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On the Size Effect in Cellular Foam Materials: A Combined Numerical and Experimental Investigation

Fenil Maganbhai Lathiya 1*, Geralf Hütter 1, Stephan Kirchhof 2, Björn Kiefer 1

1 TU Bergakademie Freiberg, Institute of Mechanics and Fluid Dynamics, Germany; 2 Faculty of Mechanical Engineering, Hochschule für Technik und Wirtschaft Dresden – University of Applied Sciences, Dresden, Germany

Generalized Continua, Metamaterials & Size Effects · C223
Wednesday, 2 September 2026, 09:25–09:50 · Chair: Martin Horák

Keywords: foam, cellular materials, size effect, virtual testing

The mechanical behavior of foam materials is of great interest in lightweight engineering due to their excellent stiffness-to-weight ratio. However, the presence of a microstructure with a characteristic length comparable to component dimensions leads to size effects that are not yet fully understood. The literature reports conflicting observations; for instance, experimental studies have shown that smaller specimens can appear stiffer (a positive size effect) [1], while other investigations have reported the opposite trend where smaller specimens appear more compliant (a negative size effect) [2]. This ambiguity motivates a deeper investigation into the underlying mechanisms. This contribution aims to shed light on the sign and magnitude of size effects in foams by combining insights from recent numerical and experimental work. Virtual testing on ceramic foams, which avoids experimental artifacts, has indicated a clear negative size effect across different loading modes [3]. In parallel, direct numerical simulations of foam-like structures have revealed that both positive and negative size effects can emerge depending on the specific loading conditions applied [4]. Our ongoing research extends these investigations to polymeric foams with the goal of creating a profound experimental database as a basis to the development of generalized continuum theories to describe these size effects.

References

  1. W. B. Anderson and R. S. Lakes, Size effects due to cosserat elasticity and surface damage in closed-cell polymethacrylimide foam, J. Mater. Sci., 29(23):6413–6419, 1994.
  2. C. Liebold and W. H. Müller, Applications of higher-order continua to size effects in bending: theory and recent experimental results, Proc. 7th Int. Conf. Coupled Probl. Sci. Eng., 2016.
  3. S. Kirchhof, A. Ams, and G. Hütter, On the question of the sign of size effects in the elastic behavior of foams, J. Elast., 153:1–24, 2023.
  4. A. Malik, G. Hütter, M. Abendroth, and B. Kiefer, Micromorphic FE² simulation of plastic deformations of foam structures, Int. J. Mech. Sci., 265:108877, 2024.