A proper generalized decomposition (PGD) approach to crack propagation in brittle materials: with application to random field material properties

Hasini Garikapati (Corresponding author), Sergio Zlotnik, Pedro Díez, Clemens V. Verhoosel, E. Harald van Brummelen

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Understanding the failure of brittle heterogeneous materials is essential in many applications. Heterogeneities in material properties are frequently modeled through random fields, which typically induces the need to solve finite element problems for a large number of realizations. In this context, we make use of reduced order modeling to solve these problems at an affordable computational cost. This paper proposes a reduced order modeling framework to predict crack propagation in brittle materials with random heterogeneities. The framework is based on a combination of the Proper Generalized Decomposition (PGD) method with Griffith’s global energy criterion. The PGD framework provides an explicit parametric solution for the physical response of the system. We illustrate that a non-intrusive sampling-based technique can be applied as a post-processing operation on the explicit solution provided by PGD. We first validate the framework using a global energy approach on a deterministic two-dimensional linear elastic fracture mechanics benchmark. Subsequently, we apply the reduced order modeling approach to a stochastic fracture propagation problem.

Original languageEnglish
Pages (from-to)451-473
Number of pages23
JournalComputational Mechanics
Issue number2
Early online date26 Oct 2019
Publication statusPublished - 1 Feb 2020



  • Brittle fracture
  • Crack propagation
  • Model order reduction
  • Monte Carlo method
  • Proper Generalized Decomposition
  • Random fields

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