Higher order continuum modelling of the compressive behaviour of snow


Stefan Liebenstein

Wednesday, 30. April 2014, 17:00
WW8, Raum 2.018, Dr.-Mack-Str. 77, Fürth

The mechanical response of snow is characterised by the underlying micro-structure which can be described as a network of connected struts or walls. The continuum modelling of such structures is advantageous due to its comparably low computational costs. However, classical (local) continuum theories, as commonly used in FE analysis, are not suitable for faithful modelling. There are, on the one hand, local inelastic effects like breaking or buckling of the inter-granular bonds under compression, resulting in a macroscopic inelastic response with strain-softening. As a consequence the solution might be non-unique and mesh-dependent. On the other hand, the internal length scale (e.g. bond length or cell size) is not directly related to the system size. Hence, size effects can be observed, i.e. geometrically similar structures of different sizes exhibit different mechanical responses.

To overcome these two problems we present a linear microstretch theory, which is a special case of the class of micromorphic continua firstly proposed by Eringen and Suhubi [1]. The theory introduces additional degrees-of-freedom into the classical continuum theory, namely a microrotation and a microstretch. In comparison with the micropolar or Cosserat theory the additional microstretch variable allows to capture size effects and to regularise softening in non-rotational settings, i.e. hydrostatic compression. This is of particular importance, because the inelastic behaviour is constitutively modelled by a pressure dependent plasticity model, similar to the one proposed in Zaiser et. al. [2]. Under compression the model shows a distinctive softening behaviour, followed by an exponential hardening. Physically, this represents the afore mentioned bond breaking, resulting in local collapse of cells, with the subsequent compaction of broken bonds.

We will discuss the identification of the additional elastic parameters of the microstretch model. Furthermore, we compare our simulations with experimental results for snow.
In addition, we briefly discuss some numerical and implementation issues, such as symmetry of the global finite element stiffness matrix.


[1] A. C. Eringen and E. S. Suhubi, Nonlinear theory of simple micro-elastic solids -- I , Int. J. Eng. Sci. 2(2), 189-203 (1964)
[2]  M. Zaiser, F. Mill, A. Konstantinidis, K. E. Aifantis, Strain localization and strain propagation in collapsible solid foams, Mat. Sci. Eng. A 567, 38-45 (2013)