Formalisation of a novel finite element design method based on the combined use of gradient elasticity and the Theory of Critical Distances
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[1] Lennart Elfgren,et al. A deformation criterion for fatigue of concrete in tension , 2011 .
[2] L. J. Sluys,et al. A classification of higher-order strain-gradient models – linear analysis , 2002 .
[3] G. L. Goudreau,et al. Evaluation of numerical integration methods in elastodynamics , 1973 .
[4] C. M. Sonsino,et al. Multiaxial fatigue of welded joints under constant and variable amplitude loadings , 2001 .
[5] Luca Susmel,et al. A stress‐based method to predict lifetime under multiaxial fatigue loadings , 2003 .
[6] David Taylor,et al. The Theory of Critical Distances to estimate the static strength of notched samples of Al6082 loaded in combined tension and torsion. Part I: Material cracking behaviour , 2010 .
[7] David Taylor,et al. A simplified approach to apply the theory of critical distances to notched components under torsional fatigue loading , 2006 .
[8] A. C. Eringen,et al. Nonlocal polar elastic continua , 1972 .
[9] Standard Test Method for Measurement of Fatigue Crack Growth Rates 1 , 2016 .
[10] David Taylor,et al. The fatigue behaviour of three-dimensional stress concentrations , 2005 .
[11] K. D. Raithby,et al. FLEXURAL FATIGUE BEHAVIOUR OF PLAIN CONCRETE , 1979 .
[12] I. Babuska,et al. Finite element solution of the Helmholtz equation with high wave number Part I: The h-version of the FEM☆ , 1995 .
[13] Lennart Elfgren,et al. Fracture energy and fatigue strength of unreinforced concrete beams at normal and low temperatures , 1990 .
[14] Ellen Kuhl,et al. Stress concentrations in fractured compact bone simulated with a special class of anisotropic gradient elasticity , 2010 .
[15] E. Aifantis. Gradient Effects at Macro, Micro, and Nano Scales , 1994 .
[16] R. D. Mindlin. Micro-structure in linear elasticity , 1964 .
[17] Andrei V. Metrikine,et al. One-dimensional dynamically consistent gradient elasticity models derived from a discrete microstructure: Part 1: Generic formulation , 2002 .
[18] David Taylor,et al. A novel formulation of the theory of critical distances to estimate lifetime of notched components in the medium-cycle fatigue regime , 2007 .
[19] A. Hobbacher. Recommendations for fatigue design of welded joints and components , 2016 .
[20] Nathan M. Newmark,et al. A Method of Computation for Structural Dynamics , 1959 .
[21] K. Miller. THE SHORT CRACK PROBLEM , 1982 .
[22] David Taylor,et al. The Modified Wöhler Curve Method applied along with the Theory of Critical Distances to estimate finite life of notched components subjected to complex multiaxial loading paths , 2008 .
[23] David Taylor,et al. Intrinsic material length, Theory of Critical Distances and Gradient Mechanics: analogies and differences in processing linear-elastic crack tip stress fields , 2013 .
[24] Ching S. Chang,et al. Micro-mechanical modelling of granular material. Part 2: Plane wave propagation in infinite media , 2001 .
[25] H. Gough. Engineering Steels under Combined Cyclic and Static Stresses , 1949 .
[26] N. Aravas,et al. Mixed finite element formulations of strain-gradient elasticity problems , 2002 .
[27] G. A. Plizzari,et al. THE FATIGUE BEHAVIOUR OF CRACKED CONCRETE , 1997 .
[28] Masahiro Endo,et al. Unified treatment of deep and shallow notches in rotating bending fatigue , 1988 .
[29] Michael F. Ashby,et al. An introduction to their properties and applications , 1980 .
[30] David Taylor,et al. Fatigue of materials used in microscopic components , 2005 .
[31] S. K. Park,et al. Variational formulation of a simplified strain gradient elasticity theory and its application to a pressurized thick-walled cylinder problem , 2007 .
[32] E. Aifantis,et al. Finite element analysis with staggered gradient elasticity , 2008 .
[33] H. Askes,et al. Non-Singular Stresses in Gradient Elasticity at Bi-Material Interface with Transverse Crack , 2009 .
[34] E. Cosserat,et al. Théorie des Corps déformables , 1909, Nature.
[35] Luca Susmel,et al. A unifying methodology to design un-notched plain and short-fibre/particle reinforced concretes against fatigue , 2014 .
