ElAM: A computer program for the analysis and representation of anisotropic elastic properties

The continuum theory of elasticity has been used for more than a century and has applications in many fields of science and engineering. It is very robust, well understood and mathematically elegant. In the isotropic case elastic properties are easily represented, but for non-isotropic materials, even in the simple cubic symmetry, it can be difficult to visualise how properties such as Young's modulus or Poisson's ratio vary with stress/strain orientation. The ElAM (Elastic Anisotropy Measures) code carries out the required tensorial operations (inversion, rotation, diagonalisation) and creates 3D models of an elastic property's anisotropy. It can also produce 2D cuts in any given plane, compute averages following diverse schemes and query a database of elastic constants to support meta-analyses.

[1]  R. Lakes.  Foam Structures with a Negative Poisson's Ratio , 1987, Science.

[2]  A. Migliori,et al.  A general elastic-anisotropy measure , 2006 .

[3]  Tungyang Chen,et al.  Poisson's ratio for anisotropic elastic materials can have no bounds , 2005 .

[4]  R. Baughman,et al.  Negative Poisson's ratios as a common feature of cubic metals , 1998, Nature.

[5]  Baughman,et al.  Materials with negative compressibilities in one or more dimensions , 1998, Science.

[6]  A. Reuss,et al.  Berechnung der Fließgrenze von Mischkristallen auf Grund der Plastizitätsbedingung für Einkristalle . , 1929 .

[7]  C. Zener.  Elasticity and anelasticity of metals , 1948 .

[8]  Antonio Maria Cazzani,et al.  Extrema of Young’s modulus for cubic and transversely isotropic solids , 2003 .

[9]  Tao Pang,et al.  An Introduction to Computational Physics , 1997 .

[10]  H. Wenk,et al.  Texture and Anisotropy , 2004 .

[11]  Andrew N. Norris,et al.  Poisson's ratio in cubic materials , 2006, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[12]  R. Hill.  The Elastic Behaviour of a Crystalline Aggregate , 1952 .

[13]  Martin T. Dove,et al.  Introduction to Lattice Dynamics: Contents , 1993 .

[14]  U. F. Kocks,et al.  Texture and Anisotropy: Preferred Orientations in Polycrystals and their Effect on Materials Properties , 1998 .

[15]  Herbert F. Wang,et al.  Single Crystal Elastic Constants and Calculated Aggregate Properties. A Handbook , 1971 .

[16]  B. Johansson,et al.  Elastic Anisotropy of Earth's Inner Core , 2008, Science.

[17]  J. Nye.  Physical Properties of Crystals: Their Representation by Tensors and Matrices , 1957 .

[18]  R. Bechmann,et al.  Numerical data and functional relationships in science and technology , 1969 .

[19]  N. Allan,et al.  Negative thermal expansion , 2005 .

[20]  Martin Ostoja-Starzewski,et al.  Universal elastic anisotropy index. , 2008, Physical review letters.