping configurations for noise reduction in sandwich panels, J. Vib. Control., vol. 26, no. 13–14, pp. 1110–1118, 2020. DOI: 10.1177/1077546320910542.
   Web of Science ®Google Scholar
• W. H. Duan, Q. Wang, and S. T. Quek, Applications of piezoelectric materials in structural health monitoring and repair: Selected research examples, Materials (Basel) , vol. 3, no. 12, pp. 5169–5194, 2010.
   PubMed Web of Science ®Google Scholar
• A. Zaszczyńska, A. Gradys, and P. Sajkiewicz, Progress in the applications of smart piezoelectric materials for medical devices, Polymers., vol. 12, no. 11, pp. 2754, 2020. DOI: 10.3390/polym12112754.
   PubMed Web of Science ®Google Scholar
• H. Allik, and T. J. R. Hughes, Finite element method for piezoelectric vibration, Int. J. Numer. Meth. Engng., vol. 2, no. 2, pp. 151–157, 1970. DOI: 10.1002/nme.1620020202.
   Google Scholar
• A. Benjeddou, Advances in piezoelectric finite element modeling of adaptive structural elements: a survey, Comput. Struct., vol. 76, no. 1–3, pp. 347–363, 2000. DOI: 10.1016/S0045-7949(99)00151-0.
   Web of Science ®Google Scholar
• M. Kuna, Finite element analyses of cracks in piezoelectric structures: a survey, Arch. Appl. Mech., vol. 76, no. 11–12, pp. 725–745, 2006. DOI: 10.1007/s00419-006-0059-z.
   Web of Science ®Google Scholar
• A. Abdollahi, and I. Arias, Phase-field modeling of crack propagation in piezoelectric and ferroelectric materials with different electromechanical crack conditions, J. Mech. Phys. Solids., vol. 60, no. 12, pp. 2100–2126, 2012. DOI: 10.1016/j.jmps.2012.06.014.
   Web of Science ®Google Scholar
• S. Mohanty, P. Y. Kumbhar, N. Swaminathan, and R. Annabattula, A phase-field model for crack growth in electro-mechanically coupled functionally graded piezo ceramics, Smart Mater. Struct., vol. 29, no. 4, pp. 045005, 2020. DOI: 10.1088/1361-665X/ab7145.
   Web of Science ®Google Scholar
• A. Sridhar, and M.-A. Keip, A phase-field model for anisotropic brittle fracturing of piezoelectric ceramics, Int. J. Fract., vol. 220, no. 2, pp. 221–242, 2019. DOI: 10.1007/s10704-019-00391-9.
   Web of Science ®Google Scholar
• Z. A. Wilson, M. J. Borden, and C. M. Landis, A phase-field model for fracture in piezoelectric ceramics, Int. J. Fract., vol. 183, no. 2, pp. 135–153, 2013. DOI: 10.1007/s10704-013-9881-9.
   Web of Science ®Google Scholar
• S. K. Singh, and I. V. Singh, Analysis of cracked functionally graded piezoelectric material using xiga, Eng. Fract. Mech., vol. 230, pp. 107015, 2020. DOI: 10.1016/j.engfracmech.2020.107015.
   Web of Science ®Google Scholar
• T. Q. Bui, Extended isogeometric dynamic and static fracture analysis for cracks in piezoelectric materials using nurbs, Comput Methods Appl Mech Engin., vol. 295, pp. 470–509, 2015. DOI: 10.1016/j.cma.2015.07.005.
   Web of Science ®Google Scholar
• T. Q. Bui, et al., Extended isogeometric analysis for dynamic fracture in multiphase piezoelectric/piezomagnetic composites, Mech. Mater., vol. 97, pp. 135–163, 2016. DOI: 10.1016/j.mechmat.2016.03.001.
   Web of Science ®Google Scholar
• G. R. Liu, K. Y. Dai, K. M. Lim, and Y. T. Gu, A point interpolation mesh free method for static and frequency analysis of two-dimensional piezoelectric structures, Comput Mech., vol. 29, no. 6, pp. 510–519, 2002. DOI: 10.1007/s00466-002-0360-9.
   Web of Science ®Google Scholar
• T. Q. Bui, and M. N. Nguyen, A moving kriging interpolation-based meshfree method for free vibration analysis of kirchhoff plates, Comput. Struct., vol. 89, no. 3–4, pp. 380–394, 2011. DOI: 10.1016/j.compstruc.2010.11.006.
   Web of Science ®Google Scholar
• R. R. Ohs, and N. R. Aluru, Meshless analysis of piezoelectric devices, Comput. Mech., vol. 27, no. 1, pp. 23–36, 2001. DOI: 10.1007/s004660000211.
