Stochastic Damage Model for Brittle Materials Subjected to Monotonic Loading

Kandarpa, S.; Kirkner, David J.; Spencer, Billie F.

doi:10.1061/(asce)0733-9399(1996)122:8(788)

Cited by 69 publications

(31 citation statements)

References 11 publications

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“…According to Kandarpa et al (1996) and Li and Zhang (2001), a structural element in uniaxial loading condition can be idealized as a series of micro-elements jointed in parallel (Fig. 1).…”

Section: Uniaxial Stochastic Damage Modelmentioning

confidence: 99%

Stochastic damage model for concrete based on energy equivalent strain

Ren

2009

International Journal of Solids and Structures

182

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a b s t r a c tStarting with the framework of conventional elastoplastic damage mechanics, a class of stochastic damage constitutive model is derived based on the concept of energy equivalent strain. The stochastic damage model derived from the parallel element model is adopted to develop the uniaxial damage evolution function. Based on the expressions of damage energy release rates (DERRs) conjugated to the damage variables thermodynamically, the concept and its tensor formulations of energy equivalent strain is proposed to bridge the gap between the uniaxial and the multiaxial constitutive models. Furthermore, a simplified coupling model is proposed to consider the evolution of plastic strain. And the analytical expressions of the constitutive model in 2-D are established from the abstract tensor expression. Several numerical simulations are presented against the biaxial loading test results of concrete, demonstrating that the proposed models can reflect the salient features for concrete under uniaxial and biaxial loading conditions.

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“…According to Kandarpa et al (1996) and Li and Zhang (2001), a structural element in uniaxial loading condition can be idealized as a series of micro-elements jointed in parallel (Fig. 1).…”

Section: Uniaxial Stochastic Damage Modelmentioning

confidence: 99%

Stochastic damage model for concrete based on energy equivalent strain

Ren

2009

International Journal of Solids and Structures

182

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“…However, even above-mentioned models are capable of addressing and modelling the nonlinearity emerged in stress-strain relationship of CA mortar, they are in deficiency of describing relative stochastic properties (e.g., the variation of strain-stress relationships induced by loading for a group of identical specimens), which limit the application of CA mortar in the engineering field inevitably. Usually, nonlinearity and randomness are two essential characteristics of materials' mechanical behaviors and could be easily observed in experiments [47,[49][50][51][52][53][54]. For heterogeneous material subjected to external load, internal pre-existing flaws (initial damage) will develop and further result in the appearance of nonlinearity in the stress-strain relationship.…”

Section: Of 31mentioning

confidence: 99%

Experimental Investigation of Stochastic Mechanical Behavior of Cement Emulsified Asphalt Mortar under Monotonic Compression

Xiao

Liu

et al. 2020

Applied Sciences

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Experimental investigation on cement emulsified asphalt mortar (CA mortar) under uniaxial monotonic compression by taking into account the stochastic properties were investigated. An analytical constitutive model based on the statistic damage approach capable of mimicking the stochastic mechanical responses of CA mortar under uniaxial compression was proposed. The comparison between the experimental results and the predictions demonstrated that the proposed model was able to characterize the salient features for CA mortar under uniaxial monotonic compression. Furthermore, the compressive stochastic evolution (SE) of CA mortar tested in this work and comparative analyses among typical China Railway Track System-I (CRTS-I) type CA mortar and concrete in several aspects were examined and performed; it was revealed that the Lognormal distribution density function can well represent the damage probability density for CA mortar, and its stochastic constitutive relationship can be reflected by a media process of transition from microscale to macroscale.

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“…The development of damage evolution function is refer to [17] and [23]. The stochastic damage evolution functions under static loading are expressed as follows (32) where Δ(x) is the 1-D micro-fracture strain random field;…”

Section: Damage Evolutionmentioning

confidence: 99%

“…[17] investigated the stochastic damage model and developed the standard deviation of damage evolution. Li and Ren [23] further improved the results of [17] and implemented the stochastic damage model into the energy based multiaxial damage-plasticity framework.…”

Section: Introductionmentioning

confidence: 99%

A rate-dependent stochastic damage–plasticity model for quasi-brittle materials

Ren

Zeng

2014

Comput Mech

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In this work, a rate-dependent model for the simulation of quasi-brittle materials experiencing damage and randomness is proposed. The bi-scalar plastic damage model is developed as the theoretical framework with the damage and the plasticity opening for further developments. The governing physical reason of the material rate-dependency under relatively low strain rates, which is defined as the Strain Delay Effect, is modeled by a differential system. Then the description of damage is established by further implementing the rate-dependent differential system into the random damage evolution. To reproduce the evolution of plasticity under a variety of stress conditions, a multi-variable phenomenological plastic model is proposed and the description of plasticity is then formulated. An explicit integration algorithm is developed to implement the proposed model in the structural simulation. The model results are validated by a series of numerical tests that cover a wide variety of stress conditions and loading rates. The proposed model and algorithm offer a package solution for the nonlinear dynamic structural simulations.

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Stochastic Damage Model for Brittle Materials Subjected to Monotonic Loading

Cited by 69 publications

References 11 publications

Stochastic damage model for concrete based on energy equivalent strain

Stochastic damage model for concrete based on energy equivalent strain

Experimental Investigation of Stochastic Mechanical Behavior of Cement Emulsified Asphalt Mortar under Monotonic Compression

A rate-dependent stochastic damage–plasticity model for quasi-brittle materials

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