Influence of micro-modulus functions on peridynamics simulation of crack propagation and branching in brittle materials

2019 ◽  
Vol 216 ◽  
pp. 106498 ◽  
Author(s):  
Zhiyong Chen ◽  
J. Woody Ju ◽  
Guoshao Su ◽  
Xiaohua Huang ◽  
Shuang Li ◽  
...  
Keyword(s):  
Crack Propagation ◽  
Brittle Materials

scholarly journals A Proper Generalized Decomposition (PGD) approach to crack propagation in brittle materials: with application to random field material properties

2019 ◽  
Vol 65 (2) ◽  
pp. 451-473 ◽  
Author(s):  
Hasini Garikapati ◽  
Sergio Zlotnik ◽  
Pedro Díez ◽  
Clemens V. Verhoosel ◽  
E. Harald van Brummelen
Keyword(s):  
Crack Propagation ◽  
Material Properties ◽  
Computational Cost ◽  
Brittle Materials ◽  
Energy Criterion ◽  
Reduced Order Modeling ◽  
Proper Generalized Decomposition ◽  
Modeling Framework ◽  
Global Energy ◽  
Reduced Order

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.

A MODEL FOR CRACK PROPAGATION BASED ON VISCOUS APPROXIMATION

2011 ◽  
Vol 21 (10) ◽  
pp. 2019-2047 ◽  
Author(s):  
GIULIANO LAZZARONI ◽  
RODICA TOADER
Keyword(s):  
Crack Propagation ◽  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
A Priori ◽  
Brittle Materials ◽  
Continuity Property ◽  
Vanishing Viscosity ◽  
Hausdorff Convergence ◽  
Linearized Elasticity

In the setting of antiplane linearized elasticity, we show the existence of quasistatic evolutions of cracks in brittle materials by using a vanishing viscosity approach, thus taking into account local minimization. The main feature of our model is that the path followed by the crack need not be prescribed a priori: indeed, it is found as the limit (in the sense of Hausdorff convergence) of curves obtained by an incremental procedure. The result is based on a continuity property for the energy release rate in a suitable class of admissible cracks.

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