   Web of Science ®Google Scholar
• T. Zhang, G. Wei, J. Ma, and H. Gao, Radial basis reproducing kernel particle method for piezoelectric materials, Eng. Anal. Boundary Elem., vol. 92, pp. 171–179, 2018. DOI: 10.1016/j.enganabound.2017.10.020.
   Web of Science ®Google Scholar
• S. A. Silling, Reformulation of elasticity theory for discontinuities and long-range forces, J. Mech. Phys. Solids., vol. 48, no. 1, pp. 175–209, 2000. DOI: 10.1016/S0022-5096(99)00029-0.
   Web of Science ®Google Scholar
• S. A. Silling, M. Epton, O. Weckner, J. Xu, and E. Askari, Peridynamic states and constitutive modeling, J. Elasticity., vol. 88, no. 2, pp. 151–184, 2007. DOI: 10.1007/s10659-007-9125-1.
   Web of Science ®Google Scholar
• E. Madenci, and E. Oterkus, Peridynamic theory. In: Peridynamic Theory and Its Applications, Springer, New York, NY, pp. 19–43, 2014.
   Google Scholar
• M. S. Breitenfeld, P. H. Geubelle, O. Weckner, and S. A. Silling, Non-ordinary state-based peridynamic analysis of stationary crack problems, Comput. Methods Appl. Mech. Engin., vol. 272, pp. 233–250, 2014. DOI: 10.1016/j.cma.2014.01.002.
   Web of Science ®Google Scholar
• C. T. Wu, and B. Ren, A stabilized non-ordinary state-based peridynamics for the nonlocal ductile material failure analysis in metal machining process, Comput. Methods Appl. Mech. Engin., vol. 291, pp. 197–215, 2015. DOI: 10.1016/j.cma.2015.03.003.
   Web of Science ®Google Scholar
• A. Yaghoobi, and M. G. Chorzepa, Higher-order approximation to suppress the zero-energy mode in non-ordinary state-based peridynamics, Comput. Struct., vol. 188, pp. 63–79, 2017. DOI: 10.1016/j.compstruc.2017.03.019.
   Web of Science ®Google Scholar
• P. Li, Z. M. Hao, and W. Q. Zhen, A stabilized non-ordinary state-based peridynamic model, Comput. Methods Appl. Mech. Engin., vol. 339, pp. 262–280, 2018. DOI: 10.1016/j.cma.2018.05.002.
   Web of Science ®Google Scholar
• S. R. Chowdhury, P. Roy, D. Roy, and, and J. N. Reddy, A modified peridynamics correspondence principle: Removal of zero-energy deformation and other implications, Comput. Methods Appl. Mech. Engin., vol. 346, pp. 530–549, 2019. DOI: 10.1016/j.cma.2018.11.025.
   Web of Science ®Google Scholar
• S. A. Silling, Stability of peridynamic correspondence material models and their particle discretizations, Comput. Methods Appl. Mech. Engin., vol. 322, pp. 42–57, 2017. DOI: 10.1016/j.cma.2017.03.043.
   Web of Science ®Google Scholar
• H. Chen, Bond-associated deformation gradients for peridynamic correspondence model, Mech. Res. Commun., vol. 90, pp. 34–41, 2018. DOI: 10.1016/j.mechrescom.2018.04.004.
   Web of Science ®Google Scholar
• H. Chen, and, and B. W. Spencer, Peridynamic bond-associated correspondence model: Stability and convergence properties, Int. J. Numer. Methods Eng., vol. 117, no. 6, pp. 713–727, 2019. DOI: 10.1002/nme.5973.
   Web of Science ®Google Scholar
• E. Madenci, M. Dorduncu, N. Phan, and X. Gu, Weak form of bond-associated non-ordinary state-based peridynamics free of zero energy modes with uniform or non-uniform discretization, Eng. Fract. Mech., vol. 218, pp. 106613, 2019. DOI: 10.1016/j.engfracmech.2019.106613.
   Web of Science ®Google Scholar
• D. Behera, P. Roy, and E. Madenci, Peridynamic correspondence model for finite elastic deformation and rupture in neo-hookean materials, Int. J. Non. Linear Mech., vol. 126, pp. 103564, 2020. DOI: 10.1016/j.ijnonlinmec.2020.103564.
   Web of Science ®Google Scholar
• D. Behera, P. Roy, and E. Madenci, Peridynamic modeling of bonded-lap joints with viscoelastic adhesives in the presence of finite deformation, Comput. Methods Appl. Mech. Engin., vol. 374, pp. 113584, 2021. DOI: 10.1016/j.cma.2020.113584.
