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The numerical assessment of fracture has gained importance in fields like the safety analysis of technical structures or the hydraulic fracturing process. The modelling technique discussed in this work is the phase field method which introduces an additional scalar field. The smooth phase field distinguishes broken from undamaged material and thus describes cracks in a continuum. The model consists of two coupled partial differential equations -the equation of motion including the constitutive behaviour of the material and a phase field evolution equation. The crack growth follows implicitly from the solution of this system of PDEs. The numerical solution with finite elements can be accelerated with an algorithm that performs computationally extensive tasks on a graphic processing unit (GPU). A numerical example illustrates the capability of the model to reproduce realistic features of dynamic brittle fracture.In this work a linear elastic body Ω with Lamé parameters λ, µ and mass density ρ is considered. The external boundary is denoted by ∂Ω = ∂Ω u ∪∂Ω t . Furthermore, the body may contain internal discontinuities, i.e. cracks, Γ, see Fig. 1. The displacement of a point x is denoted as u (x, t) where the field u (x, t) satisfies Dirichlet boundary conditions u (x, t) = u * (x, t) on ∂Ω u and Neumann boundary conditions σn = t * on ∂Ω t . Herein, σ is the stress tensor. The discontinuities Γ are approximated by a phase field s (x, t) which varies smoothly between s = 1 in undamaged material and s = 0 in the broken material (see Fig. 2). By means of s the fracture energy is approximated bywhere G c is the fracture resistance and is a length scale characterizing the crack width. In the limit → 0 the phase field ∂Ω u Ω Γ ∂Ω t t * n Fig. 1: Body with internal discontinuities (sharp cracks) Γ. s(x, t) ∂Ω t ∂Ω u Ω n t * Fig. 2: Approximation of internal discontinuities by a phase field s(x, t).approximation of the fracture energy (1) is exact, see [1]. The phase field s is connected to the elastic energy density ψ e to model the loss of stiffness in the broken material. In order to achieve a more realistic crack behaviour in compression, the compressive part of ψ e is not affected by the crack field. As in [2] the elastic energy density readswith tr − (ε) = min {0, tr(ε)}, tr + (ε) = max {0, tr(ε)}, the n-dimensional bulk modulus K n = λ + 2 n µ and the deviatoric part e of the linearized strain tensor ε = 1 2 ∇u + (∇u) T . The Cauchy stress tensor is given by σ = ∂ψ e ∂ε .

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