Smoothing gradient damage model with evolving anisotropic nonlocal interactions tailored to low-order finite elements

Nguyen, Tuan Huy; Bui, Tinh Quoc; Hirose, Sohichi

doi:10.1016/j.cma.2017.09.019

Cited by 101 publications

(53 citation statements)

References 46 publications

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“…[54][55][56][57][58][59][60][61][62][63] ) that can solve the crack problems faster than the finite element method can also be used for future fracture studies of heterogeneous asphalt mixtures. [54][55][56][57][58][59][60][61][62][63] ) that can solve the crack problems faster than the finite element method can also be used for future fracture studies of heterogeneous asphalt mixtures.…”

Section: Crack Growth Pathmentioning

confidence: 99%

“…It is finally noted that although we used the finite element method for obtaining the stress intensity factors and path of heterogeneous asphalt mixtures, but other numerical methods and simulation mesh-free damage models XFEM and Extended Iso-Geometric Analysis (XIGA) techniques used in different papers (e.g. [54][55][56][57][58][59][60][61][62][63] ) that can solve the crack problems faster than the finite element method can also be used for future fracture studies of heterogeneous asphalt mixtures.…”

Section: Crack Growth Pathmentioning

confidence: 99%

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Heterogeneity effects on mixed‐mode I/II stress intensity factors and fracture path of laboratory asphalt mixtures in the shape of SCB specimen

Aliha

Ziari

Mojaradi

et al. 2019

Fatigue Fract Eng Mat Struct

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Edge cracked semi-circular shape specimen subjected to three point bend loading is a favourite test specimen for determining fracture toughness of asphalt mixtures. However, in the vast majority of previous experimental works, the homogeneous medium assumption has been considered for determining the stress intensity factor and geometry factors of asphalt mixtures tested with this test configuration. As a more realistic model and in order to consider the effects of heterogeneity on corresponding values of stress intensity factors, the asphalt mixture was modelled as a two-phase aggregate/mastic heterogeneous mixture and its fracture behaviour was investigated using numerical models of asymmetric semi-circular bend (ASCB) specimens. The generation and packing algorithm was employed to randomly distribute the aggregates with different shapes and sizes inside the mastic part. The effect of the mechanical properties of asphalt mixture (elastic modulus and the Poisson's ratios of aggregates and mastic), coarse aggregates distribution and crack length were studied on modes I and II geometry factors by means of extensive twodimensional finite element analyses. Moreover, the effect of the elastic modulus of asphalt mixture components was evaluated on the fracture path using the maximum tangential stress criterion. It was shown that crack tip location, elastic modulus of aggregates and mastic are the most important affecting parameters on the magnitude of modes I and II geometry factors. It was also shown that the geometry factors are not sensitive to the Poisson's ratios of aggregates and mastic. In addition, fracture cracking path is affected by the elastic modulus of the asphalt mixture components such that, depending on the difference between the stiffness of stiffer coarse aggregates and softer NOMENCLATURE: K I , K II , stress intensity factors of modes I and II; K Ic , K IIc , critical stress intensity factors of modes I and II; Y I , Y II , geometry factors of modes I and II; P, applied load; P c , critical fracture load; R, radius of the SCB specimen; t, thickness of the SCB specimen; E, Young's modulus; E agg , Young's modulus of aggregates; E mastic , Young's modulus of mastic; E interface , Young's modulus of interface; D, distribution of aggregates in the SCB sample; Xi, Yi, Cartesian coordinate of new generated aggregate; R i , radius of new generated aggregate; X j , Y j , Cartesian coordinate of generated aggregate in the previous steps; R j , radius of generated aggregate in the previous steps; a, crack length; S 1 , S 2 , bottom support distances; S 1 /R, S 2 /R, bottom support distances over the radius ratios; A ij , area of aggregate j in group i; A i max , maximum summation area of aggregates in group i; A i min , minimum summation area of aggregates in group i; SCB, semicircular bending sample; MTS, maximum tangential stress; HMA, hot mix asphalt; SIF, stress intensity factor

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Section: Crack Growth Pathmentioning

confidence: 99%

Section: Crack Growth Pathmentioning

confidence: 99%

Heterogeneity effects on mixed‐mode I/II stress intensity factors and fracture path of laboratory asphalt mixtures in the shape of SCB specimen

