A hyperelastic-bilinear potential for lattice model with fracture energy conservation

Zhang, Zhennan; Ding, Jiafeng; Ghassemi, Ahmad; Ge, Xiurun

doi:10.1016/j.engfracmech.2015.06.006

Cited by 16 publications

(4 citation statements)

References 41 publications

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“…For this reason, the spring behavior can not be directly related to the uni-axial material response. Furthermore, in order to study the failure response of brittle, or quasi-brittle materials, the fracture energy is not preserved assigning to the springs a perfectly brittle behavior with the failure strain equal to the material failure strain [20]. In order to eliminate the influence of the element size on the post elastic response, different strategies are possible: calibrate the spring failure strain on the mode I fracture energy, as it is usually done in peridynamics [16]; define a softening branch for the spring constitutive behavior, always based on the material fracture energy [17].…”

Section: Failure Responsementioning

confidence: 99%

Study On The Effects Of Adding Diagonal Springs In A Rigid Body Spring Model With Quadrilateral Elements

Tateo¹

2021

14th WCCM-ECCOMAS Congress

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An improved Rigid Body-Spring model (RBSM) for in-plane analyses is here proposed. The approach has been developed starting from the model presented by Casolo [4], according to which a continuum plate is discretized in an assembly of rigid quadrilateral elements connected by elasticplastic springs. In the proposed model, not only the elements that share one edge are connected, as it usually happens in RBSMs, but also the elements that share only one node, that are the elements on the diagonals. These elements are connected through an axial spring fixed to their centers of gravity. The spring stiffnesses have been obtained through the equivalence of the stored strain energy for a plane stress state. These, for an isotropic material, results to be function of the Young's modulus (E) and of the Poisson's ratio (ν). Thanks to the addition of the diagonal springs, this quadrilateral RBSM is capable of modeling isotropic materials with a Poisson's ratio different from zero. The effectiveness of the proposed computational method was proved comparing the elastic solution with a Finite element code for an uniaxial tensile test. About the failure response, on one hand, the addition of the diagonal springs introduces a new direction in which the failure condition is verified, reducing the intrinsic anisotropy of the failure response, typical of the discrete approaches [5, 14]. On the other hand, the new springs increase the complexity of the model and the spring constitutive behavior is no longer directly related to the material uni-axial behavior. In this work, the spring post elastic response was defined considering the mode I fracture energy of the material. In the end, the model was applied to the study of a concrete notched beam in a three point bending test. The results have been compared with the experimental one find in the literature. The analyses were executed with a dynamic explicit solver and different tensile spring behaviors were compared to highlight the importance of considering a bi-linear softening law for modeling the failure response of quasi-brittle materials like concrete.

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Section: Failure Responsementioning

confidence: 99%

Study On The Effects Of Adding Diagonal Springs In A Rigid Body Spring Model With Quadrilateral Elements

Tateo¹

2021

14th WCCM-ECCOMAS Congress

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“…To quantify the area of the new crack surface in an arbitrary element, the characteristic size of a given element is defined as:

h = V^{\frac{1}{3}}

then the area of the crack surface is:

A = γ V^{\frac{2}{3}} = γ h^{2}

where

γ

is a geometric coefficient to determine the fracture area in an element using the element volume, which is also related to the element type and geometry. Zhang et al 56 . discussed how to determine

γ

for an irregular tetrahedral element and found that the values of

γ

in different cases always fluctuate around a certain value in an arbitrary mesh.…”

Section: Vmib Model With Fracture Energy Conservationmentioning

confidence: 99%

“…With smaller element size, the curves not only have lower peak loads for smaller element size, but also involve less work as indicated by the areas under the envelopes of displacement‐force curve. The fracture energy ratio,

θ

, and the ratio of the bond force,

β

, in this work have the same physical meanings as described in Zhang et al 56 . and represent the post‐peak mechanical properties of the material.…”

Section: Vmib Model With Fracture Energy Conservationmentioning

confidence: 99%

Virtual multi‐dimensional internal bonds model with fracture energy conservation for three‐dimensional numerical simulation of laboratory scale fluid pressurized fracturing

Huang

Zhang

Ghassemi

2021

Num Anal Meth Geomechanics

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Strain‐softening models have proved effective in treating fracturing under mechanical load. However, these models tend to suffer from mesh‐size dependency due to failure in preserving the fracture energy. The Virtual Multi‐Dimensional Internal Bond Model (VMIB) is derived from a particle‐based constitutive law at the micro scale that is implemented in a 3D Finite Element Method (FEM), in which material softening and energy dissipation occur in the “representative elementary volume”. However, according to the classic fracture mechanics theory, energy dissipation is due to the creation of new fracture surfaces instead of homogenized softening within the volume element. Therefore, the dissipated strain energy has to be consistent with the fracture energy during failure process. We present an improved VMIB model to bridge the energy storage in a volume and dissipation over a fracture surface. This is accomplished by developing a 3D virtual bond potential that incorporates the material fracture energy and eliminates the mesh‐size sensitivity. The virtual bond potential considers both the critical fracture energy and element size. The 3D model is calibrated and verified simulations of a group of three‐point‐bend tests. Then, by incorporating the coupled three‐dimensional element partition method, the model is applied to a series of laboratory scale fluid pressurized fracturing experiments. Multiple fracture propagation from closely‐staged cluster from a laboratory test is simulated. The comparisons between numerical and experimental results indicate that the model captures the fractures growth influenced by the stress boundary conditions and the stress shadow. The predicted breakdown pressure reasonably agrees with the experiment data.

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“…Zhang et al [24] developed the elastic-brittle DVIB to simulate the spalling fracture. e plastic and fracture energyembedded DVIB has been developed [25]. In this paper, we extend the DVIB to the creep fracture cases.…”

Section: Introductionmentioning

confidence: 99%

Modeling Creep Fracture in Rock by Using Kelvin Discretized Virtual Internal Bond

Zhang

2018

Advances in Civil Engineering

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Discretized virtual internal bond (DVIB) is a lattice model, which is composed of bond cells. Each bond cell has a finite number of bonds. The DVIB is used to model the creep fracture. It is done by introducing a viscous bond to the original hyperelastic DVIB. The hyperelastic bond is parallel coupled with a viscous bond together, forming a hybrid hyperelastic-Kelvin bond. The hyperelastic bond reflects the microfracture mechanism, whereas the viscous bond reflects the creep mechanism. Based on this hyperelastic-Kelvin bond, the constitutive relation of a cell is derived. The microbond parameters are calibrated based on the ideal cell approach. The simulation results suggest that this method can represent the typical features of creep and can simulate the creep fracture. The merit of this method lies in that the complicated 3D macrocreep problem is reduced to the 1D microbond creep problem. No creep law is previously derived. The macrocreep fracture behavior is the natural response of the assembly of the micro hyperelastic-Kelvin bonds.

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A hyperelastic-bilinear potential for lattice model with fracture energy conservation

Cited by 16 publications

References 41 publications

Study On The Effects Of Adding Diagonal Springs In A Rigid Body Spring Model With Quadrilateral Elements

Study On The Effects Of Adding Diagonal Springs In A Rigid Body Spring Model With Quadrilateral Elements

Virtual multi‐dimensional internal bonds model with fracture energy conservation for three‐dimensional numerical simulation of laboratory scale fluid pressurized fracturing

Modeling Creep Fracture in Rock by Using Kelvin Discretized Virtual Internal Bond

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