Impact of microstructure in the mechanical behavior of soft foams

Following our previous investigation of the beahvior of hyperelastic classic Voronoi closed-cell foams submitted to severe compression, we have extended the study to assess the influence of microstructure on the mechanical response of highly porous foams. To this end, two additional classes of microstructures were generated: mechanically grown Voronoi (M-Voro) closed-cell foams and open-cell foams obtained by removing material from classical Voronoi (C-Voro) structures. The porosity ranges from 75% to 95%. The polymer matrix is modeled using either a Neo-Hookean or an Ogden constitutive law to investigate the influence of the matrix constitutive behavior on the overall mechanical response.

Mechanically grown Voronoi microstructures are generated by subjecting a cubic matrix containing a monodisperse distribution of spherical pores to hydrostatic tension. This procedure produces closed-cell foams with rounded pores and highly heterogeneous wall thicknesses, resulting in a microstructure that differs significantly from that of classical Voronoi foams.

The three classes of microstructures were investigated under infinitesimal-strain loadings, large uniaxial compression, and large uniaxial tension. 

The main conclusions of the study are summarized as follows:

1. Finite-strain uniaxial compression

• For closed-cell foams, the contribution of the gas trapped within the cells is a first-order effect and must be accounted for.
• The macroscopic compressive response scales approximately with (1−c)^2, where c is the porosity.
• The influence of microstructure on the macroscopic compressive stress–strain response is relatively limited (second-order), although it significantly affects the local deformation mechanisms.

2. Finite-strain uniaxial tension

• The tensile response is strongly influenced by both the microstructure and the constitutive behavior of the polymer matrix.
• For a Neo-Hookean matrix, the analytical model proposed by Shrimali et al. (2019) provides an accurate prediction of the tensile response for closed-cell Voronoi microstructures at moderate and large strain.

3. Infinitesimal-strain response

• The classical isotropic linear elasticity relationships between Young’s modulus E, shear modulus 𝜇, and bulk modulus K are not satisfied, despite the apparently isotropic nature of the microstructures. This suggests that more than two independent elastic constants may be required to describe their effective linear elastic behavior.

You can read all about it in T. Merlette, J. Diani, 2026. 3D Finite element investigation of hyperelastic foam behavior. II. Influence of Microstructure in closed- and open-cell Foam. Mechanics of Materials https://doi.org/10.1016/j.mechmat.2026.105774