Abstract
We present the spectral decomposition of the isotropic stiffness hexadic that appears in Mindlin’s strain gradient elasticity, where the kinematic variable is the second gradient of the displacement field. It turns out that four distinct eigenmodes appear, two of which are universal for all isotropic strain gradient materials, and two depend on an additional material parameter. With the aid of the harmonic decomposition, general interpretations of the eigenmodes can be given. Further, the material parameters are related to commonly employed special cases, namely the cases tabulated in Neff et al. (Int J Solids Struct 46(25–26):4261–4276, 2009) and isotropic gradient elasticity of Helmholtz type.
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Acknowledgments
Valuable hints from Patrizio Neff and Markus Lazar are gratefully acknowledged.
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Glüge, R., Kalisch, J., Bertram, A. (2016). The Eigenmodes in Isotropic Strain Gradient Elasticity. In: Altenbach, H., Forest, S. (eds) Generalized Continua as Models for Classical and Advanced Materials. Advanced Structured Materials, vol 42. Springer, Cham. https://doi.org/10.1007/978-3-319-31721-2_8
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DOI: https://doi.org/10.1007/978-3-319-31721-2_8
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