propSym: a tool to establish relationships between property constants for material property tensors of any order

Author:

Roy Anubhav,Branch Darren W.,Jensen Daniel S.,Kube Christopher M.ORCID

Abstract

The properties of crystalline materials can be described mathematically by tensors whose components are generally known as property constants. Tabulations of these constants in terms of the independent components are well known for common material properties (e.g. elasticity, piezoelectricity etc.) aptly described by tensors of lower rank (e.g. ranks 2–4). General relationships between constants of higher rank are often unknown and sometimes reported incorrectly. A computer program is developed here to calculate the property constant relationships of a property of any order, represented by a tensor of any rank and point group. Tensors up to rank 12, e.g. the tensor of sixth-order elastic constants c_{_{6}i\,j\,k\,l\,m\,n\,p\,q\,r\,s}, can be calculated on a standard computer, while ranks higher than 12 are best handled on a supercomputer. Output is provided in either full index form or a reduced index form, e.g. the Voigt index notation common to elasticity. As higher-order tensors are often associated with nonlinear material responses, the program provides an accessible means to investigate the important constants involved in nonlinear material modeling. The routine has been used to discover several incorrect relationships reported in the literature.

Funder

Sandia National Laboratories

U.S. Department of Energy, National Nuclear Security Administration

Publisher

International Union of Crystallography (IUCr)

Subject

General Biochemistry, Genetics and Molecular Biology

Cited by 1 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. A unifying model of weakly nonlinear elastic waves; large on large theory;The Journal of the Acoustical Society of America;2022-02

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