Carlos Armando Duarte

University of Illinois, Urbana-Champaign | UIUC · Department of Civil and Environmental Engineering

A robust and efficient strategy is proposed to simulate mechanical problems involving cohesive fractures. This class of problems is characterized by a global structural behavior that is strongly affected by localized non-linearities at relatively small-sized critical regions. The proposed approach is based on the division of a simulation into a sui...

Predicting localized, nonlinear, thermoplastic behavior and residual stresses and deformations in structures subjected to intense heating is a prevalent challenge in a range of modern engineering applications. The authors present a generalized finite element method (GFEM) targeted at this class of problems, involving the solution of intrinsically p...

This paper presents a two-scale extension of the generalized finite element method (GFEM) which allows for static fracture analyses as well as fatigue crack propagation simulations on fixed, coarse hexa-hedral meshes. The approach is based on the use of specifically-tailored enrichment functions computed on-the-fly through the use of a fine-scale b...

This paper presents a coupled hydro-mechanical formulation for the simulation of non-planar three-dimensional hydraulic fractures. Deformation in the rock is modeled using linear elasticity and the lubrication theory is adopted for the fluid flow in the fracture. The governing equations of the fluid flow and elasticity and the subsequent discretiza...

In this paper, we present an extension of the Stable Generalized FEM (SGFEM) for 3-D fracture mechanics problems. Numerical experiments show that the use of available singular enrichment bases derived from the 2-D asymptotic crack tip solution leads to a severe loss of accuracy in the SGFEM. An enrichment scheme based on singular bases and linear p...

A methodology for an efficient analysis of 3-D fracture mechanics problems in linear viscoelastic media is presented. It combines the Elastic–Viscoelastic Correspondence Principle (EVCP), a Generalized Finite Element Method (GFEM), and an inverse Laplace transform (ILT) method to compute Energy Release Rate (ERR) and Crack Mouth Opening Displacemen...

Intentional creation and propagation of fractures driven by fluid under high pressure have several applications in oil and gas exploration, geological mining, disposal of toxic waste, flow of molten magma within crevices/fissures, etc. Due to the need to design hydraulic fractures, especially in the oil and gas industry, and the limitation of their...

Fully 3-D models can be prohibitively expensive when dealing with industrial-scale problems while plate and shell models are not able to capture localized 3-D effects around cracks, welds, and other structural features. This paper presents an iterative multiscale Generalized Finite Element Method (GFEM) able to automatically couple 3-D solid and sh...

This work presents a 3-D Generalized/eXtended Finite Element Method (GFEM) simulation of hydraulic fracture process by coupling the solid/rock domain equations with the fluid flow within the fracture using the algorithm reported in [1]. The GFEM, which is based on p-hierarchical FEM enrichments, is combined with mesh adaptivity for the robust and c...

Using a robust three-dimensional generalized/eXtended finite element method (G/XFEM) algorithm, this paper presents a comprehensive study on multiple hydraulic fracture propagation and their interactions under different treatment conditions. Aimed at capturing the complex multiphysics behavior, the resulting nonplanar fracture footprints under mixe...

The Generalized/eXtended Finite Element Method (G/XFEM) has been established as an approach to provide optimally convergent solutions for classes of problems that are challenging for the standard version of the Finite Element Method (FEM). For problems with non-smooth solutions, such as those within the Linear Elastic Fracture Mechanics (LEFM) cont...

In this article, a 3-D methodology for the simulation of hydraulic fracture propagation using the Generalized Finite Element Method (GFEM) is extended for the simultaneous propagation and interaction of multiple hydraulic fractures. A 3-D isotropic elastic material for the rock and Reynolds lubrication theory for the fluid flow in the fractures are...

A numerical method to extract stress intensity factors (SIFs) from 3D fractures in anisotropic materials is presented. The formulation of a displacement correlation method that is valid for linear elastic materials with arbitrary symmetry in their elastic properties is given in detail. An algorithm for the numerical implementation of the method is...

This paper proposes a novel methodology for 3-D simulations of pressure waves propagating in fluid-filled fractures in an elastic body -- the so-called Krauklis waves. The problem is governed by an approximation to the compressible Navier-Stokes equations for the viscous fluid in the fracture cavity coupled to the elastic-wave equation in the surro...

