Practical Non-Linear Elasticity Theory for Large Strains

Bosher, S. H. B.; Dunstan, D. J.

doi:10.1080/0895795031000139208

Cited by 2 publications

(2 citation statements)

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“…We have introduced effective thermodynamic elastic constants for cubic materials under general finite strain, and used them to derive the Thurston and Brugger equations independently [2,3]. Fifteen are correct, and the two that are in error have been altered (without comment or explanation) by McSkimin and Andreatch [4] in the experimental literature.…”

Section: Acoustic Determinations Of C Ijkmentioning

confidence: 96%

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Reliable non‐linear elastic constants

Dunstan

Bosher

2003

Physica Status Solidi (b)

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The values given in the literature for the third-order elastic constants c IJK of the standard semiconductors have long been suspect. We have applied modern statistical analysis to the raw data from which the databook c IJK were obtained, and we give revised values with reliable error estimates for Si, Ge and GaAs. The databook c IJK are appropriate for an expansion of the elastic energy of a body as a Taylor series in Lagrangian strain η IJ , but there are formidable mathematical difficulties in using Lagrangian strain in the analysis of physical problems. To facilitate such analysis, we introduce effective second-order elastic constants for materials under finite strain. From these, strain, stress and pressure derivatives are readily calculated. The pressure derivatives are given for Si, Ge and GaAs. Using the stress derivatives, the relationships between physical observables such as acoustic velocities and the databook c IJK can be obtained by simple algebra.Introduction Elastic constants have been measured for many materials and are required for any calculation of the effects of pressure, stress or strain. The second-order constants such as the Young's, bulk and shear moduli, and the tensor c IJ , are well-established and accurately known. The third-order constants c IJK are required for any accurate calculation of the effect of large stresses or deformations, but their literature values have long been regarded as suspect. In this paper, we show how they may be rehabilitated or refined using multi-variate linear regression analysis. We find that literature values for Ge and Si are in fact very good, while the data for GaAs requires significant reassessment. Just as important is the need to use an appropriate theory, without which good values of c IJK are vitiated.Third-order elastic constants have been regarded as suspect for at least three reasons. Firstly, there have been major discrepancies between the values of such quantities as the experimental determinations of the pressure coefficients of second-order elastic constants, c′ IJ , and the values calculated from experimental values of the third-order constants c IJK . Secondly, the experimental determinations with which we are concerned depend upon uniaxial stress experiments, and these are notoriously inaccurate. Thirdly, and perhaps most damaging, some of the authors of the experimental determinations have claimed completely unrealistic small errors. Our aim is therefore to establish reasonable values with justifiable error estimates.

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Section: Acoustic Determinations Of C Ijkmentioning

confidence: 96%

“…They are readily calculated from our effective second-order elastic constants [2,3] and are Table 1 differs by amounts significant compared with the errors and is to be preferred. The errors on the c IJK of Table 1 and of Ref.…”

Section: Xmentioning

confidence: 99%