Progressive fracture in quasi-brittle materials is often treated via strain softening models in continuum damage mechanics. Such constitutive relations favour spurious strain localization and ill-posedness of boundary value problems. The introduction of non-local damage models together with a characteristic length parameter controlling the size of the fracture process zone is known to regularize the problem. In order to account for the non-locality of these models, it is crucial to work with fine spatial discretizations at the damage progress zone. In this paper we present a non-local damage model in combination with a mesh-adaptive finite element technique that can help automatize the analysis of progressive fracture problems in an efficient manner. Classical two-dimensional examples are given to illustrate the presented approach.

A new mixed displacement-pressure element for solving solid-pore fluid interaction problems is presented. In the resulting coupled system of equations, the balance of momentum equation remains unaltered, while the mass balance equation for the pore fluid is stabilized with the inclusion of higher-order terms multiplied by arbitrary dimensions in space, following the finite calculus (FIC) procedure. The stabilized FIC-FEM formulation can be applied to any kind of interpolation for the displacements and the pressure, but in this work, we have used linear elements of equal order interpolation for both set of unknowns. Examples in 2D and 3D are presented to illustrate the accuracy of the stabilized formulation for solid-pore fluid interaction problems. 111 materials, they have been the basis for much subsequent research in geophysics, soil and rock mechanics.The first numerical solution of Biot's formulation was obtained by Ghaboussi and Wilson [11], and the work was further developed by Zienkiewicz et al. [12,13]. Later on, because of the increasing interest in nonlinear applications, Zienkiewicz and co-workers expanded the theory to a generalized incremental form for nonlinear materials and large deformation problems [14,15].The mathematical formulation of solid skeleton and pore fluid interaction presented here is based on the model proposed by Zienkiewicz et al. [12]. The problem was originally formulated for fully saturated conditions in terms of the solid matrix displacement u i , the mean fluid velocity relative to the solid phase w i and the fluid pore pressure p. However, in many geo-mechanical problems with no high-frequency phenomena involved, the fluid relative velocity w i can be neglected and so the equations can be simplified to work with only two main variables: the displacements u i and the pressure p [16].Although in this work we have solved a two-phase medium, that is, soil and water, the generalization to three-phase problems, such as those encountered in unsaturated soils or in oil-gas-soil interaction, are possible extensions of the numerical approach presented here. In this regard, a simple extension of the two-phase formulation to semi-saturated problems was proposed by Zienkiewicz et al. [17] and further development was reported by Gawin and Schrefler [18], and Khoei et al. [19].In the limit of nearly incompressible pore fluid and small permeability, the coupled poromechanics formulations suffer from instability problems. Finite elements exhibit locking in the pressure field and spurious oscillations in the numerical solution for the pressure appear near this fully incompressible limit, due to the violation of the so-called Babuska-Brezzi conditions [20,21]. The oscillations can be overcome by locally refining the mesh and by using shape functions of the displacement field one order higher than those of the pressure field. In practical applications, this is, however, not the best approach because of the increment in the computational cost. In this sense, stabilization methods have been found ...

No abstract

Double-curvature dams are unique structures for several reasons. Their behaviour changes significantly after joint grouting, when they turn from a set of independent cantilevers into a monolithic structure with arch effect. The construction process has a relevant influence on the stress state, due to the way in which self-weight loads are transmitted, and to the effect on the dissipation of the hydration heat. Temperature variations in the dam body with respect to those existing at joint grouting generate thermal stresses that may be important in the stress state of the structure. It is thus essential to have a realistic estimate of this thermal field, also called reference or