Abstract

Progressive fracture in quasi-brittle materials such as concrete, rocks, soils, is often treated as strain softening in continuum damage mechanics. Such constitutive relations favour spurious strain localization and ill-posedness of boundary value problems, and call for some kind of regularization. In the present work, two different approaches are presented: a partially regularized local damage model that adjusts the softening part of a stress-strain law depending on the size of the element, and a fully regularized non-local damage model that introduces the characteristic length as an additional material parameter controlling the size of the fracture process zone.In addition, the strain softening of such models usually results in highly complex structural responses, including the snap-back type, and thus in this work we will be discussing non-linearity associated to damage modelling, and a global arc-length method for tracing the equilibrium path will be exposed.Furthermore, in the context of non-local damage models it is crucial to work with fine spatial discretizations at the damage progress zone, so that elements are smaller than the characteristic length. In this regard, a mesh-adaptive technique has been implemented with the purpose of enhancing the efficiency of the numerical analysis.Finally, two classical examples, the three-point bending test, and the single-edge notched beam test, are performed in order to analyse the mesh objectivity of the implemented integral-type non-local damage model, and assess the strengths and limitations of the mesh-adaptive procedure.

Abstract

Progressive fracture in quasi-brittle materials is often treated via strain softening models in continuum damage mechanics. Such constitutive relations favour spurious strain localization and ill-posedness of boundary value problems. The introduction of non-local damage models together with a characteristic length parameter controlling the size of the fracture process zone is known to regularize the problem. In order to account for the non-locality of these models, it is crucial to work with fine spatial discretizations at the damage progress zone. In this paper we present a non-local damage model in combination with a mesh-adaptive finite element technique that can help automatize the analysis of progressive fracture problems in an efficient manner. Classical two-dimensional examples are given to illustrate the presented approach.

Abstract

A new non-local damage model is presented. Non-locality (of integral or gradient type) is incorporated into the model by means of non-local displacements. This contrasts with existing damage models, where a non-local strain or strain-related state variable is used. The new model is very attractive from a computational viewpoint, especially regarding the computation of the consistent tangent matrix needed to achieve quadratic convergence in Newton iterations. At the same time, its physical response is very similar to that of the standard models, including its regularization capabilities. All these aspects are discussed in detail and illustrated by means of numerical examples.