   Web of Science ®Google Scholar
• P. Roy, D. Behera, and E. Madenci, Peridynamic simulation of finite elastic deformation and rupture in polymers, Eng. Fract. Mech., vol. 236, pp. 107226, 2020. DOI: 10.1016/j.engfracmech.2020.107226.
   Web of Science ®Google Scholar
• S. Yang, X. Gu, Q. Zhang, and X. Xia, Bond-associated non-ordinary state-based peridynamic model for multiple spalling simulation of concrete, Acta Mech. Sin., pp. 1–32, 2021. DOI: 10.1007/s10409-021-01055-5.
   Web of Science ®Google Scholar
• W. Gerstle, S. Silling, D. Read, V. Tewary, and R. Lehoucq, Peridynamic simulation of electromigration, Comput Mater Continua., vol. 8, no. 2, pp. 75–92, 2008.
   Web of Science ®Google Scholar
• F. Bobaru, and M. Duangpanya, The peridynamic formulation for transient heat conduction, Int. J. Heat Mass Transf., vol. 53, no. 19–20, pp. 4047–4059, 2010. DOI: 10.1016/j.ijheatmasstransfer.2010.05.024.
   Web of Science ®Google Scholar
• F. Bobaru, and M. Duangpanya, A peridynamic formulation for transient heat conduction in bodies with evolving discontinuities, Comput. Phys., vol. 231, no. 7, pp. 2764–2785, 2012. DOI: 10.1016/j.jcp.2011.12.017.
   Google Scholar
• B. Kilic, and E. Madenci, Peridynamic theory for thermomechanical analysis, IEEE Trans. Adv. Packag., vol. 33, no. 1, pp. 97–105, 2010. DOI: 10.1109/TADVP.2009.2029079.
   Google Scholar
• A. G. Agwai, A peridynamic approach for coupled fields., PhD Dissertation, Department of Aerospace and Mechanical Engineering, University of Arizona, 2011.
   Google Scholar
• S. Oterkus, E. Madenci, and A. Agwai, Peridynamic thermal diffusion, J. Comput. Phys., vol. 265, pp. 71–96, 2014. DOI: 10.1016/j.jcp.2014.01.027.
   Web of Science ®Google Scholar
• S. Oterkus, E. Madenci, and A. Agwai, Fully coupled peridynamic thermomechanics, J. Mech. Phys. Solids., vol. 64, pp. 1–23, 2014. DOI: 10.1016/j.jmps.2013.10.011.
   Web of Science ®Google Scholar
• Y. Gao, and S. Oterkus, Ordinary state-based peridynamic modelling for fully coupled thermoelastic problems, Continuum Mech. Thermodyn., vol. 31, no. 4, pp. 907–937, 2019. DOI: 10.1007/s00161-018-0691-1.
   Web of Science ®Google Scholar
• J. Amani, E. Oterkus, P. Areias, G. Zi, T. Nguyen-Thoi, and T. Rabczuk, A non-ordinary state-based peridynamics formulation for thermoplastic fracture, Int. J. Impact Eng., vol. 87, pp. 83–94, 2016. DOI: 10.1016/j.ijimpeng.2015.06.019.
   Web of Science ®Google Scholar
• S. Bazazzadeh, F. Mossaiby, and A. Shojaei, An adaptive thermo-mechanical peridynamic model for fracture analysis in ceramics, Eng. Fract. Mech., vol. 223, pp. 106708, 2020. DOI: 10.1016/j.engfracmech.2019.106708.
   Web of Science ®Google Scholar
• Y. Wang, X. Zhou, and M. Kou, An improved coupled thermo-mechanic bond-based peridynamic model for cracking behaviors in brittle solids subjected to thermal shocks, Eur. J. Mech. -A/Solids., vol. 73, pp. 282–305, 2019. DOI: 10.1016/j.euromechsol.2018.09.007.
   Google Scholar
• Z. Chen, and F. Bobaru, Peridynamic modeling of pitting corrosion damage, J. Mech. Phys. Solids., vol. 78, pp. 352–381, 2015. DOI: 10.1016/j.jmps.2015.02.015.
   Web of Science ®Google Scholar
• Z. Chen, S. Jafarzadeh, J. Zhao, and F. Bobaru, A coupled mechano-chemical peridynamic model for pit-to-crack transition in stress-corrosion cracking, J. Mech. Phys. Solids., vol. 146, pp. 104203, 2021. DOI: 10.1016/j.jmps.2020.104203.
