A two-scale approach for fluid flow in fracturing porous media

A derivation is given of two-scale models that are able to describe defornlation and fluid flow in a progressively fracturing porous medium. From the micromechanics of the flow in the cavity, identities are derived that couple the local momentum and the mass balances to the governing equations for a porous medium, which are assumed to hold on the macroscopic scale. By exploiting the partition-of-unity property of the finite element shape functions, the position and direction of the fractures are independent from the underlying discretization. The finite element equations are derived for this two-scale approach and integrated over time. The resulting discrete equations are nonlinear due and the non-linearity of the coupling terms and the possible use of a cohesive crack model. Examples are given to show the versatility of the approach

A Non-reductionist Approach to Trust

International audienceWe develop in this chapter a conceptual and logical model of social trust. We first present a modal logic of mental attitudes and action in which the concepts of plausible belief, certain belief, and a possibility order over formulas can be characterized. Then, we apply the logic to the formalization of the truster’s expectation about some fundamental properties of the trustee (trustee’s opportunity to accomplish a given task, his skills, abilities, and willingness to perform a given action for the accomplishment of the task). A, part of this chapter is devoted to discuss and formalize some concepts related to trust such as distrust, mistrust, lack of trust, and delegation. Finally, a concept of comparative trust is presented