Continuum approach to the numerical simulation of material failure in concrete

Abstract

Some new aspects of the continuum strong discontinuity approach (CSDA) to model material failure in geomaterials are addressed. A new global algorithm, for tracking multiple crack lines/surfaces in 2D/3D cases is proposed. It is based on solving a simple heat conduction‐like problem accompanying the standard mechanical algorithm. A viscous perturbation method on the crack surface is also proposed to remedy the instabilities caused by mutual interactions of multiple developing cracks. A simple procedure to compute the critical time step that ensures algorithmic uniqueness is then provided. Numerical simulations of two‐ and three‐dimensional problems displaying a multi‐crack pattern are finally presented. Copyright © 2004 John Wiley & Sons, Ltd.

A discrete strong discontinuity approach

“…The first could be rewritten in a more general form such as: microcracking develops at the onset of strain localization. In the Continuum Strong Discontinuity Approach, this condition is automatically satisfied through the definition of the acoustic tensor, as presented in Oliver et al [25]. As it is shown in Section 5, both in the discrete-interface approach and in the DSDA this condition is replaced by an initiation criterion, which must be defined separately.…”

“…Thus, in the discrete crack approach, although continuum and non-continuum can be characterized through different material types and constitutive formats as stated in Oliver et al [25], these are not completely independent from each other. Apart from the usual traction continuity condition, the link between continuum and discontinuum is introduced through the definition of an initiation criterion, given in Section 5.…”

“…In [24,25], the strong discontinuity is obtained as a limit case of a weak discontinuity when the crack band width tends to zero. As a consequence, the discrete law can be regarded as a projection of the standard continuum constitutive law into the discontinuity.…”

“…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.…”