Vol. 1, No. 8, 2006

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ISSN: 1559-3959
A one-dimensional variational formulation for quasibrittle fracture

Claudia Comi, Stefano Mariani, Matteo Negri and Umberto Perego

Vol. 1 (2006), No. 8, 1323–1343
Abstract

Besides efficient techniques allowing for the finite-element modeling of propagating displacement discontinuities, the numerical simulation of fracture processes in quasibrittle materials requires the definition of criteria for crack initiation and propagation. Among several alternatives proposed in the literature, the possibility to characterize energetically the discontinuous solution has recently attracted special interest. In this work, the initiation and propagation of cohesive cracks in an inhomogeneous elastic bar, subject to an axial body force is considered. The incremental finite-step problem for the evolving discontinuity is formulated accounting for progressive damage in the cohesive interface. For assigned loading conditions, it is shown that the equilibrium of the system and the position where the crack actually forms can be obtained from the minimality conditions of an energy functional including the bulk elastic energy and the crack surface energy. The subsequent step-by-step propagation of the cohesive crack is also obtained from the minimality conditions of an energy functional defined for each step. The issue of the algorithmic selection of the energetically more convenient solution is briefly discussed.

Keywords
cohesive crack, variational formulation, finite-step problem
Milestones
Received: 21 November 2005
Revised: 12 April 2006
Accepted: 28 June 2006
Published: 1 December 2006
Authors
Claudia Comi
Dipartimento di Ingegneria Strutturale
Politecnico di Milano
Piazza L. da Vinci 32
20133 Milano
Italy
Stefano Mariani
Dipartimento di Ingegneria Strutturale
Politecnico di Milano
Piazza L. da Vinci 32
20133 Milano
Italy
Matteo Negri
Dipartimento di Matematica
Università degli Studi di Pavia
Via Ferrata 1
27100 Pavia
Italy
Umberto Perego
Dipartimento di Ingegneria Strutturale
Politecnico di Milano
Piazza L. da Vinci 32
20133 Milano
Italy