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In order to study the mechanical behaviour of polar ice masses, the method of continuum mechanics is used. The newly developed CAFFE model (Continuum-mechanical, Anisotropic Flow model, based on an anisotropic Flow Enhancement factor) is described, which comprises an anisotropic flow law as well as a fabric evolution equation. The flow law is an extension of the isotropic Glen's flow law, in which anisotropy enters via an enhancement factor that depends on the deformability of the polycrystal. The fabric evolution equation results from an orientational mass balance and includes constitutive relations for grain rotation and recrystallization. The CAFFE model fulfills all the fundamental principles of classical continuum mechanics, is sufficiently simple to allow numerical implementations in ice-flow models and contains only a limited number of free parameters. The applicability of the CAFFE model is demonstrated by a case study for the site of the EPICA (European Project for Ice Coring in Antarctica) ice core in Dronning Maud Land, East Antarctica., Comment: 12 pages, 11 figures, 1 table

We use the semi-inverse method to solve a St. Venant and an Almansi-Michell problem for a prismatic body made of a homogeneous and isotropic elastic material that is stress free in the reference configuration. In the St. Venant problem, only the end faces of the prismatic body are loaded by a set of self-equilibrated forces. In the Almansi-Michell problem self equilibrated surface tractions are also applied on the mantle of the body. The St. Venant problem is also analyzed for the following two cases: (i) the reference configuration is subjected to a hydrostatic pressure, and (ii) stress-strain relations contain terms that are quadratic in displacement gradients. The Signorini method is also used to analyze the St. Venant problem. Both for the St. Venant and the Almansi-Michell problems, the solution of the three dimensional problem is reduced to that of solving a sequence of two dimensional problems. For the St. Venant problem involving a second-order elastic material, the first order deformation is assumed to be an infinitesimal twist. In the solution of the Almansi-Michell problem, surface tractions on the mantle of the cylindrical body are expressed as a polynomial in the axial coordinate. When solving the problem by the semi-inverse method, displacements are also expressed as a polynomial in the axial coordinate. An explicit solution is obtained for a hollow circular cylindrical body with surface tractions on the mantle given by an affine function of the axial coordinate Master of Science

Poisson’s ratio, similar to other material parameters of isotropic elasticity, is determined via experiments corresponding to small strains. Yet at small-strain linear elasticity, Poisson’s ratio has a dual nature; although commonly understood as a geometrical parameter, Poisson’s ratio is also a material parameter. From a geometrical perspective only, the concept of Poisson’s ratio has been extended to large deformations by Beatty and Stalnaker. Here, through a variational analysis, we firstly propose an alternative relationship between the Poisson ratio and stretches at finite deformations such that the nature of Poisson’s ratio as a material parameter is retained. In doing so, we introduce relationships between the Poisson ratio and stretches at large deformations different than those established by Beatty and Stal naker. We show that all the nonlinear definitions of Poisson’s ratio coincide at the reference configuration and thus, material and geometrical descriptions too coincide, at small-strains linear elasticity. Secondly, we employ this variational approach to bring in the notion of nonlinear Poisson’s ratio in peridynamics, for the first time. In particular, we focus on bond-based peridynamics. The nonlinear Poisson’s ratio of bond-based peridynamics coincides with 1/3 for two-dimensional and 1/4 for three-dimensional problems, at the reference configuration.

We present numerical simulations of rectangular woven fabrics made of two, initially orthogonal, families of inextensible fibres. We consider an energy functional which includes both first and second gradients of the displacement. The energy density is expressed in terms of the angles between the fibres directions, using trigonometric functions and their gradients. In particular, we focus on an energy density depending on the squared tangent of the shear angle, which automatically satisfies some natural properties of the energy. The numerical results show that final configurations obtained by the second gradient energies are smoother than the first gradient ones. Moreover, we show that if a second gradient energy is considered, the shear energy is better uniformly distributed.