Problems with high strain localisation, such as those characterised by shear band formation in metals or soils or by micro crack creation and coalescence phenomena (that leads to mechanically macro cracks) typical of brittle or quasi-brittle solids, is a crucial task in material’s simulation in various engineering fields. As is well known, the numerical simulation of such class of problems can lead to several difficulties (computational instabilities, divergence or non-uniqueness of the solution, etc) due to the discontinuous displacement filed which develops in narrow highly strained zones in the material. Furthermore, by using classical smeared models for the numerical simulation of strain localisation processes, a strong mesh-dependence usually arise: the dissipated energy in strain localisation regions decreases with mesh refinement, and some specific strategies and appropriate corrections to standard approaches such as remeshing or mesh adaptivity, finite elements’ enrichment, use of interface elements, discontinuous formulations and so on, must be introduced in order to obtain realistic results. Among the above approaches, the discontinuous displacement field approach has shown to be a simple and convenient tools to tackle the fracture process phenomena in brittle solids. In the present chapter, a 2D stress-based embedded displacement discontinuities finite element formulation is proposed to represent the fracture process in brittle or quasi-brittle solids and structures. A cohesive behaviour of the crack, formulated through a fracture energy approach, is considered and a new simple stress-based implementation of the mechanical effects of a discontinuous displacement field is formulated: by introducing an appropriate FE stress field correction (stress field relaxation similar to that used in standard plasticity-like FE numerical approaches) at the level of the Gauss points, the mechanical effects of the opening and sliding stresses transmitted across the crack faces can be represented. The proposed approach does not need the explicit introduction of discontinuous or modified shape functions to reproduce the strain localisation effect. To generalise the mechanical material’s behaviour, the uncracked portion of the material is allowed to behave as a linear elastic or an elastic-plastic one. Once a crack has been introduced in a FE, appropriate crack bridging and shearing laws are considered to evaluate the normal and tangential (friction) stresses transmitted across the crack faces. In the present chapter, after a brief literature review on computational techniques developed for such a class of problems, the kinematics of a strong discontinuity is firstly presented, and its variational FE implementation is illustrated. Then the proposed discontinuous FE stress-based formulation is described and discussed. Finally, 2D fracture mechanics problems are solved through the proposed procedure to predict the load-displacement behaviour of brittle structures as well as the crack paths inside the material. In order to assess the capability of the proposed formulation, some comparisons with literature and with experimental results are presented.

Computational Fracture Mechanics: a Novel Discontinuous-Like FE Approach for Brittle Solids / Brighenti, Roberto. - (2010), pp. 231-264.

Computational Fracture Mechanics: a Novel Discontinuous-Like FE Approach for Brittle Solids

BRIGHENTI, Roberto
2010-01-01

Abstract

Problems with high strain localisation, such as those characterised by shear band formation in metals or soils or by micro crack creation and coalescence phenomena (that leads to mechanically macro cracks) typical of brittle or quasi-brittle solids, is a crucial task in material’s simulation in various engineering fields. As is well known, the numerical simulation of such class of problems can lead to several difficulties (computational instabilities, divergence or non-uniqueness of the solution, etc) due to the discontinuous displacement filed which develops in narrow highly strained zones in the material. Furthermore, by using classical smeared models for the numerical simulation of strain localisation processes, a strong mesh-dependence usually arise: the dissipated energy in strain localisation regions decreases with mesh refinement, and some specific strategies and appropriate corrections to standard approaches such as remeshing or mesh adaptivity, finite elements’ enrichment, use of interface elements, discontinuous formulations and so on, must be introduced in order to obtain realistic results. Among the above approaches, the discontinuous displacement field approach has shown to be a simple and convenient tools to tackle the fracture process phenomena in brittle solids. In the present chapter, a 2D stress-based embedded displacement discontinuities finite element formulation is proposed to represent the fracture process in brittle or quasi-brittle solids and structures. A cohesive behaviour of the crack, formulated through a fracture energy approach, is considered and a new simple stress-based implementation of the mechanical effects of a discontinuous displacement field is formulated: by introducing an appropriate FE stress field correction (stress field relaxation similar to that used in standard plasticity-like FE numerical approaches) at the level of the Gauss points, the mechanical effects of the opening and sliding stresses transmitted across the crack faces can be represented. The proposed approach does not need the explicit introduction of discontinuous or modified shape functions to reproduce the strain localisation effect. To generalise the mechanical material’s behaviour, the uncracked portion of the material is allowed to behave as a linear elastic or an elastic-plastic one. Once a crack has been introduced in a FE, appropriate crack bridging and shearing laws are considered to evaluate the normal and tangential (friction) stresses transmitted across the crack faces. In the present chapter, after a brief literature review on computational techniques developed for such a class of problems, the kinematics of a strong discontinuity is firstly presented, and its variational FE implementation is illustrated. Then the proposed discontinuous FE stress-based formulation is described and discussed. Finally, 2D fracture mechanics problems are solved through the proposed procedure to predict the load-displacement behaviour of brittle structures as well as the crack paths inside the material. In order to assess the capability of the proposed formulation, some comparisons with literature and with experimental results are presented.
2010
9781617281051
9781617287046
Computational Fracture Mechanics: a Novel Discontinuous-Like FE Approach for Brittle Solids / Brighenti, Roberto. - (2010), pp. 231-264.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11381/2304954
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