# Topology Optimization of Periodic Materials employing the Finite- Volume Theory

## Palavras-chave:

Topology Optimization, Finite-Volume Theory, Homogenization, Material Design## Resumo

This paper presents a computational tool for designing composite materials with periodic

microstructures for optimal effective elastic properties. The effective elastic properties of the periodic porous

material are evaluated through a combination of the homogenization method and finite-volume theory analysis.

The finite-volume theory results are employed in the topology optimization procedure, combining this technique

with the dual optimization algorithm of convex programming. In this approach, to find the optimal microstructural

topology for the periodic unit cell, specific linear combinations of the components of the effective elastic tensor

are considered to obtain extreme elastic properties, such as the maximum shear or bulk modulus under a prescribed

volume constraint. Some numerical examples involving materials with periodic porous microstructures are

analyzed, and the results demonstrate the finite-volume theory formulation’s performance for the optimal design

of composite porous materials.