In many technical and geomechanics applications, for example tire and ski design or avalanche prediction, the capability to model the mechanical behaviour of snow is of high importance. To this end, we propose in the present study to extend the 3-D H-model, a multi-scale constitutive law originally developed for granular materials, to densely packed snow. In the model, single ice grains are described by spherical particles bonded by brittle elasto-viscoplastic bridges. Snow is thus described explicitly through its ice skeleton microstructure. As a validation, confined compression test results from the litterature are used to assess the suitability of the model to correctly describe snow behaviour. Multiple parameter studies were conducted to demonstrate the capability of the model to capture the behaviour of different snow types over a significant range of temperatures and loading rates at small deformations. Notably, the initial bond radius emerges as an effective proxy for snow aging under isothermal conditions, with stress levels increasing directly with the initial bond radius. Additionally, low strain rates and elevated temperatures are shown to influence the viscous response of ice bonds, their failure rates and the overall stress within the snow material.

The response of ice to applied stress on ice-sheet flow timescales is commonly described by a non-linear incompressible viscous fluid, for which the deviatoric stress has a quadratic relation in the strain rate with two response coefficient functions depending on two principal strain-rate invariants I2 and I3. Commonly, a coaxial (linear) relation between the deviatoric stress and strain rate, with dependence on one strain-rate invariant I2 in a stress formulation, equivalently dependence on one deviatoric stress invariant in a strain-rate formulation, is adopted. Glen's uni-axial stress experiments determined such a coaxial law for a strain-rate formulation. The criterion for both uni-axial and shear data to determine the same relation is determined. Here, we apply Steinemann's uni-axial stress and torsion data to determine the two stress response coefficients in a quadratic relation with dependence on a single invariant I2. There is a non-negligible quadratic term for some ranges of I2; that is, a coaxial relation with dependence on one invariant is not valid. The data does not, however, rule out a coaxial relation with dependence on two invariants.

A hyperelastic constitutive law, for use in anatomically accurate finite element models ofliving structures, is suggested for the passive and the active mechanical properties of incompressiblebiological tissues. This law considers the passive and active states as a same hyperelastic continuummedium, and uses an activation function in order to describe the whole contraction phase.The variational and the FE formulations are also presented, and the FE code has been validatedand applied to describe the biomechanical behavior of a thick-walled anisotropic cylinder underdifferent active loading conditions.

We derive a constitutive law for the myocardium from the description of both the geometrical arrangement ofcardiomyocytes and their individual mechanical behaviour. We model a set of cardiomyocytes by a quasiperiodic discretelattice of elastic bars interacting by means of moments. We work in a large displacement framework and we use a discretehomogenization technique. The macroscopic constitutive law is obtained through the resolution of anonlinear self-equilibrum system of the discrete lattice reference cell.