Modelling the dry-contact interface of rigid blocks under torsion and combined loadings: Concavity vs. convexity formulation

A non-smooth-contact-dynamics analysis of Brunelleschi’s cupola: an octagonal vault or a circular dome?

“…This technique is complementary to the introduction of a regularization term that, as discussed at length in [8], annihilates at each time-step the shear-induced dilatation consequent to the associative version of the frictional model used in the numerical solution. This formulation increases the numerical efficiency, it is in agreement with experiments on dry joints [38,12,11] and implies that the frictional response becomes non-associative as the dilatations progress.…”

The role of different sliding resistances in limit analysis of hemispherical masonry domes

“…In the literature, 2D thrust-line, membrane, and 3D thrust-network [4,5], along with convex and concave contact models [3,6,7], have been developed within the limit analysis framework to find the ultimate load factor (or the minimum thickness) for the feasible models of masonry structures. Referring to basic geometries, 2D thrust-line and membrane were applied to find the limit equilibrium of semi-circular arches [8][9][10][11][12][13][14][15][16], hemispherical domes [17][18][19][20] and vaults of given geometries including skew arches, and pavilion, cross and groin vaults [21][22][23][24][25][26].…”

“…A dry joint can be separated, rock, and slide along the locks, while a lock can be cracked at the fracture plane due to bending, shear, torsion or combinations of them. Convex contact model addressed in [7] idealizes the stress state at an interface to the internal forces at the centre of the interface including the normal force fn, two tangential forces ft1 and ft2 normal to each other, two bending moments normal to each other bn 1 and bn 2 and torsion moment t r (Fig. 16a).…”

“…17b). Applying this coefficient, a combination of shear and torsion of the lock is considered, which becomes pure torsion for cf k = 0 and pure shear for cf k = 1 [7]. Given ft2, the tangential force at each lock can be considered as a component of ft2 (ft2 k ) subjected to an intersection point of f t2 and the centreline of the k th lock ( Fig.…”

“…: a) Contact point at the interface centroid according to the convex contact model in[7]; b) contact point as the intersection point of the interface and the network of forces according to the proposed convex contact model for the hemispherical dome; c) internal force on the contact point of the proposed convex contact model.…”