A note on the linear deformations close to the boundaries of a cellular material

Abstract

Previously reported measurements of uniaxial compression of cellular acoustic materials have shown an intriguing loss of stiffness in the regions close to the boundaries. The present contribution attempts to further investigate if these effects may be modelled by assuming a local alteration of the microstructure in these regions close to the boundaries resulting from cutting a block of material into smaller samples. Assuming that fewer struts contribute locally to the mechanical behaviour, implies a reduced equivalent porosity, or relative density, in the boundary region. The approach explored here consists in randomly removing a portion of the struts constituting the microstructure of the cells because of damage incurred in the cutting process. The analysis is performed using a linear elastic deformation behaviour at the boundary of cellular acoustic materials.For the modelling of the microstructure, the Kelvin cell geometry is chosen. Applying the assumption that struts are damaged in the process of cutting a block of material into smaller samples, as an explanation for the observed high-strain boundary regions, it is shown that the experimental observations may be qualitatively reproduced. It is also shown that the equivalent density in the boundary regions may be estimated from the ratio of the boundary compressive modulus to that of the interior region of the sample. Through the presented results, the approximation errors in compression stiffness measurements performed for a real material may be estimated. Although providing a viable explanation of the experimentally observed behaviour of the boundary regions, it should be understood that the proposed approach primarily offers a simple, accurate equivalent description of this phenomenon.