A Hybrid Variational Formulation for Strain Gradient Elasticity Part I: Finite Element Implementation
N.A. Dumont 1, D. Huamán1
CMES-Computer Modeling in Engineering & Sciences, Vol.101, No.6, pp. 387-419, 2014, DOI:10.3970/cmes.2014.101.387
Abstract The present paper starts with Mindlin’s theory of the strain gradient elasticity, based on three additional constants for homogeneous materials (besides the Lamé’s constants), to arrive at a proposition made by Aifantis with just one additional parameter. Aifantis’characteristic material length g2, as it multiplies the Laplacian of the Cauchy stresses, may be seen as a penalty parameter to enforce interelement displacement gradient compatibility also in the case of a material in which the microstructure peculiarities are in principle not too relevant, but where high stress gradients occur. It is shown that the hybrid finite element formulation… More >
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