[36] L. Susmel. VALIDAZIONE DI UN CRITERIO DI RESISTENZA A FATICA MULTIASSIALE FONDATO SULL’INDIVIDUAZIONE DI UN PIANO DI VERIFICA , 2008 .
[37] V. Kouznetsova,et al. Size of a representative volume element in a second-order computational homogenization framework , 2004 .
[38] K. Bathe. Finite Element Procedures , 1995 .
[39] H. Askes,et al. Unified finite element methodology for gradient elasticity , 2015 .
[40] Tim Topper,et al. The influence of static mean stresses applied normal to the maximum shear planes in multiaxial fatigue , 2003 .
[41] Luca Susmel,et al. The theory of critical distances: a review of its applications in fatigue☆ , 2008 .
[42] H. Askes,et al. Microstructural length scale parameters to model the high-cycle fatigue behaviour of notched plain concrete , 2016 .
[43] E. Aifantis,et al. Gradient elasticity in statics and dynamics: An overview of formulations, length scale identification procedures, finite element implementations and new results , 2011 .
[44] Tomokazu Matake. An Explanation on Fatigue Limit under Combined Stress , 1977 .
[45] E. Aifantis,et al. On the structure of the mode III crack-tip in gradient elasticity , 1992 .
[46] Fusao Oka,et al. Dispersion and wave propagation in discrete and continuous models for granular materials , 1996 .
[47] Mauro Filippini,et al. Independence of the torsional fatigue limit upon a mean shear stress , 2003 .
[48] Edward L. Wilson,et al. Structural analysis of axisymmetric solids. , 1965 .
[49] Harald Zenner,et al. On the fatigue limit of ductile metals under complex multiaxial loading , 2000 .
[50] L. Susmel,et al. A bi-parametric Wöhler curve for high cycle multiaxial fatigue assessment , 2002 .
[51] Elias C. Aifantis,et al. Dislocations and Disclinations in Gradient Elasticity , 1999 .
[52] Darrell F. Socie,et al. Multiaxial Fatigue Damage Models , 1987 .
[53] N. Fleck,et al. FINITE ELEMENTS FOR MATERIALS WITH STRAIN GRADIENT EFFECTS , 1999 .
[54] A. Cemal Eringen,et al. Linear theory of nonlocal elasticity and dispersion of plane waves , 1972 .
[55] E Haibach,et al. Some Considerations in the Statistical Determination of the Shape of S-N Curves , 1981 .
[56] F. Berto,et al. Local strain energy density applied to martensitic steel plates weakened by U-notches under mixed mode loading , 2012 .
[57] David Taylor,et al. Predicting the fracture strength of ceramic materials using the theory of critical distances , 2004 .
[58] H. Askes,et al. A generalised approach to rapid finite element design of notched materials against static loading using the Theory of Critical Distances , 2016 .
[59] Chanakya Arya,et al. Eurocode 3: Design of steel structures , 2018, Design of Structural Elements.
[60] David Taylor,et al. On the use of the Theory of Critical Distances to predict static failures in ductile metallic materials containing different geometrical features , 2008 .
[61] W. Findley. A Theory for the Effect of Mean Stress on Fatigue of Metals Under Combined Torsion and Axial Load or Bending , 1959 .
[62] R E Franklin,et al. Design of normal concrete mixes , 1975 .
[63] Jacob Fish,et al. Non‐local dispersive model for wave propagation in heterogeneous media: one‐dimensional case , 2002 .
[64] N. Frost,et al. Non-Propagating Cracks in Vee- Notched Specimens Subject to Fatigue Loading , 1957 .
[65] R. Tovo,et al. Numerical methods for calculating the structural reliability of fatigue-loaded welds , 2014 .
[66] M. K. Lee,et al. An overview of the fatigue behaviour of plain and fibre reinforced concrete , 2004 .
[67] David Taylor,et al. Some new methods for predicting fatigue in welded joints , 2002 .
[68] Satya N. Atluri,et al. Analysis of Materials with Strain-Gradient Effects: A Meshless Local Petrov-Galerkin(MLPG) Approach, with Nodal Displacements only , 2003 .
[69] E. Aifantis,et al. A Two-dimensional Finite Element Implementation of a Special Form of Gradient Elasticity , 2002 .
[70] J. Crank,et al. A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type , 1947 .
[71] Harm Askes,et al. Implicit gradient elasticity , 2006 .
