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Phase field approximation of dynamic brittle fracture. (English) Zbl 1311.74106
Summary: Numerical methods that are able to predict the failure of technical structures due to fracture are important in many engineering applications. One of these approaches, the so-called phase field method, represents cracks by means of an additional continuous field variable. This strategy avoids some of the main drawbacks of a sharp interface description of cracks. For example, it is not necessary to track or model crack faces explicitly, which allows a simple algorithmic treatment. The phase field model for brittle fracture presented by C. Kuhn and R. Müller [“A continuum phase field model for fracture”, Eng. Fract. Mech. 77, No. 18, 3625–3634 (2010)] assumes quasi-static loading conditions. However dynamic effects have a great impact on the crack growth in many practical applications. Therefore this investigation presents an extension of the quasi-static phase field model for fracture from [loc. cit.] to the dynamic case. First of all Hamilton’s principle is applied to derive a coupled set of Euler-Lagrange equations that govern the mechanical behaviour of the body as well as the crack growth. Subsequently the model is implemented in a finite element scheme which allows to solve several test problems numerically. The numerical examples illustrate the capabilities of the developed approach to dynamic fracture in brittle materials.

##### MSC:
 74R10 Brittle fracture 74S05 Finite element methods applied to problems in solid mechanics
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