This paper introduces a high-order multiscale Generalized/eXtended Finite Element Method (GFEM) tailored for the solution of structural dynamics and wave propagation problems exhibiting fine-scale and/or localized solution features such as singularities and discontinuities. The proposed method uses an explicit time-marching scheme together with a b...

This paper presents a multiscale computational framework able to resolve localized defects and features such as cracks and welds in large structures. It couples Abaqus models and 3-D Generalized Finite Element (GFEM) discretizations enriched with numerically-defined functions -- the GFEM with global-local enrichments (GFEMgl). The structural-scale...

In this talk, we present a multi-scale computational framework that couples Abaqus models and 3-D Generalized FEM discretizations based on numerically-defined enrichment functions – the GFEMgl. The structural-scale problem is modelled in Abaqus using a coarse mesh of 3D or shell elements suitable for capturing the macro-scale response of the struct...

This paper investigates the accuracy and robustness of stress intensity factor (SIF) extraction using the p-Hierarchical Discontinuous Interpolant Stable Generalized Finite Element Method (pFEM-DSGFEM). This method is well-conditioned and optimally convergent for fracture mechanics problems if a proper enrichment strategy and mesh refinement are us...

In this paper, a Stable Generalized/eXtended Finite Element Method (SGFEM) is combined with mesh adaptivity for the robust and computationally efficient simulation of mixed-mode brittle fracture propagation. Both h-refinement around the fracture front and p-enrichment of the analysis domain are used to control discretization errors. A Linear Elasti...

This paper proposes a first-order Generalized/eXtended Finite Element Method (G/XFEM) for 2-D and 3-D linear elastic fracture mechanics problems. The conditioning of the method is of the same order as the standard FEM and it is robust with respect to the position of the mesh relative to 2-D or 3-D fractures. The method achieves an optimal rate of c...

This paper presents a methodology for the analysis of three-dimensional static fractures in fiber-reinforced materials. Fibers are discretely modeled using a modification of the Embedded Reinforcement method with bond Slip (mERS) that allows its combination with a Generalized Finite Element Method (GFEM) for three-dimensional fractures. Since the G...

In this article, 3-D simulations of hydraulic fracture propagation with the Generalized Finite Element Method (GFEM) are compared with several experiments. The GFEM in this work uses mesh adaptivity and a quadratic basis to control discretization error while avoiding the mapping of 3-D solutions between propagation steps. Linear Elastic Fracture Me...

In this paper, the quadratic Stable Generalized Finite Element Method (SGFEM) proposed in [A.G. Sanchez-Rivadeneira, C.A. Duarte, Computer Methods in Applied Mechanics and Engineering 345 (2019) 876-918] is extended to 3-D fracture problems with non-planar crack surfaces and curved crack fronts. This SGFEM is based on p-hierarchical FEM enrichments...

Crack propagation in polycrystalline specimens is studied by means of a generalized finite element method with linear elastic isotropic grains and cohesive grain boundaries. The corresponding mode-I intergranular cracks are characterized using a grain boundary brittleness criterion that depends on cohesive law parameters and average grain boundary...

The Generalized or eXtended Finite Element Method (GFEM) has been intensively developed in the last two decades and today is available in mainstream commercial Finite Element software like Abaqus, ANSYS, and LS-DYNA. The GFEM offers several advantages over the classical Finite Element Method (FEM) in modeling problems involving crack propagation, m...

This paper focuses on preconditioners for the conjugate gradient method and their applications to the Generalized FEM with global-local enrichments (GFEMgl) and the Stable GFEMgl. The preconditioners take advantage of the hierarchical struture of the matrices in these methods and the fact that most of the matrix does not change when simulating for...

This paper reports recent improvements to the work by Gupta and Duarte [1] to simulate 3-D hydraulic fracturing with the Generalized Finite Element Method (GFEM). Three optimizations are presented and analyzed. First, an improved initial guess based on solving a 3-D elastic problem with the pressure from the previous step is shown to decrease the n...

This paper presents a two-scale Generalized Finite Element Method with global-local enrichments (GFEMgl) for the evaluation of stress intensity factors (SIFs) at spot welds subjected to thermomechanical loads. The method uses the solution of local boundary value problems as enrichment functions for the global/structural model and can provide accura...

