Elastic properties of isotropic discrete systems with skew contact normals

conference paper

English

The macroscopic elastic properties of discrete assemblies are fundamental characteristics of such systems. The contribution uses homogenization procedure based on equivalence of virtual work between the isotropic elastic continuum and the discrete system to develop analytical formulas for estimation of macroscopic elastic modulus and Poisson’s ratio. Such homogenization was recently used to derive formulas for discrete assemblies where (i) there is no vacant space between the discrete units, (ii) the orientation of contacts is uniformly distributed and (iii) the contact normals are parallel to contact vectors (directions connecting centers of discrete units). The third assumption is now removed, three dimensional systems with arbitrary relation between contact vectors and contact normals are studied here. It is shown that the limits of Poisson’s ratio of such system depends on the relation between contact normal and contact vector. The widest limits are however obtained when these two vectors are parallel. This means that arbitrary manipulations with discrete geometry cannot extend Poisson’s ratio of the system outside the known boundaries.

Discrete model, homogenization, elasticity, Poisson’s ratio, normal vector

ELIÁŠ, J.

3. 9. 2019

978-84-949194-7-3

XV International Conference on Computational Plasticity. Fundamentals and Applications (COMPLAS 2019)

305

313

9

https://congress.cimne.com/complas2019/frontal/default.asp