A microstructure-based constitutive law for snow

Abstract

A constitutive theory of snow is developed to describe the mechanical properties of snow in terms of the properties of the ice grains and the necks that interconnect them. The principle of virtual work is used to calculate the stresses in the particles and necks. A number of different deformation mechanisms are investigated and, depending upon the deformation mechanism which is dominant for given load conditions, different equations are used to calculate the strains in the grains and necks. These strains around a representative ice grain are then averaged and scaled to obtain the global strains in the snow. The theory is then compared with experimental data to determine if the mechanical properties of snow can be adequately represented. Results show that the constitutive theory does work, but that it is cumbersome to implement, and that for practical use substantial computational capability is needed.

Triaxial tests on snow at low strain rate. Part II. Constitutive behaviour

“…Subsequently, the influence of the microstructure on the material behaviour has not been determined. This makes developing Hansen and Brown (1988) and Mahajan and Brown (1993).The load-bearing`c hain''concept of Gubler (1978).…”

“…The model considers the fracture of grain bonds, reorganization of the grains, building of new bonds and neck growth. Mahajan and Brown (1993) presented a second microstructural constitutive theory of snow that describes the mechanical properties of snow in terms of the properties of the ice grains and the necks that interconnect them. That is, the kinematics of the ice skeleton are assumed to control the macroscopic behaviour.…”

“…The load is carried by``force chains'' (Gubler, 1978) (Fig.1) consisting of a series of ice grains. The most important work in this category was carried out by Brown (1980), Hansen and Brown (1988) and Mahajan and Brown (1993). A simplified microstructural model based on these works was presented by Bartelt and von Moos (2000).…”

Determination of failure envelope for faceted snow through numerical simulations

“…Carney et al (2006) and Sain and Narasimhan (2011) modeled the brittle failure of ice using a elastoviscoplastic constitutive law combined with damage and used strain rates exceeding 10 −3 s − 1 . The localized strain rates in the narrow constricted regions in the ice matrix of snow are expected to be at least one order higher than the macroscopic applied strain rate (Mahajan and Brown, 1993). The strain rates assigned to snow to obtain its compressive strength by Chandel et al (2014a) was 2 × 10 −4 s −1 and for tensile strength by Hagenmuller et al (2014a) was 2.5 × 10 −4 s −1 .…”

Stochastic reconstruction of the microstructure of equilibrium form snow and computation of effective elastic properties

“…A comprehensive review of snow mechanics (Shapiro and others, 1997) has pointed out the need to establish an effective snow classification scheme using parameters that reflect microscopic information on snow such that specific macroscopic stress-strain relationships can be ascertained as a function of snow microstructure. Earlier attempts to solve this problem have suffered from the lack of an experimentally based technique to define and measure snow microstructure that allows a correlation to the thermal (Kaempfer and others, 2005) and macroscopic mechanical properties (Brown, 1980;Mahajan and Brown, 1993; Bartelt and Lehning, 2002;Schneebeli, 2004) of snow; additional information can be found using the references cited in this paper.…”