Numerical modeling of intraplate deformation: Simple mechanical models of continental collision

Abstract

We study a model of continental collision in which one of the continents acts as a rigid die indenting the other plate which flows as an incompressible viscoplastic medium. We consider two extreme cases of plane deformation: (1) plane strain which corresponds to an infinitely thick lithospheric plate, and (2) plane stress corresponding to a very thin plate. Deformation of the lithosphere, a thick plate, should be intermediate between those extremes. We found that the flow in the plane strain case is quite similar to that obtained by slip line, theory. The plane stress results are quite different, since in this case most of the plate shortening is taken up by the thickening of the lithosphere. We also explored the role of boundary conditions on the flow, in particular, the role of the side walls containing the flow of the lithosphere. In the case of a free lateral boundary the main feature is a flow of matter toward this free wall and a S‐like pattern for the horizontal stress field. For a rigid wall, on the other hand, the plane strain and the plane stress results are quite different. In the first case, there is a large return flow on the sides of the punch, the material being extruded along the only free surface available. In the plane stress case, the return flow disappears, and the material displaced by the penetration of the die tends to thicken the plate. The role of a nonlinear constitutive relation is studied for power law creep. As the power of the flow limit increases, the flow retains its general features, but the deformation localizes creating sharper contrasts between high and low strain rate areas; in plane stress, the effect of nonlinearity is to increase the contrasts in vertical motion. Available data for Asia are discussed in the light of the new results.