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https://docs.lib.purdue.edu/ses2014/mss/cfm
Recent Events in Computational Fracture Mechanicsen-usSun, 14 Jan 2024 18:59:48 PST3600A dynamic multiscale phase-field method for cracks
https://docs.lib.purdue.edu/ses2014/mss/cfm/27
https://docs.lib.purdue.edu/ses2014/mss/cfm/27
The displacement discontinuity at a crack poses severe challenges to numerical solutions. Dynamic crack growth simulations using the standard continuum framework require careful treatment of appropriate jump and boundary conditions at the crack faces as well as crack kinetics to ensure unique solutions. This is difficult to implement and computationally expensive particularly when there can be multiple interacting cracks. An alternative approach that has been developed is to use phase-field methods. These introduce a phase parameter that tracks the cracked and uncracked regions of the body. A spatial regularization ensures that the phase field does not have singularities. This is coupled to standard momentum balance with the elastic stiffness going to zero in the cracked region. The evolution of the crack is then governed by the interplay between momentum balance and the evolution of the phase field. An important shortcoming of these existing phase-field methods is that the phase field evolution is typically a simple gradient flow. Therefore, the kinetics of the crack motion is restricted to fairly simple possibilities, and the dynamics of fracture is based only on the interaction with momentum balance. We present a phase-field formulation for dynamic fracture with the key feature that complex crack kinetics can be readily prescribed. We use a geometric interpretation of the gradient of the phase parameter field as a linear density (density per unit length) of crack faces. For any curve in 3D space, we write a balance for these crack faces by accounting for appropriate flux and source terms. This balance in addition introduces a crack velocity field – distinct from the material velocity – that can be constitutively prescribed as a function of crack driving force, temperature, and any other relevant fields. The net result of our approach is an evolution equation for the crack faces for which complex kinetics (e.g., stick-slip) can be easily prescribed, yet the field remains nonsingular and amenable to simple numerical methods. The balance law additionally contains a source term that enables a straightforward and transparent prescription of crack nucleation. We show that this model can simulate cracks faster than shear wave speeds by using anisotropic kinetics. We analyze energy flow around the crack tip to understand crack branching and reasons for crack speeds being limited by elastic wave speeds.
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Vaibhav Agrawal et al.Phase field modeling of crack propagation in double cantilever beam under Mode I
https://docs.lib.purdue.edu/ses2014/mss/cfm/26
https://docs.lib.purdue.edu/ses2014/mss/cfm/26
A smeared crack approach using a phase-field approach to fracture with unilateral contact condition was used to study the stress distribution and crack propagation in a double cantilever beam (DCB) specimen. The parameters in the numerical model were informed from atomistic simulations and validated with experimental data for poly(methyl methacrylate) that included data for damage initiation under different levels of volumetric and deviatoric stress components and fracture toughness measurements obtained under Mode I conditions. The phase field model includes two quantities, a length scale that controls the width of the crack and the critical fracture energy density. The study considered a sensitivity analysis of the influence of these two parameters to obtain optimal values. Experiments and simulations of DCB are shown to study the toughness of polymer and polymer composite specimens that include residual stresses developed in the specimen during cure.
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Oleksandr Kravchenko et al.Computing stress intensity factors for curvilinear fractures
https://docs.lib.purdue.edu/ses2014/mss/cfm/25
https://docs.lib.purdue.edu/ses2014/mss/cfm/25
Computing stress intensity factors around curvilinear fractures from numerical approximations of the elastic fields could be said to be still a largely open problem in computational fracture mechanics. Existing methods fail to provide a convergent rate >0.5, if at all. In this study, I will describe a new formulation of interaction integrals for curvilinear cracks that enable us to compute stress intensity factors around curved fractures with first and second order convergence rates, depending on the accuracy of the approximation used for the elastic fields. We verify the proposed methods through several examples including the benchmark of the circular arc crack problem as well as body force and crack face loaded problems, for which we construct analytical solutions. We further validate and showcase the robustness of the method for the simulation of curvilinear crack propagation [1] where the proposed numerical tools allow for the convergent computation of crack paths in complex fracturing problems. This study is a collaboration with Yongxing Shen, Leon Keer, and Maurizio Chiaramonte. REFERENCE [1] Rangarajan R., Chiaramonte M.M., Shen Y., Hunsweck M.J., Lew A.J. Simulating curvilinear crack propagation with universal meshes. Int. J Numer Meth Engng. (in press).
