Micro-cracks informed damage models for brittle solids

Ren, Xiaodan; Chen, Jiun‐Shyan; Li, Jie; Slawson, Thomas R.; Roth, Michael

doi:10.1016/j.ijsolstr.2011.02.001

Cited by 45 publications

(36 citation statements)

References 27 publications

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“…The total displacement field is decomposed based on asymptotic expansion.

u^{ε} ((), x) = \sum_{i = 0}^{\infty} ε^{i} u^{[i]} ((), bold-italicx bold, bold-italicy)

The decomposition in Equation is substituted into the governing equations, ie, Equations to , and the expansion is performed; the details of the derivation and formal solutions have been reported in the literature (Guedes and Kikuchi; Cheng; Fish et al; Ren et al). Only significant results are detailed, and the resulting macroscopic/microscopic equations will be summarized.…”

Section: Problem Statement and Multiscale Settingmentioning

confidence: 99%

“…As mentioned above, the HFE of the cracked microcell,

Ψ_{0}^{ε}

, is defined as

Ψ_{0}^{ε} = \frac{1}{2} σ^{ε} : e^{ε} .

In this manuscript, the evolution of damage of the microconstituents is modeled as a consequence of the microcrack propagation; hence, a microcrack informed damage model (MIDM) is employed to model this behavior. Ren et al introduced the relationship between the HFE of the damaged continuum and the averaged HFE of the microcell degraded by microcracks. Volume‐averaging the microcell HFE and the respective microcell displacement field, u ε , over the domain of the microstructure, Ω y , yields the homogenized macroscale HFE

\overset{Ψ}{true} = \frac{1}{V_{y}} ((), \int_{{normalΩ}_{y}} Ψ^{ε} d normalΩ + \frac{1}{2} \int_{{normalΓ}_{c}} u^{ε} \cdot bold-italich d normalΓ)

where, V y is the microcell volume.…”

Section: Energy Bridging and Damage Modelmentioning

confidence: 99%

“…Combining Equations and and taking the derivative of the microcell HFE with respect to the Y yields

d^{+} = 1 - \frac{\partial \overset{Ψ}{true}}{\partial Y^{+}} \approx 1 - \frac{∆ \overset{Ψ}{true}}{∆ Y^{+}} .

For the remainder of the paper, the damage law evaluated is with respect to the tensile contribution d + . A summary of the key features of the MIDM has been discussed; for in‐depth derivations, refer to Ren et al The next section will detail how d + is computed.…”

Section: Energy Bridging and Damage Modelmentioning

confidence: 99%

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Penetration modeling of ultra‐high performance concrete using multiscale meshfree methods

Sparks

Sherburn

Heard

et al. 2019

Num Anal Meth Geomechanics

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Summary Terminal ballistics of concrete is of extreme importance to the military and civil communities. Over the past few decades, ultra‐high performance concrete (UHPC) has been developed for various applications in the design of protective structures because UHPC has an enhanced ballistic resistance over conventional strength concrete. Developing predictive numerical models of UHPC subjected to penetration is critical in understanding the material's enhanced performance. This study employs the advanced fundamental concrete (AFC) model, and it will run inside the reproducing kernel particle method (RKPM)‐based code known as the nonlinear meshfree analysis program (NMAP). NMAP is advantageous for modeling impact and penetration problems that exhibit extreme deformation and material fragmentation. A comprehensive experimental study was conducted to characterize the UHPC. The investigation consisted of fracture toughness testing, the utilization of nondestructive microcomputed tomography analysis, and lastly projectile penetration shots on the UHPC targets. To improve the accuracy of the model, a new scaled damage evolution law (SDEL) is employed within the microcrack informed damage model. During the homogenized macroscopic calculation, the corresponding microscopic cell needs to be dimensionally equivalent to the mesh dimension when the partial differential equation becomes ill posed and strain softening ensues. To ensure arbitrary mesh geometry for which the homogenized stress‐strain curves are derived, a size scaling law is incorporated into the homogenized tensile damage evolution law. This ensures energy‐bridging equivalence of the microscopic cell to the homogenized medium irrespective of arbitrary mesh geometry. Results of numerical investigations will be compared with results of penetration experiments.

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“…The total displacement field is decomposed based on asymptotic expansion.

u^{ε} ((), x) = \sum_{i = 0}^{\infty} ε^{i} u^{[i]} ((), bold-italicx bold, bold-italicy)

Section: Problem Statement and Multiscale Settingmentioning

confidence: 99%

“…As mentioned above, the HFE of the cracked microcell,

Ψ_{0}^{ε}

, is defined as

Ψ_{0}^{ε} = \frac{1}{2} σ^{ε} : e^{ε} .

