We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
A Proper Generalized Decomposition (PGD) approach to crack propagation in brittle materials: with application to random field material properties.
- Authors
Garikapati, Hasini; Zlotnik, Sergio; Díez, Pedro; Verhoosel, Clemens V.; van Brummelen, E. Harald
- Abstract
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.
- Subjects
BRITTLE materials; MARKOV random fields; LINEAR elastic fracture mechanics; MECHANICAL properties of condensed matter; RANDOM fields; INHOMOGENEOUS materials; MONTE Carlo method
- Publication
Computational Mechanics, 2020, Vol 65, Issue 2, p451
- ISSN
0178-7675
- Publication type
Academic Journal
- DOI
10.1007/s00466-019-01778-0