No abstract

In computational structural analyses, strong discontinuities, such as propagating cracks in concrete structures, joints in rocks or shear bands in soft soils, the highly accelerated moisture transport in the opening discontinuities has to be taken into account. The paper is concerned with an Extended Finite Element model for the numerical representation of crack propagation in partially saturated porous materials. Based on an extended variational formulation for the simulation of moisture transport in cracks, enhanced approximations of the displacement field and the moisture flux across the discontinuity are adopted. Model descriptionDiscontinuities, such as propagating cracks, are characterized by a disturbance of the overall distribution of the field variables within a very small length. To resolve the small and the large scale portion of the solution, the Extended Finite Element method [4], exploiting the Partition of Unity property of shape functions, offers the possibility to include arbitrary enhancement functions into the finite element approximation to improve the local approximation of non-smooth distributions of field variables, such as discontinuities of the displacement field or the fluid pressure field across cracks [3,5]. For an element fully crossed by a crack, the Sign function is used for the representation of the discontinuous displacement field across the crack.where n r is the number of nodes used for the spatial discretization of the regular displacement field (superscript r). In coupled hygro-mechanical problems, involving porous materials with cracks, the flow of the pore fluid across the crack will be discontinuous (Fig.1). Adopting poromechanics as the modeling framework, and assuming pores to be filled by an ideal mixture of water vapor and dry air (subscript g), the two-field problem is characterized by the displacement field u and the capillary pressure p c as degrees of freedom. Considering a jump of the moisture flux across the discontinuity denoted by ∂ S leads to the weak form of the mass balanceConsidering the local mass balance at the discontinuity (i.e. on the small scale level) provides the normal component of the moisture flux across the crack as q * n = n S · q l,∂ S Ω = w ρ

No abstract