Numerical homogenization techniques for the evaluation of mechanical behavior of a composite with SMA inclusions

Numerical procedures are developed for the homogenization and evaluation of the stress field in a composite as a consequence of the presence of embedded SMA (shape-memory alloy) wires. In particular, the elastic field developed at the end of the SMA wire self-strain process is studied, knowledge of which is necessary to evaluate the feasibility of such a hybrid composite. First, the numerical procedures are applied to the study of both a representative volume element (RVE) included in a theoretically infinite periodic medium and a RVE located near the medium free boundary, in order to evaluate the tangential stress field generated at the end of the fiber; then they are applied to the study of a plate able to bend after the effect of self-strain of the SMA wire. Observations are reported about the obtained results and about the similarities and the differences between the two problems.

[1]  D. Lagoudas,et al.  Thermomechanical Response of Shape Memory Composites , 1994 .

[2]  Yan Li,et al.  Partial transformation behavior of prestrained TiNi fibers in composites , 2001 .

[3]  J. D. Eshelby.  The determination of the elastic field of an ellipsoidal inclusion, and related problems , 1957, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[4]  J. Schrooten,et al.  Qualitative and quantitative evaluation of the interface in activated shape memory alloy composites , 2003 .

[5]  H. Ishii,et al.  Deformation Behavior of NiTi/Polymer Shape Memory Alloy Composites – Experimental Verifications , 2004 .

[6]  Paulo B. Lourenço,et al.  Homogenization approach for the limit analysis of out-of-plane loaded masonry walls , 2006 .

[7]  A. Love.  A treatise on the mathematical theory of elasticity , 1892 .

[8]  Jacob Aboudi,et al.  The response of shape memory alloy composites , 1997 .

[9]  M. Gurtin,et al.  An introduction to continuum mechanics , 1981 .

[10]  Gabriele Milani,et al.  Validation of Analytical Multiparameter Homogenization Models for Out-of-Plane Loaded Masonry Walls by Means of the Finite Element Method , 2005 .

[11]  Sonia Marfia,et al.  Analysis of SMA composite laminates using a multiscale modelling technique , 2007 .

[12]  S. Marfia.  Micro–macro analysis of shape memory alloy composites , 2005 .

[13]  Jan-Anders E. Månson,et al.  Adaptive composite materials processing , 2000 .

[14]  A. Anthoine.  HOMOGENIZATION OF PERIODIC MASONRY: PLANE STRESS, GENERALIZED PLANE STRAIN OR 3D MODELLING? , 1997 .

[15]  E. Sacco,et al.  Micromechanics and Homogenization of SMA-Wire-Reinforced Materials , 2005 .

[16]  A. Anthoine.  Derivation of the in-plane elastic characteristics of masonry through homogenization theory , 1995 .

[17]  G. Duvaut.  Homogeneisation materiaux composites , 1984 .

[18]  Y. H. Zhao,et al.  Effective Elastic Moduli of Ribbon-Reinforced Composites , 1990 .

[19]  K. Tanaka,et al.  Average stress in matrix and average elastic energy of materials with misfitting inclusions , 1973 .

[20]  Peter Wall,et al.  Some engineering and mathematical aspects on the homogenization method , 1994 .

[21]  A. R. Cooper,et al.  Comparison of residual stress effects on the yielding and fracture of metal and glass composites , 1970 .

[22]  Ron Barrett,et al.  Super-active shape-memory alloy composites , 1996 .

[23]  Hideki Nagai,et al.  A new method for fabricating SMA/CFRP smart hybrid composites , 2002 .

[24]  J. Schrooten,et al.  Part II. Thermomechanical characteristics of shape memory alloy composites , 2004 .

[25]  W. Lee,et al.  Design and fabrication of intelligent composites based on shape memory alloys , 1997 .