Rotational invariance conditions in elasticity, gradient elasticity and its connection to isotropy

Elasticity theory connection rules for epitaxial interfaces

Elasticity theory provides an accurate description of the long-wavelength vibrational dynamics of homogeneous crystalline solids, and with supplemental boundary conditions on the displacement field can also be applied to abrupt heterojunctions and interfaces. The conventional interface boundary conditions, often referred to as ‘‘connection rules,’’ require that the displacement field and its as...

Stress invariance and redundant moduli in three-dimensional elasticity

A three-dimensional framework is established for generating invariant stress configurations and associated shifts in the elastic compliance. Under these shifts the stress throughout an elastic body is unaltered, while the compatibility equations for the strain are automatically satisfied. The types of invariant stress fields and translations of the compliance identified here generalize the resu...

Computational Evaluation of Strain Gradient Elasticity Constants

Classical effective descriptions of heterogeneous materials fail to capture the influence of the spatial scale of the heterogeneity on the overall response of components. This influence may become important when the scale at which the effective continuum fields vary approaches that of the microstructure of the material and may then give rise to size effects and other deviations from the classic...

The Elasticity of Elasticity

In this talk I assert that the usual interpretation of what one means by “elasticity” is much too insular and illustrate my thesis by introducing implicit constitutive theories that can describe the nondissipative response of solids. I show that response which was hitherto untenable within the context of Cauchy or Green Elasticity are not only possible, they can explain phenomena that have thus...

Artificial boundary conditions to compute correctors in linear elasticity