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24
Universal Nucleation Length for SlipWeakening Rupture Instability under NonUniform Fault Loading
 J. GEOPHYS. RES
, 2003
"... We consider the nucleation of instability on a slipweakening fault subjected to a heterogeneous, locally peaked "loading" stress. That stress is assumed to gradually increase due to tectonic loading but to retain its peaked character. The case of a linear stress versus slip law is conside ..."
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Cited by 17 (2 self)
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We consider the nucleation of instability on a slipweakening fault subjected to a heterogeneous, locally peaked "loading" stress. That stress is assumed to gradually increase due to tectonic loading but to retain its peaked character. The case of a linear stress versus slip law is considered in the framework of twodimensional quasistatic elasticity for a planar fault. Slip initiates when the peak of the loading stress first reaches the strength level of the fault to start slip weakening. Then the size of the slipping region grows under increased loading stress until finally a critical nucleation length is reached, at which no further quasistatic solution exists for additional increase of the loading. That marks the onset of a dynamically controlled instability. We prove that the nucleation length is independent of the shape of the loading stress distribution. Its universal value is proportional to an elastic modulus and inversely proportional to the slipweakening rate, and is given by the solution to an eigenvalue problem. That is the same eigenvalue problem as introduced by Campillo, Ionescu and collaborators for dynamic slip nucleation under spatially uniform prestress on a fault segment of fixed length; the critical length we derive is the same as in their case. To illustrate the nucleation process, and its universal feature, in specific examples, we consider cases for which the loading stress is peaked symmetrically or nonsymmetrically, and employ a numerical approach based on a Chebyshev polynomial representation. Laboratoryderived and earthquakeinferred data are used to evaluate the nucleation size.
Simulation of crack propagation in functionally graded materials under mixedmode and nonproportional loading
, 2003
"... Abstract. Automatic simulation of crack propagation in homogeneous and functionally graded materials is performed by means of a remeshing algorithm in conjunction with the finite element method. The crack propagation is performed under mixedmode and nonproportional loading. Each step of crack grow ..."
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Cited by 6 (3 self)
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Abstract. Automatic simulation of crack propagation in homogeneous and functionally graded materials is performed by means of a remeshing algorithm in conjunction with the finite element method. The crack propagation is performed under mixedmode and nonproportional loading. Each step of crack growth simulation consists of calculation of mixedmode stress intensity factors by means of a novel formulation of the interaction integral method, determination of crack growth direction based on a specific fracture criterion, and local automatic remeshing along the crack path. The present approach requires a userdefined crack increment at the beginning of the simulation. Crack trajectories obtained by the present numerical simulation are compared with available experimental results. Key words: functionally graded material (FGM), fracture mechanics, stress intensity factors, interaction integral, twostate integral, finite element method (FEM), automatic crack propagation 1.
Conservation integrals in couple stress elasticity
 J. Mech. Phys. Solids
, 2000
"... Abstract Noether's theorem on invariant variational principles is applied in the case of in®nitesimal couple stress elasticity, thereby extending the analysis of ..."
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Cited by 5 (0 self)
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Abstract Noether's theorem on invariant variational principles is applied in the case of in®nitesimal couple stress elasticity, thereby extending the analysis of
On dual conservation laws in linear elasticity: Stress function formalism. Nonlinear Dyn
"... Abstract. Dual conservation laws of linear planar elasticity theory have been systematically studied based on stress function formalism. By employing generalized symmetry transformation or the Lie–Bäcklund transformation, a class of new dual conservation laws in planar elasticity have been discove ..."
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Cited by 4 (1 self)
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Abstract. Dual conservation laws of linear planar elasticity theory have been systematically studied based on stress function formalism. By employing generalized symmetry transformation or the Lie–Bäcklund transformation, a class of new dual conservation laws in planar elasticity have been discovered based on the Noether theorem and its Bessel–Hagen generalization. The physical implications of these dual conservation laws are discussed briefly. Key words: conservation laws, elasticity, Jintegral, Lie group, Lie–Bäcklund transformation 1.
