A continuum level-set model of fracture
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ORIGINAL PAPER
A continuum level-set model of fracture Antonios I. Arvanitakis
Received: 19 March 2020 / Accepted: 20 August 2020 © Springer Nature B.V. 2020
Abstract This work is devoted to the modeling of brittle and ductile fracture under the use of the levelset method. Within the proposed model a level-set function is taken as a smooth function that represents brittle damage in an implicit manner, that is the zero level-set of the continuous function coincides with the boundaries of the damage. Under the utilization of a regularization parameter that can be interpreted as a material’s internal length, crack faces of zero width are replaced by interfaces of finite width scaled by the length parameter. An energy functional is adopted and after following a variational field approach the equations of damage nucleation and propagation are revealed. Simple numerical examples indicate that the proposed levelset model is in good agreement with other successful models for brittle fracture. Moreover, ductile fracture is successfully captured by introducing an additional level set function so as to describe three distinct phases within the body: the damaged area, the rigid-perfectly plastic region and the elastic region. A simple example of damage propagation provides the behavior of a ductile material.
A. I. Arvanitakis (B) Department of Materials Science and Engineering, Laboratory of Mathematical Modeling and Scientific Computing, University of Ioannina, 45110 Ioannina, Greece e-mail: [email protected]
Keywords Level-set function · Variational fracture approach · Brittle fracture · Ductile fracture · Crack propagation
1 Introduction Fracture is the most common physical phenomenon in solids standing as a significant failure mechanism. Almost every engineering structure is constructed with primary consideration the prevention of crack nucleation and crack propagation. A qualitative and quantitative study of fracture was proposed in the celebrated work by Griffith (1920) and later by Irwin (1957) defining the well known theory of Linear Elastic Fracture Mechanics. Griffith’s motivation started by searching a way to explain the failure of brittle materials. According to Griffith the growth of a crack within a material requires an increase in the surface energy in expense of the elastic energy in the bulk material. On the other hand, Irwin’s modification provided a way to explain crack propagation in ductile materials also. Linear Elastic Fracture Mechanics provides a useful tool for crack propagation in linear materials that can be used to make exact predictions on the failure of cracked structures and components. In the continuum mechanics regime a crack is identified as a sharp surface of zero thickness, where certain quantities suffer discontinuities. This explicit interpretation of the crack in a continuum causes multiple numerical issues restricting crack tracking to simpler
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topologies. However, there have been developed new approaches that provide regularized crack models s
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