A novel procedure, called the method of neighborhoods, for calculation of a hierarchy of upper and lower convergent bounds on constitutive response of random microstructures, is outlined. The method is presented in the setting of a regular planar network of equilateral triangles with randomness present in the constitutive constants of vertex-vertex linear viscoelastic laws. Results on linear elastic networks indicate that a very good improvement on the conventional Voigt and Reuss bounds may be achieved with rather small neighborhoods, and thus with only a modest increase of the computational effort.
ASJC Scopus subject areas
- Civil and Structural Engineering
- Modeling and Simulation
- Materials Science(all)
- Mechanical Engineering
- Computer Science Applications