Document Type : Research Paper


Faculty of Mechanical Engineering, K.N. Toosi University of Technology, Tehran, Iran


In the present research, in contrast to the available papers, not only the superelasticity but also the shape memory effects are taken into account in determination of the impact responses. At the same time, in addition to modifying Brinson’s model for the shape memory alloys (SMAs), to include new parameters and loading events, and Hertz contact law, distributions of the SMA phases are considered to be both localized and time-dependent. Furthermore, effects of the impact-induced heat generation and mechanical energy on the resulting histories of the martensite phase volume fraction, stress-strain, temperature, lateral deflection, and contact force are investigated. The generated heat in the SMA wires during the impact is determined through using a Helmholtz free energy function including the latent heat of the phase transformation. The resulting governing equations are solved by the finite element method. The nonlinear refined constitutive laws are solved through a return-mapping Newton-Raphson procedure. Results reveal that incorporation of the heat generation effects is significant in medium/high-velocity impacts or when the stress field is almost uniform.

Graphical Abstract

Influence of heat generation on the phase transformations and impact responses of composite plates with embedded SMA wires


Main Subjects

[1]         S .M. R. Khalili, A. Shokuhfar, and F. Ashenai Ghasemi, “Effect of smart stiffening procedure on low-velocity impact response of smart structures”, J. Mater Proc. Tech., Vol. 190, No. 1-3, pp. 142-152, (2007).

[2]         A. Shokuhfar, S. M. R. Khalili, F. Ashenai Ghasemi, K. Malekzadeh, and S. Raissi, “Analysis and optimization of smart hybrid composite plates subjected to low-velocity impact using the response surface methodology (RSM)”, Thin-Wall Struct, Vol. 46, No. 11, pp. 1204-1212, (2008).

[3]         M. Meo, F. Marulo, M. Guida, and S. Russo, “Shape memory alloy hybrid composites for improved impact properties for aeronautical applications”, Compos. Struct., Vol. 95, pp.756-766, (2013).

[4]         E. H. Kim, I. Lee, J. H. Roh, J. S. Bae, I. H. Choi, and K. N. Koo, “Effects of shape memory alloys on low velocity impact characteristics of composite plate”, Compos. Struct., Vol. 93, No. 11, pp. 2903-2909, (2011).

[5]         J. H. Roh and J. H. Kim, “Adaptability of hybrid smart composite plate under low velocity impact”, Compos. Part B, Vol. 34, No. 2, pp.117-125, (2003).

[6]         M. Shariyat and R. Jafari, “Nonlinear low-velocity impact response analysis of a radially preloaded two-directional-functionally graded circular plate: A refined contact stiffness approach”, Compos. Part B,Vol. 45, No .1, pp. 981-994, (2013).

[7]         M. Shariyat and F. Farzan, “Nonlinear eccentric low-velocity impact analysis of a highly prestressed FGM rectangular plate, using a refined contact law”, Arch. Appl. Mech., Vol. 83, No .4, pp. 623-641, (2013).

[8]         M. Shariyat and F. Farzan Nasab, “Low-velocity impact analysis of the hierarchical viscoelastic FGM plates, using an explicit shear-bending decomposition theory and the new DQ method”, Compos. Struct., Vol. 113, No.1, pp. 63-73, (2014).

[9]         M. Shariyat and M. Moradi, “Enhanced algorithm for nonlinear impact of rectangular composite plates with SMA wires, accurately tracing the instantaneous and local phase changes”, Compos. Struct.,Vol. 108, pp. 834-847, (2014).

[10]     M. Shariyat and S. H. Hosseini, “Accurate eccentric impact analysis of the preloaded SMA composite plates, based on a novel mixed-order hyperbolic global–local theory”, Compos. Struct.,Vol. 124, pp. 140-151, (2015).

[11]     D. Helm and P. Haupt, “Shape memory behaviour: modeling within continuum thermo-mechanics”, Int. J. Solids Struct., Vol. 40, No. 4, pp. 827-849, (2003).

[12]     H. Tobushi and Y. Shimeno, T. Hachisuka, and K. Tanaka, “Influence of strain rate on super elastic properties of TiNi shape memory alloy”, Mech. Mater., Vol. 30, No. 2, pp. 141-150, (1998).