   Web of Science ®Google Scholar
• H. Wang, E. Oterkus, and S. Oterkus, Predicting fracture evolution during lithiation process using peridynamics, Eng. Fract. Mech., vol. 192, pp. 176–191, 2018. DOI: 10.1016/j.engfracmech.2018.02.009.
   Web of Science ®Google Scholar
• E. Madenci, A. Barut, and M. Futch, Peridynamic differential operator and its applications, Comput. Methods Appl. Mech. Engin., vol. 304, pp. 408–451, 2016. DOI: 10.1016/j.cma.2016.02.028.
   Web of Science ®Google Scholar
• Y. Gao, and S. Oterkus, Nonlocal numerical simulation of low reynolds number laminar fluid motion by using peridynamic differential operator, Ocean Eng., vol. 179, pp. 135–158, 2019. DOI: 10.1016/j.oceaneng.2019.03.035.
   Web of Science ®Google Scholar
• Y. Gao, and S. Oterkus, Non-local modeling for fluid flow coupled with heat transfer by using peridynamic differential operator, Eng. Anal. Boundary Elem., vol. 105, pp. 104–121, 2019. DOI: 10.1016/j.enganabound.2019.04.007.
   Web of Science ®Google Scholar
• Y. Gao, and S. Oterkus, Fluid-elastic structure interaction simulation by using ordinary state-based peridynamics and peridynamic differential operator, Eng. Anal. Boundary Elem., vol. 121, pp. 126–142, 2020. DOI: 10.1016/j.enganabound.2020.09.012.
   Web of Science ®Google Scholar
• R. Wildman, and G. Gazonas, A dynamic electro-thermo-mechanical model of dielectric breakdown in solids using peridynamics, J. Mech. Mater. Struct., vol. 10, no. 5, pp. 613–630, 2015. DOI: 10.2140/jomms.2015.10.613.
   Web of Science ®Google Scholar
• N. Prakash, and G. D. Seidel, Electromechanical peridynamics modeling of piezoresistive response of carbon nanotube nanocomposites, Comput. Mater. Sci., vol. 113, pp. 154–170, 2016. DOI: 10.1016/j.commatsci.2015.11.008.
   Web of Science ®Google Scholar
• N. Prakash, and G. D. Seidel, Computational electromechanical peridynamics modeling of strain and damage sensing in nanocomposite bonded explosive materials (ncbx), Eng. Fract. Mech., vol. 177, pp. 180–202, 2017. DOI: 10.1016/j.engfracmech.2017.04.003.
   Web of Science ®Google Scholar
• P. Roy, and D. Roy, Peridynamics model for flexoelectricity and damage, Appl. Math. Modell., vol. 68, pp. 82–112, 2019. DOI: 10.1016/j.apm.2018.11.013.
   Web of Science ®Google Scholar
• V. Diana, and V. Carvelli, An electromechanical micropolar peridynamic model, Comput. Methods Appl. Mech. Engin., vol. 365, pp. 112998, 2020. DOI: 10.1016/j.cma.2020.112998.
   Web of Science ®Google Scholar
• H. Ren, X. Zhuang, E. Oterkus, H. Zhu, and T. Rabczuk, Nonlocal strong forms of thin plate, gradient elasticity, magneto-electro-elasticity and phase field fracture by nonlocal operator method. arXiv preprint arXiv:2103.08696, 2021.
   Google Scholar
• S. A. Silling, and, and R. B. Lehoucq, Peridynamic theory of solid mechanics, Adv. Appl. Mech., vol. 44, pp. 73–168, 2010.
   Web of Science ®Google Scholar
• A. Javili, R. Morasata, E. Oterkus, and S. Oterkus, Peridynamics review, Math. Mech. Solids., vol. 24, no. 11, pp. 3714–3739, 2019. DOI: 10.1177/1081286518803411.
   Web of Science ®Google Scholar
• H. F. Tiersten, Linear Piezoelectric Plate Vibrations: Elements of the Linear Theory of Piezoelectricity and the Vibrations Piezoelectric Plates, Springer, New York, 2013.
   Google Scholar
• A. Yaghoobi, and M. G. Chorzepa, Formulation of symmetry boundary modeling in non-ordinary state-based peridynamics and coupling with finite element analysis, Math. Mech. Solids., vol. 23, no. 8, pp. 1156–1176, 2018. DOI: 10.1177/1081286517711495.
   Web of Science ®Google Scholar
• P. Seleson, and D. J. Littlewood, Convergence studies in meshfree peridynamic simulations, Comput. Math. Appl., vol. 71, no. 11, pp. 2432–2448, 2016. DOI: 10.1016/j.camwa.2015.12.021.
   Web of Science ®Google Scholar