[72] H. Neuber. Theory of notch stresses : principles for exact calculation of strength with reference to structural form and material , 1958 .
[73] E. Aifantis,et al. A simple approach to solve boundary-value problems in gradient elasticity , 1993 .
[74] Ching S. Chang,et al. Micro-mechanical modelling of granular material. Part 1: Derivation of a second-gradient micro-polar constitutive theory , 2001 .
[75] Luca Susmel. The Modified Wöhler Curve Method calibrated by using standard fatigue curves and applied in conjunction with the Theory of Critical Distances to estimate fatigue lifetime of aluminium weldments , 2009 .
[76] Andrei V. Metrikine,et al. An isotropic dynamically consistent gradient elasticity model derived from a 2D lattice , 2006 .
[77] L. Susmel,et al. The Theory of Critical Distances to estimate finite lifetime of notched components subjected to constant and variable amplitude torsional loading , 2013 .
[78] A. Eringen. On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves , 1983 .
[79] Luca Susmel. Four stress analysis strategies to use the Modified Wöhler Curve Method to perform the fatigue assessment of weldments subjected to constant and variable amplitude multiaxial fatigue loading , 2014 .
[80] E. Aifantis,et al. Dislocations in the theory of gradient elasticity , 1999 .
[81] Elias C. Aifantis,et al. Gradient Deformation Models at Nano, Micro, and Macro Scales , 1999 .
[82] Binsheng Zhang,et al. Relationship Between Pore Structure and Mechanical Properties of Ordinary Concrete Under Bending Fatigue , 1998 .
[83] G. Irwin. ANALYSIS OF STRESS AND STRAINS NEAR THE END OF A CRACK TRAVERSING A PLATE , 1957 .
[84] Elias C. Aifantis,et al. Edge dislocation in gradient elasticity , 1997 .
[85] David Taylor,et al. Theory of Critical Distances versus Gradient Mechanics in modelling the transition from the short to long crack regime at the fatigue limit , 2013 .
[86] David Taylor,et al. Geometrical effects in fatigue: a unifying theoretical model , 1999 .
[87] Ching S. Chang,et al. Second-gradient constitutive theory for granular material with random packing structure , 1995 .
[88] L. Richardson. The Approximate Arithmetical Solution by Finite Differences of Physical Problems Involving Differential Equations, with an Application to the Stresses in a Masonry Dam , 1911 .
[89] A. Zervos. Finite elements for elasticity with microstructure and gradient elasticity , 2008 .
[90] R. Peterson,et al. Stress Concentration Factors , 1974 .
[91] David Taylor,et al. The effect of stress concentrations on the fracture strength of polymethylmethacrylate , 2004 .
[92] N. Frost,et al. A Relation between the Critical Alternating Propagation Stress and Crack Length for Mild Steel , 1959 .
[93] L. Susmel,et al. The mean stress effect on the high-cycle fatigue strength from a multiaxial fatigue point of view , 2005 .
[94] Paolo Lazzarin,et al. Fracture Mechanics and Notch Sensitivity , 2003 .
[95] Nicola Petrone,et al. Multiaxial fatigue life estimations for 6082-T6 cylindrical specimens under in-phase and out-of-phase biaxial loadings , 2003 .
[96] Richard B. Hathaway,et al. Fatigue testing and analysis , 2005 .
[97] C. M. Sonsino,et al. Multiaxial fatigue of welded joints under in-phase and out-of-phase local strains and stresses , 1995 .
[98] F. Hartmann,et al. The discrete Babuška-Brezzi condition , 1986 .
[99] Filippo Berto,et al. Fracture assessment of U-notches under three point bending by means of local energy density , 2011 .
[100] Harm Askes,et al. The Representative Volume Size in Static and Dynamic Micro-Macro Transitions , 2005 .
[101] M. Yu. NANOSCOPICS OF DISLOCATIONS AND DISCLINATIONS IN GRADIENT ELASTICITY , 2000 .
[102] H. Askes,et al. Understanding cracked materials: is Linear Elastic Fracture Mechanics obsolete? , 2015 .
[103] E. Aifantis. On the Microstructural Origin of Certain Inelastic Models , 1984 .
[104] M. E. Haddad,et al. Prediction of non propagating cracks , 1979 .
[105] T. Anderson,et al. Fracture mechanics - Fundamentals and applications , 2017 .
[106] Jan Reininghaus,et al. The Arnold–Winther mixed FEM in linear elasticity. Part I: Implementation and numerical verification☆ , 2008 .