[13]     M. Kadkhodaei, RKND. Rajapakse, M. Mahzoon and M. Salimi, “Modeling of the cyclic thermo-mechanical response of SMA wires at different strain rates”, Smart Mater. Struct., Vol. 16, No. 6, pp. 2091-2101, (2007).

[14]     P. C. C. Monteiro, M. A. Savi , T. A. Netto, and P. M. C. Pacheco, “A Phenomenological description of the thermo-mechanical coupling and the rate-dependent behavior of shape memory alloys”, J. Intell. Mater. Sys. Struct., Vol. 20, No. 14, pp. 1675-1687, (2009).

[15]     C. Morin, Z. Moumni and W. Zaki, “A constitutive model for shape memory alloys accounting for thermomechanical coupling”, Int. J. Plast., Vol.  27, No. 5, pp. 748-767, (2011).

[16]     J. H. Roh, “Thermomechanical Modeling of shape memory alloys with rate dependency on the pseudoelastic behavior”, Math. Prob. Eng., Vol. 20, No. 1, pp.41-65, (2014).

[17]     J. Ignaczak and M. Ostoja-Starzewski, Thermoelasticity with finite wave speeds, Oxford University Press, United States, New York, (2010).

[18]     M. R. Eslami, R. B. Hetnarski, J. Ignaczak , N. Noda, N. Sumi and Y. Tanigawa, Theory of elasticity and thermal stresses, Springer, (2013).

[19]     L. C. Brinson, “One dimensional constitutive behavior shape memory alloys: Thermo-mechanical derivation with non-constant material functions and redefined martensite internal variable”, J. Intell. Mater Syst. Struct., Vol. 4, No. 2, pp. 229-242, (1993).

[20]     D. C. Lagoudas, Shape Memory Alloys: Modeling and Engineering Applications, Springer, (2008).

[21]     J. N. Reddy, Mechanics of Laminated Composite Plates and Shells-Theory and Analysis, CRC Press, Boca Raton, (2003).

[22]     V. Birman, “An approach to optimization of shape memory alloy hybrid composite plates subjected to low-velocity impact”, Composites: Part B, Vol. 27, No. 5, pp. 439-446, (1996).

[23]     J. R. Turner, “Contact on a transversely isotropic half-space, or between two transversely isotropic bodies”, Int. J. Solids Struct., Vol. 16, No. 5, pp. 409-19, (1980).

[24]     A. Niknami and M. Shariyat, “Refined constitutive, bridging, and contact laws for including effects of the impact-induced temperature rise in impact responses of composite plates with embedded SMA wires”, Thin-WalledStruct.,  Vol. 106, pp. 166-178, (2016).

[25]     S. H. Yang and C.T. Sun, “Indentation law for composite laminates”, In: Composite materials: testing and design (6th conference), ASTM STP-787, pp. 425- 49, (1982).

[26]     M. R. Eslami, Finite elements methods in mechanics, Springer, (2014).

[27]     E. Serra and M. Bonaldi, “A finite element formulation for thermoelastic damping analysis”, Int. J. Numer. Meth. Eng., Vol. 78, No. 6, pp. 671-691, (2009).

[28]     M. Shariyat and A. Niknami, “Impact analysis of strain-rate-dependent composite plates with SMA wires in thermal environments: Proposing refined coupled thermoelasticity, constitutive, and contact models”,  Compos. Struct., Vol.  136, pp. 191-120, (2016).

[29]     M. Shariyat and A. Niknami, “Layerwise numerical and experimental impact analysis of temperature-dependent transversely flexible composite plates with embedded SMA wires in thermal environments”,  Compos. Struct., Vol. 153, pp. 692–703, (2016).

[30]     R. Tiberkak, M. Bachene, S. Rechak and B. Necib, “Damage prediction in composite plates subjected to low velocity impact”, Compos. Struct., Vol. 83, No. 1, pp.73-82, (2008).

[31]     L. C. Brinson and R. Lammering, “Finite element analysis of the behavior of shape memory alloys and their applications”, Int. J. Solids Struct., Vol. 30, No. 23, pp.3261-3280, (1993).