Stress singularities in a poroelastic wedge with stringer-reinforced faces

Source abstract

Within the framework of the Cowin–Nunziato theory for poroelastic continua, we analyze the stress field in the neighborhood of the apex of a poroelastic wedge under plane-strain conditions. The configuration considered involves radial wedge faces that are mechanically coupled to two reinforcing elements (stringers), idealized as perfectly rigid in tension and perfectly flexible in bending, and subjected to prescribed tensile loads. On the basis of asymptotic representations of the governing poroelasticity equations in the vicinity of the wedge apex, a local solution to the associated homogeneous boundary-value problem is derived, and the class of energetically admissible (i.e. real-valued) solutions is determined. Several particular configurations corresponding to distinct wedge opening angles are examined. The resulting singularity exponents are purely geometric in nature: they depend solely on the wedge opening angle and reproduce the classical elastic spectrum. In contrast, the Cowin–Nunziato constitutive parameters, namely, the void diffusion coefficient, the micro–macro coupling parameter, and the void rigidity, affect only the amplitude of the near-apex field and do not influence the order of its singularity. Similarly, the tensile forces transmitted by the stringers determine the amplitude of the local field but leave the singularity exponents unchanged. The dependence of these exponents on the wedge opening angle is illustrated graphically, and the critical opening angles delimiting the transition between the low-stress regime and the stress-concentration regime are identified.