Aliha

Ziari

Mojaradi

et al. 2019

Fatigue Fract Eng Mat Struct

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Section: The Derivatives Of Consistent Tangent Modulusmentioning

confidence: 99%

“…In order to compute the derivatives of the tangent modulus, the variation of the macroscopic strain must be performed following an unloading process, as the tangent modulus (38) is computed based on an unloading condition. Moreover, a numerical-analytical scheme is adopted here since it is not possible to take the derivative directly from Equation (38). Consider that the current state of an RVE is denoted by the state (1) and that the incremental state of the RVE through the variation of the macroscopic strain d I at the direction I is denoted by the state (2), the following tangent moduli can therefore be defined for the two states:…”

Section: The Derivatives Of Consistent Tangent Modulusmentioning

confidence: 99%

“…32 In the present study, the conventional nonlocal gradient enhancement method is utilized to regularize the softening behavior in both the microscale and macroscale levels, although there are several alternative approaches proposed in the literature to obtain the localized damage in the microscale and macroscale levels. [33][34][35][36][37][38][39] It should be mentioned that the term of the RVE proposed throughout this research is referred to as a unit cell, or a microsample, as it is aimed at extending the capability of the continuous homogenization method for softening materials; hence, the unit cell is chosen as an RVE to capture the global response of the system, such as the force-displacement diagram. It is shown here that if the regular microstructure is utilized, the unit cell is, in fact, a real RVE that can be employed to capture the local response of the system, such as the localization band width, local stress, strain, etc.…”

mentioning

confidence: 99%

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A nonlocal computational homogenization of softening quasi‐brittle materials

Khoei

Saadat

2019

Numerical Meth Engineering

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Summary In this paper, a computational counterpart of the experimental investigation is presented based on a nonlocal computational homogenization technique for extracting damage model parameters in quasi‐brittle materials with softening behavior. The technique is illustrated by introducing the macroscopic nonlocal strain to eliminate the mesh sensitivity in the macroscale level as well as the size dependence of the representative volume element (RVE) in the first‐order continuous homogenization. The macroscopic nonlocal strains are computed at each direction, and both the local and nonlocal strains are transferred to the microscale level. Two RVEs with similar geometries and material properties are introduced for each macroscopic Gauss point, in which the microscopic damage variables and the macroscale consistent tangent modulus and its derivatives are obtained by imposing the macroscopic nonlocal strain on the first RVE, and the macroscopic stress is computed by employing the microscopic damage variables and imposing the macroscopic local strain over the second RVE. Finally, numerical examples are solved to illustrate the performance of the proposed nonlocal computational homogenization technique for softening quasi‐brittle materials.

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Dispersion and isogeometric analyses of second‐order and fourth‐order implicit gradient‐enhanced plasticity models

Kolo

Borst

2018

Numerical Meth Engineering

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Summary Implicit gradient plasticity models incorporate higher‐order spatial gradients via an additional Helmholtz type equation for the plastic multiplier. So far, the enrichment has been limited to second‐order spatial gradients, resulting in a formulation that can be discretised using C0‐continuous finite elements. Herein, an implicit gradient plasticity model is formulated that includes a fourth‐order gradient term as well. A comparison between the localisation properties of both the implicit gradient plasticity formulations and the explicit second‐order gradient plasticity model is made using a dispersion analysis. The higher‐order continuity requirement for the fourth‐order implicit gradient plasticity model has been met by exploiting the higher‐order continuity property of isogeometric analysis, which uses nonuniform rational B‐splines as shape functions instead of Lagrange polynomials. The discretised variables, displacements, and plastic multiplier may require different orders of interpolation, an issue that is also addressed. Numerical results show that both formulations can be used as a localisation limiter, but that quantitative differences occur, and a different evolution of the localisation band is obtained for 2‐dimensional problems.

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Smoothing gradient damage model with evolving anisotropic nonlocal interactions tailored to low-order finite elements

Cited by 101 publications

References 46 publications

Heterogeneity effects on mixed‐mode I/II stress intensity factors and fracture path of laboratory asphalt mixtures in the shape of SCB specimen

Heterogeneity effects on mixed‐mode I/II stress intensity factors and fracture path of laboratory asphalt mixtures in the shape of SCB specimen

A nonlocal computational homogenization of softening quasi‐brittle materials

Dispersion and isogeometric analyses of second‐order and fourth‐order implicit gradient‐enhanced plasticity models

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