On the Stress Singularities at Multimaterial Interfaces and Related Analogies With Fluid Dynamics and Diffusion

Indentation of an elastic half-plane (a) by a frictionless rigid flat punch and (b) by an elastic punch with corner angles other than π∕2

Intersection of a solid or liquid island with a solid substrate. θ is the wetting angle and γsv, γis, and γvi are, respectively, the interfacial tensions associated with substrate-vapor, island-substrate, and vapor-island interfaces.

Scheme of the geometry of a grain triple junction. The grains are composed of the same material, and grain boundaries are assumed to be freely sliding.

Atomic structure of the multiple-twin junction obtained after MD simulation (a). Shaded rings indicate the grain boundaries. Contour plot of the stress field in the vertical direction around the triple junction (b). The right scale stress are in units of kbar (reprinted from Ref. 34).

Scheme of a multimaterial junction

Some interface problems addressed by Rao (reprinted from Ref. 64)

Schemes of a two-dimensional single-material wedge (a) and of a two-dimensional composite wedge (b)

Scheme of a multimaterial junction with a geometric symmetry and subjected to symmetric (Mode I) (a) and to skew-symmetric (Mode II) (b) deformation

Scheme of a multimaterial junction with a reentrant corner (a) and with a crack (b). Case (a) is usually referred to as a multimaterial wedge.

Subproblems for the evaluation of the eigenequation for a bimaterial junction with (a) E1→∞ and (b) E2→∞

Subproblems for the evaluation of the eigenequation for a trimaterial junction with (a) E3→∞ and (b) E3→0

Three examples of trimaterial junctions whose limit eigenvalues are reported in Table 3

A scheme of a corner negotiated by three immiscible viscous fluids

Sketch of the stream lines for symmetric (a) and (b) and skew-symmetric (c) and (d) flows around a corner

Sketch of the stream lines in corner eddies for γ=60deg, reprinted from Ref. 123. The relative dimensions of the eddies are approximately correct and the relative intensities are indicated.

Scheme of a composite material subjected to antiplane shear deformation

Scheme of the St. Venant torsion problem with a composite cylinder (a). Relationship between the displacements in polar coordinates computed in the reference systems with origin O (singular point) and C (center of twist) (b).

Scheme of a FGM bimaterial junction (a) and variation of the elastic moduli in the two-material regions (b). This variation can be completely general, without any kind of symmetry.