Use of negative stiffness in failure analysis of concrete beams

Abstract

A new concrete analysis method is presented entitled continuous, incremental-only, tangential analysis (CITA). CITA employs piece-wise linear stress-strain curve and a tangent elasticity modulus to calculate stiffness including parts with negative values. Since indefinite structure stiffness matrices generally indicate instability, traditionally they have been avoided. However, since CITA analysis involves introducing damage in steps, the full range of concrete behaviour including the softening portion under tensile cracking can be addressed. Herein CITA is verified against numerical and experimental results for concrete beams, thereby showing faster solutions for non-linear problems than sequentially-linear analysis, while reducing self-imposed restrictions against negative stiffness.

Progressive failure of ductile metals: Description via a three-dimensional coupled CZM–XFEM based approach

“…This coincides with the appearance of a negative eigenvalue of the tangent stiffness operator. This is to be expected as soon as negative eigenvalues signify energy release [60], a phenomenon involved in the creation of damage localization bands. Simply put, in this work an element is considered as a potential candidate for localization when negative work leading to softening is detected, i.e.…”

Numerical study of the behavior of intermeshed steel connections under mixed-mode loading

“…Motivated by the increasing interest in developing more cost-effective steel connections, recent research has focused on a relatively simple intermeshed connection [10][11][12], in which the top and bottom flanges of the beam are connected with dovetails, and the webs are connected by means of a stepped web pattern ( Figure 1). The dovetail connection is intended to resist the axial tension and compression forces in the flanges under bending and/or axial loading, while the stepped web connection is intended to resist primarily shear forces in a single direction.…”

Incremental sequentially linear analysis to control failure for quasi-brittle materials and structures including non-proportional loading

“…If the propagation criterion is met simultaneously in more than one element, the crack is added in the critical element. Other improved approaches are Non-iterative energy based method (NIEM) [25] and Continuous incremental-only tangential analysis (CITA) [26], both of which adopt piecewise linear continuum laws. NIEM uses tangent stiffness to scale the global load increments according to the local discontinuity in the multi-linear stress-strain diagram.…”