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Adrian LewA locking-free and optimally convergent discontinuous-Galerkin-based extended finite element method for cracked nearly incompressible solids
https://docs.lib.purdue.edu/ses2014/mss/cfm/24
https://docs.lib.purdue.edu/ses2014/mss/cfm/24
For nearly incompressible elasticity, volumetric locking is a well-known phenomenon with low-order (cubic or lower) finite element method methods, of which continuous extended finite element methods (XFEMs) are no exception. We will present an XFEM that is simultaneously lock-free and optimally convergent. Based on our earlier work of an optimally convergent discontinuous-Galerkin-based XFEM, the method herein consists in enriching a region surrounding the crack tip that contains a fixed ball, i.e., the enrichment zone does not shrink with the mesh parameter, and the enrichment space consists of modes I and II asymptotic solutions without the use of partition of unity. To achieve a locking-free method, the discontinuous Galerkin method is used between all neighboring elements, and specially designed lifting operators are adopted whose lifting space and testing space are no longer polynomials but instead contain the singular strain and stress components, respectively.
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Yongxing ShenA micromechanical damage and fracture model for polymers based on fractional strain-gradient elasticity
https://docs.lib.purdue.edu/ses2014/mss/cfm/23
https://docs.lib.purdue.edu/ses2014/mss/cfm/23
We formulate a simple one-parameter macroscopic model of distributed damage and fracture of polymers that is amenable to a straightforward and efficient numerical implementation. We show that the macroscopic model can be rigorously derived, in the sense of optimal scaling, from a micromechanical model of chain elasticity and failure regularized by means of fractional strain-gradient elasticity. In particular, we derive optimal scaling laws that supply a link between the single parameter of the macroscopic model, namely, thecritical energy-release rate of the material, and micromechanical parameters pertaining to the elasticity and strength of the polymer chains and to the strain-gradient elasticity regularization. We show how the critical energy-release rate of specific materials can be determined from test data. Finally, we demonstrate the scope and fidelity of the model by means of an example of application, namely, Taylor-impact experiments of polyurea 1000 rods.
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Stefanie Heyden et al.Peridynamic model for fatigue cracks
https://docs.lib.purdue.edu/ses2014/mss/cfm/22
https://docs.lib.purdue.edu/ses2014/mss/cfm/22
The peridynamic theory of solid mechanics is an extension of the classical theory whose field equations can be applied on evolving discontinuities, such as cracks and dislocations. As such, it potentially offers increased generality in the modeling of the nucleation, growth, and mutual interaction of cracks and other defects. Although most applications of the peridynamic theory to date have concerned dynamic fracture, a recent advance extends the theory to fatigue cracking under cyclic loading. The method consists of a peridynamic bond failure criterion that depends on the history of cyclic bond strain. Each bond has associated with it a scalar variable called the remaining life that decays over many loading cycles. The bond breaks irreversibly when this variable becomes zero. By calibrating the model to S–N data and Paris law curves, the essential features of fatigue crack nucleation and growth are reproduced while retaining the main advantages of the peridynamic formulation. A mapping from simulation time to the number of loading cycles avoids the need to explicitly simulate large numbers of cycles. This discussion will cover the basic equations of the peridynamic theory and the new fatigue model. The calibration method for real materials will be discussed, demonstrating good agreement with laboratory test data in computational modeling of fatigue crack growth in an aluminum alloy. Extension of the fatigue model to variable cycling loading amplitude will also be discussed.
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Stewart Silling et al.Three-dimensional fracture growth as a standard dissipative system: some general theorems and numerical simulations
https://docs.lib.purdue.edu/ses2014/mss/cfm/21
https://docs.lib.purdue.edu/ses2014/mss/cfm/21
Crack propagation in brittle materials has been studied by several authors exploiting its analogy with standard dissipative systems theory. In recent publications, minimum theorems were derived in terms of crack tip “quasi static velocity” for two-dimensional fracture mechanics. Following the cornerstone work of Rice on weight function theories, Leblond and coworkers proposed asymptotic expansions for stress intensity factors in three dimensions. In view of the expression of the expansions proposed by Leblond, however, symmetry of Ceradini’s theorem operators was not evident and the extension to 3D of outcomes proposed in 2D not straightforward. Following a different path of reasoning, minimum theorems have been finally derived. Moving from well-established theorems in plasticity, algorithms for crack advancing have been finally formulated. Their performance is here presented within a set of classical benchmarks.