This paper presents a two-scale Generalized Finite Element Method with global-local enrichments (GFEMgl) for the evaluation of stress intensity factors (SIFs) at spot welds subjected to thermomechanical loads. The method uses the solution of local boundary value problems as enrichment functions for the global/structural model and can provide accura...

An algorithm for non-intrusively coupling a commercial finite element software with a research code implementing a hierarchical enrichment of finite element spaces is presented. Examples of hierarchical methods supported by the algorithm are the Generalized or eXtended FEM (GFEM), the scale-bridging GFEM with numerically defined enrichment function...

This paper focuses on preconditioners for the conjugate gradient method and their applications to the Generalized FEM with global-local enrichments (GFEMgl) and the Stable GFEMgl. The preconditioners take advantage of the hierarchical struture of the matrices in these methods and the fact that most of the matrix does not change when simulating for...

This paper presents numerical studies with three classes of quadratic Generalized FEM (GFEM) approximations and show that all of them lead to errors that are orders of magnitude smaller than the FEM with quarter-point elements, provided that appropriate enrichments are selected. However, all of them lead to severely ill-conditioned system of equati...

This paper presents a new stress recovery technique for the Generalized/eXtended Finite Element Method (G/XFEM) and for the Stable Generalized FEM (SGFEM). The recovery procedure is based on a locally weighted L² projection of raw stresses over element patches--the set of elements sharing a node. Such projection leads to a block-diagonal system of...

The diameter of spot welds used in the automotive and aerospace industry is orders of magnitude smaller than the dimensions of the structural components. Automotive bodies typically have between three and five thousand spot welds which makes 3-D Direct Finite Element Analysis (DFEA) of this class problem not practical. To circumvent these limitatio...

This paper presents an algorithm and a fully coupled hydro-mechanical-fracture formulation for the simulation of three-dimensional non-planar hydraulic fracture propagation. The propagation algorithm automatically estimates the magnitude of time steps such that a regularized form of Irwin’s criterion is satisfied along the predicted 3-D fracture fr...

Although extensive research efforts have focused on the design and response of structures under isolated earthquake loading or tsunami inundation, very few studies have considered their combined effect. Moreover, very little research has been conducted on heavy timber structures such as timber pile bridges. This study focuses on the performance of...

Although extensive research efforts have focused on the design and response of structures under isolated earthquake loading or tsunami inundation, very few studies have considered their combined effect. Moreover, very little research has been conducted on heavy timber structures such as timber pile bridges. This study focuses on the performance of...

This paper investigates the accuracy and robustness of three Stress Intensity Factor (SIF) extraction methods for the Generalized/eXtended Finite Element Method (G/XFEM): The Cutoff Function Method (CFM), the Contour Integral Method (CIM) and the Displacement Correlation Method (DCM). Challenges in SIF extraction from G/XFEM solutions using energy-...

This study investigates the performance of a recovery-based a-posteriori error estimator in the framework of the Stable Generalized FEM (SGFEM). Different types of enrichment functions can be considered. When applied to linear Fracture Mechanics problems, this estimator is based on a splitting of the recovered stress field into two distinct parts:...

Interactions among multiple spatial scales are pervasive in many engineering applications. Structural failure is often caused by the onset of localized damage like cracks or shear bands that are orders of magnitude smaller than the structural dimensions. In this talk, we present a Generalized FEM (GFEM) based on the solution of interdependent macro...

There are two key technologies behind the recent boom in gas and oil production in the U.S. The first one is horizontal drilling and the second one is multistage fracturing in which between three and eight fractures are simultaneously propagated. Each fracture starts from a cluster of perforations connecting the well to the reservoir. The near well...

This paper presents the application of a two-scale generalized finite element method (GFEM) which allows for static fracture analyses as well as fatigue crack propagation simulations involving the interaction of multiple crack surfaces on fixed, coarse finite element (FE) meshes. The approach is based on the use of numerically-generated enrichment...

Singular enrichment functions are broadly used in Generalized or Extended Finite Element Methods (GFEM/XFEM) for linear elastic fracture mechanics problems. These functions are used at finite element nodes within an enrichment zone around the crack tip/front in 2- and 3-D problems, respectively. Small zones lead to suboptimal convergence rate of th...

