Robert Gracie

Bio: Robert Gracie is an academic researcher from University of Waterloo. The author has contributed to research in topics: Extended finite element method & Finite element method. The author has an hindex of 16, co-authored 61 publications receiving 2402 citations. Previous affiliations of Robert Gracie include Geological Survey of Canada & Northwestern University.

A review of extended/generalized finite element methods for material modeling

Abstract: The extended and generalized finite element methods are reviewed with an emphasis on their applications to problems in material science: (1) fracture, (2) dislocations, (3) grain boundaries and (4) phases interfaces. These methods facilitate the modeling of complicated geometries and the evolution of such geometries, particularly when combined with level set methods, as for example in the simulation growing cracks or moving phase interfaces. The state of the art for these problems is described along with the history of developments.

Immersed particle method for fluid–structure interaction

Abstract: A method for treating fluid-structure interaction of fracturing structures under impulsive loads is described. The coupling method is simple and does not require any modifications when the structure fails and allows fluid to flow through openings between crack surfaces. Both the fluid and the structure are treated by meshfree methods. For the structure, a Kirchhoff-Love shell theory is adopted and the cracks are treated by introducing either discrete (cracking particle method) or continuous (partition of unity-based method) discontinuities into the approximation. Coupling is realized by a master-slave scheme where the structure is slave to the fluid. The method is aimed at problems with high-pressure and low-velocity fluids, and is illustrated by the simulation of three problems involving fracturing cylindrical shells coupled with fluids.

An adaptive multiscale method for quasi-static crack growth

Abstract: This paper proposes an adaptive atomistic- continuum numerical method for quasi-static crack growth. The phantom node method is used to model the crack in the continuum region and a molecular statics model is used near the crack tip. To ensure self-consistency in the bulk, a virtual atom cluster is used to model the material of the coarse scale. The coupling between the coarse scale and fine scale is realized through ghost atoms. The ghost atom positions are interpolated from the coarse scale solution and enforced as boundary conditions on the fine scale. The fine scale region is adaptively enlarged as the crack propagates and the region behind the crack tip is adaptively coarsened. An energy criterion is used to detect the crack tip location. The triangular lattice in the fine scale region corresponds to the lattice structure of the (111) plane of an FCC crystal. The Lennard-Jones potential is used to model the atom---atom interactions. The method is implemented in two dimensions. The results are compared to pure atomistic simulations; they show excellent agreement.

Fast integration and weight function blending in the extended finite element method

Abstract: Two issues in the extended finite element method (XFEM) are addressed: efficient numerical integration of the weak form when the enrichment function is self-equilibrating and blending of the enrichment. The integration is based on transforming the domain integrals in the weak form into equivalent contour integrals. It is shown that the contour form is computationally more efficient than the domain form, especially when the enrichment function is singular and/or discontinuous. A method for alleviating the errors in the blending elements is also studied. In this method, the enrichment function is pre-multiplied by a smooth weight function with compact support to allow for a completely smooth transition between enriched and unenriched subdomains. A method for blending step function enrichment with singular enrichments is described. It is also shown that if the enrichment is not shifted properly, the weighted enrichment is equivalent to the standard enrichment. An edge dislocation and a crack problem are used to benchmark the technique; the influence of the variables that parameterize the weight function is analyzed. The resulting method shows both improved accuracy and optimum convergence rates and is easily implemented into existing XFEM codes

The extended/generalized finite element method: An overview of the method and its applications

Abstract: An overview of the extended/generalized finite element method (GEFM/XFEM) with emphasis on methodological issues is presented. This method enables the accurate approximation of solutions that involve jumps, kinks, singularities, and other locally non-smooth features within elements. This is achieved by enriching the polynomial approximation space of the classical finite element method. The GEFM/XFEM has shown its potential in a variety of applications that involve non-smooth solutions near interfaces: Among them are the simulation of cracks, shear bands, dislocations, solidification, and multi-field problems. Copyright © 2010 John Wiley & Sons, Ltd.

A review of extended/generalized finite element methods for material modeling

Abstract: The extended and generalized finite element methods are reviewed with an emphasis on their applications to problems in material science: (1) fracture, (2) dislocations, (3) grain boundaries and (4) phases interfaces. These methods facilitate the modeling of complicated geometries and the evolution of such geometries, particularly when combined with level set methods, as for example in the simulation growing cracks or moving phase interfaces. The state of the art for these problems is described along with the history of developments.

Dual‐horizon peridynamics

Abstract: Summary In this paper, we develop a dual-horizon peridynamics (DH-PD) formulation that naturally includes varying horizon sizes and completely solves the ‘ghost force’ issue Therefore, the concept of dual horizon is introduced to consider the unbalanced interactions between the particles with different horizon sizes The present formulation fulfills both the balances of linear momentum and angular momentum exactly Neither the ‘partial stress tensor’ nor the ‘slice’ technique is needed to ameliorate the ghost force issue We will show that the traditional peridynamics can be derived as a special case of the present DH-PD All three peridynamic formulations, namely, bond-based, ordinary state-based, and non-ordinary state-based peridynamics, can be implemented within the DH-PD framework Our DH-PD formulation allows for h-adaptivity and can be implemented in any existing peridynamics code with minimal changes A simple adaptive refinement procedure is proposed, reducing the computational cost Both two-dimensional and three-dimensional examples including the Kalthoff–Winkler experiment and plate with branching cracks are tested to demonstrate the capability of the method Copyright © 2016 John Wiley & Sons, Ltd

A unified phase-field theory for the mechanics of damage and quasi-brittle failure

Abstract: Being one of the most promising candidates for the modeling of localized failure in solids, so far the phase-field method has been applied only to brittle fracture with very few exceptions. In this work, a unified phase-field theory for the mechanics of damage and quasi-brittle failure is proposed within the framework of thermodynamics. Specifically, the crack phase-field and its gradient are introduced to regularize the sharp crack topology in a purely geometric context. The energy dissipation functional due to crack evolution and the stored energy functional of the bulk are characterized by a crack geometric function of polynomial type and an energetic degradation function of rational type, respectively. Standard arguments of thermodynamics then yield the macroscopic balance equation coupled with an extra evolution law of gradient type for the crack phase-field, governed by the aforesaid constitutive functions. The classical phase-field models for brittle fracture are recovered as particular examples. More importantly, the constitutive functions optimal for quasi-brittle failure are determined such that the proposed phase-field theory converges to a cohesive zone model for a vanishing length scale. Those general softening laws frequently adopted for quasi-brittle failure, e.g., linear, exponential, hyperbolic and Cornelissen et al. (1986) ones, etc., can be reproduced or fit with high precision. Except for the internal length scale, all the other model parameters can be determined from standard material properties (i.e., Young’s modulus, failure strength, fracture energy and the target softening law). Some representative numerical examples are presented for the validation. It is found that both the internal length scale and the mesh size have little influences on the overall global responses, so long as the former can be well resolved by sufficiently fine mesh. In particular, for the benchmark tests of concrete the numerical results of load versus displacement curve and crack paths both agree well with the experimental data, showing validity of the proposed phase-field theory for the modeling of damage and quasi-brittle failure in solids.