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Alberto Salvadori et al.A discrete damage zone model for mixed-mode delamination of composites under high-cycle fatigue
https://docs.lib.purdue.edu/ses2014/mss/cfm/20
https://docs.lib.purdue.edu/ses2014/mss/cfm/20
A discrete damage zone model (DDZM) is developed within the finite element framework to simulate mode-mix ratio- and temperature-dependent delamination in laminated composite materials undergoing high cycle fatigue loading. In the DDZM, discrete spring elements are placed at the finite element nodes along the laminate interface. Static and fatigue damage laws are used to define the behavior of the spring elements and model irreversible damage growth. The static damage model parameters are obtained from known material properties and fracture mechanics principles. The fatigue damage model parameters are obtained by calibrating the model to fit published experimental data, and the variation of fatigue parameters with mode-mix ratio is given by a quadratic relation. The DDZM predicts crack growth rates that are in agreement with those given from published literature in which a quadratic relation is used to obtain Paris law parameters for different mode-mix ratios, thus validating the approach. Temperature dependance is implemented using an Arrhenius relation for fatigue damage model parameters, and the critical fracture energy varies with temperature as well. Although the model captures the temperature effects on delamination for mode I and 50% mode II, the prediction deviates from experiments for pure mode II, because the corresponding damage mechanism entirely changes with temperature. The DDZM converges upon mesh refinement, given that the mesh size used for calibrating model parameters is sufficiently small. The mechanisms driving static and fatigue damage for different static model parameters (i.e., initial stiffness and critical separation) and their influence on overall damage growth are also investigated. It was found that for a low initial spring stiffness fatigue damage dominates the total damage growth, whereas for a large initial stiffness static damage dominates. For intermediate initial stiffnesses, the growth of static and fatigue damage becomes sensitive to mesh size, and model convergence is difficult to attain.
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Stephen JimenezToughening due to shear kinking in composites
https://docs.lib.purdue.edu/ses2014/mss/cfm/19
https://docs.lib.purdue.edu/ses2014/mss/cfm/19
In the current study, we explore the regimes of two competing crack growth mechanisms in composites: self-similar crack extension as a result of fiber tensile damage and 90o kinking as a result of matrix shear damage. Through finite element calculations it is shown that the two damage zones extend and simultaneously shield each other under loading. Such cooperative shielding of the damage zones has a synergistic effect on the composite strength and toughness. Although the constitutive properties of the damage zones determine their relative extent, it is assumed that the preferred direction of crack extension is governed by the maximum energy release rate. The numerical values of strength and toughness against tensile/shear damage are obtained for a range of relative strength and ductility of the two damage zones. It is shown that a relatively weak and ductile shear zone is capable of increasing the macroscopic toughness by orders of magnitude. Conditions for the existence of such shear bands are stated for a range of orthotropy and a comparison is made on the toughness, strength, and preferred crack growth directions. The numerical model is then applied for an elliptical hole to examine the other extreme form of stress concentration. The extent of the shear damage is enhanced by the severity of orthotropy and initial stress concentration. As a result of this, for sufficiently long shear damage zones a panel with a sharp crack is much tougher and stronger than the one with a circular hole.
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Harika Tankasala et al.3D fracture analysis of concrete under uniaxial tension at the mesoscale
https://docs.lib.purdue.edu/ses2014/mss/cfm/18
https://docs.lib.purdue.edu/ses2014/mss/cfm/18
Modeling the structural behavior of concrete has always been an important engineering problem because of the importance and widespread usage of concrete in construction of various structures. Numerical simulations are often used to explore the mechanical behavior of concrete. In this study, the dynamic fracture response of concrete under uniaxial tension is investigated within a three-dimensional computational framework. Most of the efforts for the numerical analysis of concrete in the literature are limited to two-dimensional studies since three-dimensional numerical analyses are computationally expensive, which makes the use of parallel computing vital. Hence, a scalable parallel implementation for the finite-element analysis of concrete specimens is proposed. Concrete is modeled at the mesoscale allowing the representation of first level heterogeneities, namely the modeling of aggregates and mortar paste explicitly using linear elastic continuum finite elements. Crack initiation and propagation are modeled with dynamically inserted cohesive elements. The macroscopic tensile stress-strain response of the specimen is investigated at both prepeak and postpeak strength regions and the results obtained are compared with earlier simulations, which were conducted in two dimensions. Microcrack density and crack percolation in the mesostructure models of both two and three-dimensional setups are compared under different strain rates using cohesive crack maps and dissipated fracture energy.
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Okan Yilmaz et al.