On Fracture Criteria for MixedMode Crack Propagation in Functionally Graded Materials
"... This paper addresses mixedmode crack growth in twodimensional functionally graded materials, and assesses the predictive capability of some fracture criteria on both crack growth direction and crack initiation condition. Automatic simulation of mixedmode crack propagation in homogeneous and func ..."
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This paper addresses mixedmode crack growth in twodimensional functionally graded materials, and assesses the predictive capability of some fracture criteria on both crack growth direction and crack initiation condition. Automatic simulation of mixedmode crack propagation in homogeneous and functionally graded materials is performed by means of the finite element method in conjunction with a remeshing algorithm. Crack growth simulation consists of iterative procedures for the calculation of mixedmode stress intensity factors by means of the interaction integral method, determination of crack growth direction and crack initiation, and local automatic remeshing along the crack path. The present approach requires a userdefined crack increment at the beginning of the simulation. Crack trajectories obtained by the present simulation are compared with available experimental results. Keywords functionally graded material (FGM), interaction integral method, finite element method (FEM), crack propagation, fracture criteria, remeshing algorithm. 1.
Weak variations of lipschitz graphs and stability of phase boundaries. Continuum Mechanics and Thermodynamics
, 2010
"... In the case of Lipschitz extremals of vectorial variational problems an important class of strong variations originates from smooth deformations of the corresponding nonsmooth graphs. These seemingly singular variations, which can be viewed as combinations of weak inner and outer variations, produc ..."
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In the case of Lipschitz extremals of vectorial variational problems an important class of strong variations originates from smooth deformations of the corresponding nonsmooth graphs. These seemingly singular variations, which can be viewed as combinations of weak inner and outer variations, produce directions of differentiability of the functional and lead to singularitycentered necessary conditions on strong local minima: an equality, arising from stationarity, and an inequality, implying configurational stability of the singularity set. To illustrate the underlying coupling between inner and outer variations we study in detail the case of smooth surfaces of gradient discontinuity
ENERGY RELEASE RATES FOR A PLANE CRACK SUBJECTED TO GENERAL LOADING AND THEIR RELATION TO STRESSINTENSITY FACTORS
, 1981
"... The wellknown J integral of elastic fracture mechanics has been related to potential energyrelease rate associated with crack extension and has proved to be of great value in fracture testing. In particular, the pathindependence of the J integral has been used to an advantage in performing acous ..."
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Cited by 1 (1 self)
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The wellknown J integral of elastic fracture mechanics has been related to potential energyrelease rate associated with crack extension and has proved to be of great value in fracture testing. In particular, the pathindependence of the J integral has been used to an advantage in performing acoustoelastic measurements along a closed contour surrounding a crack tip.s In Mode I (opening mode) for example, the J integral depends essentially only on the corresponding stress intensity factor KI which can thus be determined. Actually, J is the component of a vector in the plane of the crack and there exists a component of this vector normal to the crack plane, which, however, has not been interpreted properly in the past. It is one aim of this paper to supply a valid interpretation of this pathindependent integral and to relate
Towards Material Modelling within ContinuumAtomistics
"... Synopsis: With the burgeoning computing power available, multiscale modelling and simulation has these days become increasingly capable of capturing the details of physical processes on different scales. The mechanical behavior of solids is oftentimes the result of interaction between multiple spa ..."
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Synopsis: With the burgeoning computing power available, multiscale modelling and simulation has these days become increasingly capable of capturing the details of physical processes on different scales. The mechanical behavior of solids is oftentimes the result of interaction between multiple spatial and temporal scales at different levels and hence it is a typical phenomena of interest exhibiting multiscale characteristic. At the most basic level, properties of solids can be attributed to atomic interactions and crystal structure that can be described on nano scale. Mechanical properties at the macro scale are modeled using continuum mechanics for which we mention stresses and strains. Continuum models, however they offer an efficient way of studying material properties they are not accurate enough and lack microstructural information behind the microscopic mechanics that cause the material to behave in a way it does. Atomistic models are concerned with phenomenon at the level of lattice thereby allowing investigation of detailed crystalline and defect structures, and yet the length scales of interest are inevitably far beyond the reach of full atomistic computation and is prohibitively expensive. This makes it necessary the need for multiscale models. The bottom line and a possible avenue to this end is, coupling different length scales, the