In this study, a recovery-based a-posteriori error estimator originally proposed for the Corrected XFEM is investigated in the framework of the stable generalized FEM (SGFEM). Both Heaviside and branch functions are adopted to enrich the approximations in the SGFEM. Some necessary adjustments to adapt the expressions defining the enhanced stresses...

Interactions among multiple spatial scales are pervasive in many engineering applications. Structural failure is often caused by the onset of localized damage like cracks or shear bands that are orders of magnitude smaller than the structural dimensions. Another class of engineering problems involving multiple scales of interest is the case of hete...

It is a poster showing work on the coupled fluid-flow/mechanical/fracture formulation for simulations of hydraulic fracturing. For any details, please contact Piyush Gupta at gupta61@illinois.edu

An adaptive refinement scheme is presented to reduce the geometry discretization error and provide higher-order enrichment functions for the interface-enriched generalized FEM. The proposed method relies on the h-adaptive and p-adaptive refinement techniques to reduce the discrepancy between the exact and discretized geometries of curved material i...

This work addresses computational modeling challenges associated with structures subjected to sharp, local heating, where complex temperature gradients in the materials cause three-dimensional, localized, intense stress and strain variation. Due to the nature of the applied loadings, multiphysics analysis is necessary to accurately predict thermal...

This paper presents a novel numerical framework based on the generalized finite element method with global-local enrichments (GFEMgl) for two-scale simulations of propagating fractures in three dimensions. A non-linear cohesive law is adopted to capture objectively the dissipated energy during the process of material degradation without the need of...

This paper introduces the generalized finite element method with global-local enrichment functions using the preconditioned conjugate gradient method. The proposed methodology is able to generate enrichment functions for problems where limited a-priori knowledge on the solution is available and to utilize a preconditioner and initial guess of high...

Hydraulic fracturing is the method of choice to enhance reservoir permeability and well efficiency for extraction of shale gas. Multi-stranded non-planar hydraulic fractures are often observed in stimulation sites. Non-planar fractures propagating from wellbores inclined from the direction of maximum horizontal stress have also been reported. The p...

This paper presents a generalized FEM based on the solution of interdependent coarse-scale (global) and fine-scale (local) problems in order to resolve multiscale effects due to fine-scale heterogeneities. Overall structural behavior is captured by the global problem, while local problems focus on the resolution of fine-scale solution features in r...

We investigate the application and performance of high-order approximation techniques to one-dimensional nonlocal elastic rods. Governing equations and corresponding discrete forms are derived for the integro-differential formulation proposed by Eringen and the laplacian-based strain gradient formulation developed by Aifantis and coworkers. Accurac...

This paper presents improvements to three-dimensional crack propagation simulation capabilities of the generalized finite element method. In particular, it presents new update algorithms suitable for explicit crack surface representations and simulations in which the initial crack surfaces grow significantly in size (one order of magnitude or more)...

In this paper, we investigate the accuracy and conditioning of the Stable Generalized FEM (SGFEM) and compare it with standard Generalized FEM (GFEM) for a 2-D fracture mechanics problem. The SGFEM involves localized modifications of enrichments used in the GFEM and the conditioning of the stiffness matrix in this method is of the same order as in...

This paper presents an extension of a two-scale generalized finite element method (GFEM) to three-dimensional fracture problems involving confined plasticity. This two-scale procedure, also known as the generalized finite element method with global-local enrichments (GFEMgl), involves the solution of a fine-scale boundary value problem defined arou...

In this paper, the mechanism of near-surface cracking under critical loading conditions was investigated using mechanistic modeling approaches. These loading conditions were represented by a combination of nonuniform tire contact stresses in three directions generated during vehicle maneuvers (free rolling, acceleration/braking, and cornering) that...

This research utilized the novel computational framework of the generalized finite element method (GFEM) to predict the potential for crack propagation in concrete slabs. A two-scale approach, using the global–local concept within the GFEM framework (GFEMg–l), is applied to multi-site cracking problems (MSC), where different crack geometries are pl...

This paper considers four types of error measures, each tailored to the generalized finite element method. Particular attention is given to two-dimensional elasticity problems with singular stress fields. The first error measure is obtained using the equilibrated element residual method. The other three estimators overcome the necessity of equilibr...