Coefficient of thermal expansion of stacked auxetic and negative thermal expansion laminates

Abstract

Analytical expressions for the in-plane and out-of-plane coefficients of thermal expansion for laminates with isotropic laminas are presented herein based on (i) zero net force on the laminate edges, (ii) equal displacement of the lamina edges, and (iii) Hooke's law in three dimensions. Results show that a laminate consisting of alternating auxetic (with positive coefficient of thermal expansion, CTE) and negative thermal expansion (NTE) (with positive Poisson's ratio) laminas exhibit a more negative effective CTE than a laminate of alternating conventional laminas (positive Poisson's ratio and positive CTE) with unconventional laminas (auxetic and NTE). Finally, temperature-dependent CTE for such laminates are developed and plotted for special cases. It is herein shown that under certain circumstances, the magnitude of temperature-dependent effective CTE tends to infinity. [47][48][49][50][51][52], and phase transition [53-56], among others. As a result of their novel properties, a number of applications have been suggested or developed using auxetic (e.g., in Refs. [57][58][59][60][61]) and NTE (e.g.,) materials. For example, auxetic materials have been identified for use in aerospace structural materials [6], while the CTE of dental fillings can be tailored to match that of the tooth to reduce thermal stress between the tooth and the dental filling or as composites that are useful for reducing thermal stresses in various applications [68]. To date, a number of studies on the effect of alternating positive and negative Poisson's ratio laminas on the effective laminate

Negative Poisson's Ratio in Modern Functional Materials

“…It has also been demonstrated that auxetic materials offer a widespread range of applications in the biomedical industry . Moreover, materials that simultaneously have a negative Poisson's ratio and other negative indexes, such as negative compressibility and thermal expansion, could have more emergent physical properties. Such materials with unconventional negative indices have many practical applications, especially in the electronics, medical, aerospace, and defense industries.…”

Partially auxetic behavior in fcc crystals of hard-core repulsive Yukawa particles

“…Depending on whether negative values of Poisson ratio are observed in all crystallographic directions, in some of them or in none of them, one can define all materials as auxetics, partial auxetics and nonauxetics, respectively (). Recently, increasing interest in studies of auxetic materials and models was observed .…”

Applications of ice‐templated ceramics

“…35 ) However, neither predicted the experimental CTE accurately, since they fail to consider material anisotropy. Using Lim's model for stacked laminates, 36 the predicted CTE is À25 9 10 À6 K À1 in the transverse direction (vs À3.5 9 10 À6 K À1 in the longitudinal direction), much more negative than the observed value. However, the observed microstructure is not purely lamellar due to the presence of many bridges between the lamellae.…”