Journal of computational physics

We investigate the curvature effect of a thin, curved elastic interface that separates twosubdomains and exerts a pressure due to a curvature effect. This pressure, which we referto as interface pressure, is similar to the surface tension in fluid mechanics. It is important insome applications, such as the canopy of parachutes, biological membranes of cells, balloons, airbags, etc., as it partially balances a pressure jump between the two sides of aninterface. In this paper, we show that the interface pressure is equal to the trace of thematrix product of the curvature tensor and the Cauchy stress tensor in the tangent plane. We derive the theory for interfaces in both 2-D and 3-D, and present numerical discretizationsfor computing the quality over triangulated surfaces.