In this post, I will introduce the acoustic tensor of linearly elastic materials. Closed-form expressions of the inverse of this tensor can be derived in the case of isotropic materials. This will later come in handy to derive closed-form expressions of the periodic Green operator for strains.
We consider a …
In the previous instalments of this series (see Part 1 and Part 2), I have shown that regardless of the dimensionality (3D or plane strain elasticity), the constitutive law of an isotropically elastic material reads
$$\sigma_{ij}=\kappa\varepsilon_{kk}\delta_{ij}+2\mu\left(\varepsilon_{ij}-\frac{\varepsilon_{kk …
In the previous instalment of this series, I introduced the constitutive law of an isotropically elastic material, and the related material constants, within the framework of 3D elasticity. I will now address the case of plane strain elasticity.
Problems of plane strain elasticity are defined as problems where the following …
Among all classes of materials, the class of linearly elastic and isotropic materials is probably the simplest. Such materials are defined by two elastic constants: for example, Young\'s modulus $E$ and Poisson\'s ratio $\nu$. However, depending on the situation, this pair of constants might not be the most …