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407
Comparison of finite difference and boundary integral solutions to threedimensional spontaneous rupture
, 2005
"... [1] The spontaneously propagating shear crack on a frictional interface has proven to be a useful idealization of a natural earthquake. The corresponding boundary value problems are nonlinear and usually require computationally intensive numerical methods for their solution. Assessing the convergenc ..."
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Cited by 45 (11 self)
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[1] The spontaneously propagating shear crack on a frictional interface has proven to be a useful idealization of a natural earthquake. The corresponding boundary value problems are nonlinear and usually require computationally intensive numerical methods for their solution. Assessing the convergence and accuracy of the numerical methods is challenging, as we lack appropriate analytical solutions for comparison. As a complement to other methods of assessment, we compare solutions obtained by two independent numerical methods, a finite difference method and a boundary integral (BI) method. The finite difference implementation, called DFM, uses a tractionatsplitnode formulation of the fault discontinuity. The BI implementation employs spectral representation of the stress transfer functional. The threedimensional (3D) test problem involves spontaneous rupture spreading on a planar interface governed by linear slipweakening friction that essentially defines a cohesive law. To get a priori understanding of the spatial resolution that would be required in this and similar problems, we review and combine some simple estimates of the cohesive zone sizes which correspond quite well to the sizes observed in simulations. We have assessed agreement between the methods in terms of the RMS
MixedMode Decohesion Finite Elements for the Simulation of Delamination in Composite Materials
, 2002
"... A new decohesion element with mixedmode capability is proposed and demonstrated. The element is used at the interface between solid finite elements to model the initiation and nonselfsimilar growth of delaminations. ..."
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Cited by 45 (4 self)
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A new decohesion element with mixedmode capability is proposed and demonstrated. The element is used at the interface between solid finite elements to model the initiation and nonselfsimilar growth of delaminations.
Calculation of Fracture Mechanics Parameters for Arbitrary ThreeDimensional Crack by the ‘Equivalent
 Domain Integral’ Method,” International Journal of Numerical Methods in Engineering
, 1987
"... In this paper, an equivalent domain integral (EDI) method and the attendant numerical algorithms arc presented for the computation of a nearcracktip field parameter, the vector Jεintegral, and its variation along the front of an arbitrary threedimensional crack in a structural component. Account ..."
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Cited by 37 (11 self)
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In this paper, an equivalent domain integral (EDI) method and the attendant numerical algorithms arc presented for the computation of a nearcracktip field parameter, the vector Jεintegral, and its variation along the front of an arbitrary threedimensional crack in a structural component. Account is taken of possible nonelastic strains present in the structure; in this case the neartip Jεvalues may be significantly different from the farfield values Jf, especially under nonproportional loading.
Conservation laws and energyrelease rate
 ASME Journal of Applied Mechanics
, 1973
"... New pathindependent integrals recently discovered by Knowles and Sternberg are related to energyrelease rates associated with cavity or crack rotation and expansion. Complexvariable~forms are presented for the conservation laws in the cases of linear" isotropic, plane elasticity. A special ..."
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Cited by 25 (2 self)
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New pathindependent integrals recently discovered by Knowles and Sternberg are related to energyrelease rates associated with cavity or crack rotation and expansion. Complexvariable~forms are presented for the conservation laws in the cases of linear" isotropic, plane elasticity. A special point concerning plastic stress distributions around cracks is discussed briefly. Professor, Division of Engineering,
Conservation laws in elasticity. II. Linear homogeneous isotropic elastostatics
 Arch. Rational Mech. Anal
, 1984
"... In 1956 ESHELBY, [5], introduced his celebrated energymomentum tensor in his study of lattice defects. This tensor had the useful property of providing nontrivial pathindependent integrals for the equations of finite elasticity, or, in other words, providing densities of nontrivial conservation la ..."
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Cited by 22 (8 self)
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In 1956 ESHELBY, [5], introduced his celebrated energymomentum tensor in his study of lattice defects. This tensor had the useful property of providing nontrivial pathindependent integrals for the equations of finite elasticity, or, in other words, providing densities of nontrivial conservation laws. The importance
An Analysis
 of Fatal Work Zone Crashes in Texas, Texas Transportation Institute Report
, 2004
"... ic pac ing mat coo en 2 s an e co itie the nsition in the of cert istance n on f ductio ared wi r Voss s also ..."
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Cited by 20 (0 self)
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ic pac ing mat coo en 2 s an e co itie the nsition in the of cert istance n on f ductio ared wi r Voss s also
On Dual Configurational Forces
, 2006
"... The dual conservation laws of elasticity are systematically reexamined by using both Noether’s variational approach and Coleman–Noll–Gurtin’s thermodynamics approach. These dual conservation laws can be interpreted as the dual configurational force, and therefore they provide the dual energy–momen ..."
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Cited by 16 (0 self)
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The dual conservation laws of elasticity are systematically reexamined by using both Noether’s variational approach and Coleman–Noll–Gurtin’s thermodynamics approach. These dual conservation laws can be interpreted as the dual configurational force, and therefore they provide the dual energy–momentum tensor. Some previously unknown and yet interesting results in elasticity theory have been discovered. As an example, we note the following duality condition between the configuration force (energy–momentum tensor) P and the dual configuration force (dual energy–momentum tensor) L, P LðP: FÞ1 rðP xÞ: This and other results derived in this paper may lead to a better understanding of configurational mechanics and therefore of mechanics of defects.
An Interface Damage Model for the Simulation of Delamination Under VariableMode Ratio in Composite Materials
, 2004
"... ..."
Estimation of mixedmode stress intensity factors using digital image correlation and an interaction integral
, 2005
"... Abstract. This paper presents a technique for the experimental measurement of stress intensity factors in cracked specimens under mixedmode loading. This technique is based on fullfield measurement using digital image correlation and an interaction integral. Such domainindependent integrals are o ..."
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Cited by 13 (4 self)
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Abstract. This paper presents a technique for the experimental measurement of stress intensity factors in cracked specimens under mixedmode loading. This technique is based on fullfield measurement using digital image correlation and an interaction integral. Such domainindependent integrals are often used in the finite element method to calculate stress intensity factors. The main advantage of this technique is that the errors made in the estimation of the measured displacement field near the crack’s tip do not affect the measurement of the stress intensity factors. The capabilities of the method are illustrated through fracture measurements on compact tension specimens made of maraging steel. Another test under mixedmode loading is presented. Key words: Digital image correlation, elastic plastic transition, interaction integral, stress intensity factors.
Calculation of JIntegral and Stress Intensity Factors using
 the Material Point Method,” Computer Modeling in Engineering & Sciences, submitted
, 2004
"... is a particlebased, meshless method that discretizes material bodies into a collection of material points (the particles), is a new method for numerical analysis of dynamic solid mechanics problems. Recently, MPM has been generalized to include dynamic stress analysis of structures with explicit cr ..."
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Cited by 12 (6 self)
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is a particlebased, meshless method that discretizes material bodies into a collection of material points (the particles), is a new method for numerical analysis of dynamic solid mechanics problems. Recently, MPM has been generalized to include dynamic stress analysis of structures with explicit cracks. This paper considers evaluation of cracktip parameters, such as Jintegral and stress intensity factors, from MPM calculations involving explicit cracks. Examples for both static and dynamic problems for pure modes I and II or mixed mode loading show that MPM works well for calculation of fracture parameters. The MPM results agree well with results obtained by other numerical methods and with analytical solutions.