Homogenization for inhomogeneous elastic body containing gas bubbles

Abstract

We consider the homogenization problem for an elastic material which contains a distributed array of gas bubbles in the first part of this research. We assume that the spacing of the holes and their diameters are of the same order of magnitude. The main result is that such a spongy material can be approximated by an elastic material with no holes. In the second part of this work, we extend the results to the elastodynamics. In both cases we derive expressions for the effective moduli of the limiting material.

Keywords:

• Elasticity
• gas bubbles
• effective moduli
• homogenization

AMS:

• 35B40
• 35J50
• 73C40

¹Current address: Department of Mathematics, Penn State, Scuuylkill, 200 University Drive, Schuylkill Haven, PA 17972.

¹Current address: Department of Mathematics, Penn State, Scuuylkill, 200 University Drive, Schuylkill Haven, PA 17972.

Notes

¹Current address: Department of Mathematics, Penn State, Scuuylkill, 200 University Drive, Schuylkill Haven, PA 17972.