## Continuum damage model

Continuum damage mechanics describes the deterioration of material due to a progressive increase of damage (damage means

Figure 62.2 Simulation of crevasse formations in the west face hanging glacier of the Eiger, Switzerland. According to Pralong et al. (2003), the damage is assumed to be isotropic. The crevasses appear in the model as concentration of damage. The dark grey colour represents ice without microcracks (D = 0). Light grey corresponds to broken ice (D = 1), i.e., ice with a very high density of microcracks. In the simulation, the frontal crevasse grows. The fracture process zone at its tip is depicted in black and corresponds to intermediate values of D. (See www.blackwellpublishing.com/knight for colour version.)

Figure 62.2 Simulation of crevasse formations in the west face hanging glacier of the Eiger, Switzerland. According to Pralong et al. (2003), the damage is assumed to be isotropic. The crevasses appear in the model as concentration of damage. The dark grey colour represents ice without microcracks (D = 0). Light grey corresponds to broken ice (D = 1), i.e., ice with a very high density of microcracks. In the simulation, the frontal crevasse grows. The fracture process zone at its tip is depicted in black and corresponds to intermediate values of D. (See www.blackwellpublishing.com/knight for colour version.)

the density of microcracks, which affect the mechanical behaviour of the material). This approach consists of three elements: (i) quantification of the damage with a variable D (called 'damage variable'), (ii) description of the influence of the damage on the material rheology and (iii) description of the evolution of the damage in time and space. The damage variable D is defined at the mesoscale. As the mesoscale is much smaller than the size of the crevasses, D is, for the modelling of crevassing, a local variable. It has the following meaning: D = 0 represents no damage and D = 1 corresponds to a fully damaged ice element. The damage variable should adequately describe the level of anisotropy: isotropic damage is represented by a scalar variable and anisotropic damage by a second- or fourth-order tensor. The influence of the microcracks on the ice flow is calculated by assuming a dependence of D on the ice viscosity. For anisotropic damage, the viscosity becomes anisotropic. The increase of damage in material is modelled using a local progressive accumulation law valid for creep materials.

With such an approach, ductile crevassing is handled naturally:

1 In the model, a concentration of damage appears at the crevasse tip and forms the FPZ, thereby taking into account the influence of the FPZ on the ice flow.

2 The subcritical crevassing is reproduced by modelling the local and progressive accumulation of damage.

The crevassing in a hanging glacier is computed (Fig. 62.2) by applying the isotropic damage model developed by Pralong et al. (2003). The simulation reproduces the subcritical crevasse growth and the formation of the FPZ.

The physics of ductile crevassing is not well understood at present. The microprocesses of fracture and the spatial organization of microcracks should be analysed in greater depth. Field and laboratory measurements should also be carried out in order to quantify more precisely subcritical crack-growth for ice.