\overset{Ψ}{true} = \frac{1}{V_{y}} ((), \int_{{normalΩ}_{y}} Ψ^{ε} d normalΩ + \frac{1}{2} \int_{{normalΓ}_{c}} u^{ε} \cdot bold-italich d normalΓ)

where, V y is the microcell volume.…”

Section: Energy Bridging and Damage Modelmentioning

confidence: 99%

“…Combining Equations and and taking the derivative of the microcell HFE with respect to the Y yields

d^{+} = 1 - \frac{\partial \overset{Ψ}{true}}{\partial Y^{+}} \approx 1 - \frac{∆ \overset{Ψ}{true}}{∆ Y^{+}} .

Section: Energy Bridging and Damage Modelmentioning

confidence: 99%

See 1 more Smart Citation

Penetration modeling of ultra‐high performance concrete using multiscale meshfree methods

Sparks

Sherburn

Heard

et al. 2019

Num Anal Meth Geomechanics

View full text Add to dashboard Cite

show abstract

“…The damage value is allowed to increase only to a value of 1.0. Tensile damage evolution in the AFC bi-scalar damage description is defined by a microcrack-informed damage model (MIDM) proposed by Ren et al (2011). The MIDM was proposed to improve the description of softening behavior of brittle solids by replacing the continuum-scale phenomenological description of tensile damage with a damage evolution function that is derived from a model of fracture in the concrete microstructure.…”

Section: Materials Modelmentioning

confidence: 99%

Modeling finite thickness slab perforation using a coupled Eulerian–Lagrangian approach

Sherburn

Hammons

Roth

2014

International Journal of Solids and Structures

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a b s t r a c tA coupled Eulerian-Lagrangian (CEL) method can be used to model many types of dynamic events. Projectile penetration through solids is particularly well-suited to a CEL method. In this study the CEL method in the commercially-available code Abaqus was used to model a near rigid projectile perforating finite thickness concrete slabs. A near rigid projectile can be modeled as a Lagrangian material with distinct material interfaces, while the solid target can be modeled as an Eulerian material capable of large deformations. An improved concrete constitutive model is also described that was implemented into Abaqus as a user material model. A simplified stochastic model was also implemented to capture some of the heterogeneous nature of concrete. The CEL simulations are compared to experimental data to demonstrate the utility of this method for this type of perforation event.Published by Elsevier Ltd.

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“…For common reinforced concrete members, lots of experimental investigations have been conducted (Nilson and Arthur 1968;Bathe and Ramaswamg 1979;Priestly and Benzoni 1996;Lehman et al 1995;Phan et al 2007;Hindi 2005;Hindi et al 2005;Wang et al 2014;Afefy and El-Tony 2016;Jiong 2004;Li and Ren 2009;Elmorsi et al 1998;Esmaeily and Shirmohammadi 2014;Shao et al 2005;Zendaoui et al 2016;Ren et al 2010). Previous studies of reinforced concrete members have demonstrated that slender ratio, material property, axial compression ratio, reinforcement ratio, detailing art and stirrups played significant roles in the seismic behavior, especially the hysteretic performance of reinforced concrete members.…”

Section: Introductionmentioning

confidence: 99%

Experimental and Numerical Researches on the Seismic Behavior of Tubular Reinforced Concrete Columns of Air-Cooling Structures

Bai

et al. 2017

Int J Concr Struct Mater

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Tubular reinforced concrete columns of air-cooling condenser structures, which undertake the most weight of air cooling equipment, are the major components to resist lateral forces under earthquake. Once collapsed, huge casualties and economic loss would be caused. Thus, four 1/8 scaled specimens were fabricated and tested through the pseudo-static testing method. Failure modes and crack patterns of the specimens under cyclic loading were observed. Then, finite element models of tubular reinforced concrete columns were established using OpenSees and were verified with the experimental results. Finally, the influence of axial compression ratio and longitudinal reinforcement on energy dissipation capacity and stiffness degradation were studied based on the validated finite element modes. It is confirmed that tubular reinforced concrete columns of air-cooling condenser structure exhibit a moderate ability of energy dissipation, and the nonlinear finite element model could reasonably simulate its seismic behavior. Furthermore, axial compression ratio and longitudinal reinforcement are main factors which affect the seismic behavior of the tubular reinforced concrete columns. The experimental results and simulation method provide an available way to design this kind of large tubular reinforced concrete columns with thin-wall.

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Micro-cracks informed damage models for brittle solids

Cited by 45 publications

References 27 publications

Penetration modeling of ultra‐high performance concrete using multiscale meshfree methods

Penetration modeling of ultra‐high performance concrete using multiscale meshfree methods

Modeling finite thickness slab perforation using a coupled Eulerian–Lagrangian approach

Experimental and Numerical Researches on the Seismic Behavior of Tubular Reinforced Concrete Columns of Air-Cooling Structures

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