Bond Based Peridynamic Formulation for Thermoelectric Materials


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Modeling of heat and electrical current flow simultaneously in thermoelectric convertor using classical theories do not consider the influence of defects in the material. This is because traditional methods are developed based on partial differential equations (PDEs) and lead to infinite fluxes and stress fields at the crack tips. The usual way of solving such PDEs is by using numerical technique, like Finite Element Method (FEM). Although FEM is robust and versatile, it is not suitable to model evolving discontinuities since discontinuous fields are mathematically singular at the crack tip and required an external criterion for the prediction of crack growth. In this paper, we follow the concept of peridynamic (PD) theory to overcome the shortcomings above. Therefore, the main aim of this paper is to develop the peridynamic equations for the generalized Fourier’s and Ohm’s laws. Furthermore, we derived the peridynamic equations for the conservation of energy and charge for the coupled thermoelectric phenomena.



Edited by:

Viboon Sangveraphunsir and Prof. Osman Adiguzel




M. A. Zeleke et al., "Bond Based Peridynamic Formulation for Thermoelectric Materials", Materials Science Forum, Vol. 883, pp. 51-59, 2017

Online since:

January 2017




* - Corresponding Author

[1] D.K. Misra, S. Sumithra, N.S. Chauhan, W.M. Nolting, P.F.P. Poudeu, KevinL. Stokes, Materials Science in Semiconductor Processing Vol. 40(2015), p.453.

[2] A. Bhardwaj, N.S. Chauhan, D.K. Misra, J. Mater. Chem. A, vol. 3 (2015), p.10777.

[3] K. Yang, A. Cantarero, A. Rubio, and R. D'Agosta, Nano Research vol. 8 (2015), p.2611.

[4] S. Muthiah, B. Sivaiah, B. Gahtori, K. Tyagi, A.K. Srivastava, B.D. Pathak, A. Dhar and R.C. Budhani, J. of Electronic Materials, Vol. 43, No. 6(2014), p. (2035).


[5] Li-D. Zhao, S. H. Lo, Y. Zhang, H. Sun, G. Tan, C. Uher, C. Wolverton, V. P. Dravid and M. G. Kanatzidis, Nature Letters, Vol. 508, (2014), p.373.

[6] S. N. Guin, D. S. Negi, R. Datta and K. Biswas, J. Mater. Chem. A, vol. 2, (2014) p.4324.

[7] G. J. Snyder and E. S. Toberer, Nature Materials vol. 7, (2008) p.105.

[8] M. H. Elsheikh, D. A. Shnawah, M. F. M. Sabri, S. B. M. Said, M. H. Hassan, M. B. A. Bashir,M. Mohamad, Renewable and Sustainable Energy Reviews vol. 30, (2014) p.337.

[9] CRC Handbook of Thermoelectrics, Edited by D.M. Rowe, CRC Press, (1995).

[10] M. Gigliotti, M. Christine L. Frenot, Y. Lin and A. Pugliese, Composite Structures vol. 127 (2015) p.436.

[11] Dolbow, J.E., An extended finite element method with discontinuous enrichment for applied mechanics, (1999) Northwestern University, USA.

[12] Dolbow, J. and T. Belytschko, Computational Mechanics, vol. 23, (1999) p.219.

[13] S. A. Silling, Physics of Solids, vol. 48, no. 1 (2000), p.175.

[14] T. Belytschko and T. Black, Int. J. Numer. Meth. Engngvol. 45 (1999) p.601.

[15] T. Belytschko, C. Parimi, N. Moes, N. Sukumar and S. Usui, Int. J. Numer. Meth. Engngvol. 56 (2003) p.609.

[16] N. Moes, J. Dolbow, and T. Belytschko, Int. J. Numer. Meth. Eng, vol. 46 (1999), p.131.

[17] Areias, P., Belytschko, T., Int. J. for Num. Meth. in Eng, vol. 63 (2005), p.760.

[18] L. Liu, International Journal of Engineering Science vol. 55 (2012) p.35.

[19] A.B. Zhang, B.L. Wang, Theoretical and Appl. Frac. Mechanics, vol. 66 (2013) p.33.

[20] J.L. P-Aparicio R.L. Taylor, D. Gavela, Comput. Mech. vol. 40 (2007) p.35.

[21] J.L. P-Aparicio,R. Palma, R.L. Taylor, Int. J. of Heat and Mass Transfer vol. 55 (2012) p.1363.

[22] E. E. Antonova and D. C. Looman, IEEE Int. Conference on Thermoelectrics (2005).

[23] Kunin I.A. Elastic media with microstructure I: one dimensional models. Berlin: Springer-Verlag; 1982. p.27.

[24] Silling, S. A., Zimmermann, M., Abeyaratne, R., J. of Elasticity, vol. 73(2003), p.173.

[25] Silling, S. A., Epton, M., Weckner, O., Xu, J., Askari, E., J. of Elasticity, vol. 88(2007), p.151.

[26] N. Prakash, G.D. Seidel, Computational Materials Science vol. 113 (2016) p.154.

[27] F. Bobaru and M. Duangpanya, Int. J. Heat Mass Transf, vol. 53, no. 19-20 (2010), p.4047.

[28] F. Bobaru and M. Duangpanya, J. Comput. Phys, vol. 231, no. 7 (2012), p.2764.