A study on finite elements for capturing strong discontinuities

Abstract

SUMMARYThe work focuses on the presently existing families of ÿnite elements with embedded discontinuities and explores the possibilities of obtaining symmetric statically consistent ÿnite elements that alleviate the stress-locking problem. For this purpose, mixed (reduced integration) and assumed enhanced strain techniques are applied to the basic symmetric four-noded element. Numerical simulations show the e ectiveness of the proposed measures.

Embedded strong discontinuity finite elements for fractured geomaterials with variable friction

“…This method is in contrast to a global strategy described in [30,31] or level set methods employed in [44]. The idea is to track the band as it propagates from element to element, explicitly keeping track of the co-ordinates where the band intersects an element edge.…”

“…To some extent, this reflects a physical process in that changing directions on surfaces do create an increased resistance to slip. Elements with opening and perhaps rotational degrees of freedom to the surface, such as [30,48], could change the kinematics of slip, allowing for local areas of opening. For comparison, we also rerun the problem but force the band to propagate in a straight line.…”

“…Other sub-classes of this element type have been described and differ primarily in the way the extra degrees of freedom are condensed; see [30,39] for reviews of the various types of these elements. The amount of slip along the surface is determined by a surface constitutive law.…”

A discrete strong discontinuity approach

“…Many examples of the strong discontinuity approach can be found in literature [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22], which are compared and discussed in [23]. Moreover, towards a unified view of both weak and strong discontinuities, Oliver et al [24,25] introduced a continuum strong discontinuity approach (CSDA), in which a strong discontinuity is consistently obtained from a weak discontinuity when the crack band width tends to zero. In all these works, constant displacement jumps are adopted within each parent finite element, the parent element is a constant strain triangle, a local formulation at element level is introduced and a non-symmetric variational formulation is built.…”

“…As a consequence, the jumps are not continuous across element boundaries and stress locking may occur, depending on the relative position of the discontinuity with respect to the element edges [23,17,26]. Oliver et al [24,25], developed an algorithm aiming to eliminate stress locking. In the work presented in Sancho et al [27], a different approach is introduced where crack path continuity is not enforced and the element is always crossed in the best possible way, thus also avoiding locking.…”