[107] Jaime Planas,et al. The cohesive crack concept: application to PMMA at −60 °C , 2005 .
[108] Bo Liu,et al. Study on the flexural fatigue performance and fractal mechanism of concrete with high proportions of ground granulated blast-furnace slag , 2007 .
[109] David Taylor,et al. The Theory of Critical Distances: A New Perspective in Fracture Mechanics , 2010 .
[110] M. Elices,et al. Local strain energy to assess the static failure of U-notches in plates under mixed mode loading , 2007 .
[111] R. Tovo,et al. An implicit gradient application to fatigue of sharp notches and weldments , 2007 .
[112] David Taylor,et al. The theory of critical distances to predict static strength of notched brittle components subjected to mixed-mode loading , 2008 .
[113] Luca Susmel,et al. Gradient elasticity: a transformative stress analysis tool to design notched components against uniaxial/multiaxial high‐cycle fatigue , 2016 .
[114] L. Susmel,et al. The Theory of Critical Distances as an alternative experimental strategy for the determination of KIc and ΔKth , 2010 .
[115] W. Dixon. The Up-and-Down Method for Small Samples , 1965 .
[116] I. Vardoulakis,et al. A three‐dimensional C1 finite element for gradient elasticity , 2009 .
[117] Luca Susmel,et al. Fatigue design in the presence of stress concentrations , 2003 .
[118] T. Topper,et al. An Analysis of Notch-Size Effects at the Fatigue Limit , 1988 .
[119] E. Aifantis,et al. Gradient-enriched finite element methodology for axisymmetric problems , 2017 .
[120] J. Fish,et al. A Dispersive Model for Wave Propagation in Periodic Heterogeneous Media Based on Homogenization With Multiple Spatial and Temporal Scales , 2001 .
[121] Luca Susmel,et al. Multiaxial fatigue limits and material sensitivity to non‐zero mean stresses normal to the critical planes , 2008 .
[122] H. Askes,et al. Elasticity Theories with Higher-order Gradients of Inertia and Stiffness for the Modelling of Wave Dispersion in Laminates , 2007 .
[123] E. Aifantis,et al. Numerical modeling of size effects with gradient elasticity - Formulation, meshless discretization and examples , 2002 .
[124] Yoshikazu Nakai,et al. PROPAGATION AND NON-PROPAGATION OF SHORT FATIGUE CRACKS AT A SHARP NOTCH , 1983 .
[125] R. Tovo,et al. The effect of throat underflushing on the fatigue strength of fillet weldments , 2013 .
[126] David Taylor,et al. The Theory of Critical Distances to estimate the static strength of notched samples of Al6082 loaded in combined tension and torsion. Part II: Multiaxial static assessment , 2010 .
[127] Douglas N. Arnold,et al. Mixed finite elements for elasticity , 2002, Numerische Mathematik.
[128] E. Aifantis. On the role of gradients in the localization of deformation and fracture , 1992 .
[129] Petr Lukáš,et al. NON‐DAMAGING NOTCHES IN FATIGUE* , 1986 .
[130] Wang,et al. The validation of some methods of notch fatigue analysis , 2000 .
[131] P. Gudmundson. Modelling of length scale effects in viscoelastic materials , 2006 .
[132] Glaucio H. Paulino,et al. Wave propagation and dynamic analysis of smoothly graded heterogeneous continua using graded finite elements , 2007 .
[133] Luca Susmel,et al. Multiaxial notch fatigue : from nominal to local stress/strain quantities , 2009 .
[134] F. V. Lawrence,et al. A CRACK CLOSURE MODEL FOR PREDICTING THE THRESHOLD STRESSES OF NOTCHES , 1993 .
[135] Luca Susmel,et al. Gradient enriched linear-elastic crack tip stresses to estimate the static strength of cracked engineering ceramics , 2013 .
[136] Elias C. Aifantis,et al. The physics of plastic deformation , 1987 .
[137] Luca Susmel,et al. A unifying approach to estimate the high‐cycle fatigue strength of notched components subjected to both uniaxial and multiaxial cyclic loadings , 2004 .
[138] H. Askes,et al. A micro-inertia gradient visco-elastic motivation for proportional damping , 2015 .
[139] A. Cauchy. Oeuvres complètes: Mémoire sur les vibrations d'un double système de molécules et de l'éther contenu dans un corps cristallisé , 2009 .