Fractional viscoplasticity

Sumelka, Wojciech

doi:10.1016/j.mechrescom.2013.11.005

Cited by 118 publications

(55 citation statements)

References 19 publications

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“…Quasi-static tests were carried out at strain rate equal to 0.005 1/s whereas dynamic tests were performed at strain rate equal to 800/s. Split Hopkinson Pressure Bar [3][4][5][6][7][8][9], presented in Fig. 1, was equipped with incident and transmitter bars 20 mm in diameter and 2000 mm in length, which were made of high strength maraging steel, σ y = 2100 MPa.…”

Section: Experimental Methodsmentioning

confidence: 99%

Comparative experimental study of dynamic compressive strength of mortar with glass and basalt fibres

Kruszka

Moćko

Fenu

et al. 2015

EPJ Web of Conferences

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Abstract. Specimen reinforced with glass and basalt fibers were prepared using Standard Portland cement (CEM I, 52.5 R as prescribed by EN 197-1) and standard sand, in accordance with EN 196-1. From this cementitious mixture, a reference cement mortar without fibers was first prepared. Compressive strength, modulus of elasticity, and mod of fracture were determined for all specimens. Static and dynamic properties were investigated using Instron testing machine and split Hopkinson pressure bar, respectively. Content of the glass fibers in the mortar does not influence the fracture stress at static loading conditions in a clearly observed way. Moreover at dynamic range 5% content of the fiber results in a significant drop of fracture stress. Analysis of the basalt fibers influence on the fracture stress shows that optimal content of this reinforcement is equal to 3% for both static and dynamic loading conditions. Further increase of the fiber share gives the opposite effect, i.e. drop of the fracture stress.

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Section: Experimental Methodsmentioning

confidence: 99%

Comparative experimental study of dynamic compressive strength of mortar with glass and basalt fibres

Kruszka

Moćko

Fenu

et al. 2015

EPJ Web of Conferences

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“…[7,8]) employing fractional-order models. Recently, fractional calculus has been employed as a novel tool for modelling material of heterogeneity/multi-scale effects to the constitutive model [9,10], where the fractional viscoplasticity has been introduced as a generalization of classical Perzynas type viscoplasticity [11]. The fundamental role in the formulation plays the definition of the directions of a viscoplastic strains given as a fractional gradient of plastic potential.…”

Section: Introductionmentioning

confidence: 99%

Fractional-order uniaxial visco-elasto-plastic models for structural analysis

Suzuki

Zayernouri

Bittencourt

et al. 2016

Computer Methods in Applied Mechanics and Engineering

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Abstract. Three fractional-order models for uniaxial large strains and rate-dependent plastic behavior of materials in structural analysis are proposed. Our approach is amenable to modeling nonlinear and more sophisticated effects namely visco-elasto-plastic response of materials. This approach seamlessly interpolates between the standard elasto-plastic and visco-plastic models in plasticity, taking into account the history-dependency of the accumulated plastic strain to specify the state of stress. To this end, we propose three models namely i) viscoelasto-plastic with linear hardening plastic model, ii) elastoviscoplastic model, and iii) visco-elasto-plastic model, which combines the first the second models. We employ a fractional-order constitutive law that relates the Kirchhoff stress to its Caputo time-fractional derivative of order α ∈ (0, 1]. When α → 0 the standard elasto-plastic (rate-independent) model and when α = 1, the corresponding visco-plastic model is recovered. Since the material behavior is path-dependent the evolution of the plastic strain is achieved by fractional-order time integration of the plastic strain rate with respect to time. The strain rate is then obtained by means of the corresponding plastic multiplier and deriving proper consistency conditions. Finally, we develop a so called 386

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“…Under certain mathematical assumptions, the operators used in (2) and (3) could perhaps be fit into the general framework for non-local calculus proposed in [34]. Other similar non-local models of kinematics based on fractional calculus can be found in [35][36][37][38][39][40][41][42][43][44][45].…”

Section: and Let χ χ χ(·; T α α α(T))mentioning

confidence: 99%

Poiseuille Flow of a Non-Local Non-Newtonian Fluid with Wall Slip: A First Step in Modeling Cerebral Microaneurysms

Drapaca

2018

Fractal Fract

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Cerebral aneurysms and microaneurysms are abnormal vascular dilatations with high risk of rupture. An aneurysmal rupture could cause permanent disability and even death. Finding and treating aneurysms before their rupture is very difficult since symptoms can be easily attributed mistakenly to other common brain diseases. Mathematical models could highlight possible mechanisms of aneurysmal development and suggest specialized biomarkers for aneurysms. Existing mathematical models of intracranial aneurysms focus on mechanical interactions between blood flow and arteries. However, these models cannot be applied to microaneurysms since the anatomy and physiology at the length scale of cerebral microcirculation are different. In this paper, we propose a mechanism for the formation of microaneurysms that involves the chemo-mechanical coupling of blood and endothelial and neuroglial cells. We model the blood as a non-local non-Newtonian incompressible fluid and solve analytically the Poiseuille flow of such a fluid through an axi-symmetric circular rigid and impermeable pipe in the presence of wall slip. The spatial derivatives of the proposed generalization of the rate of deformation tensor are expressed using Caputo fractional derivatives. The wall slip is represented by the classic Navier law and a generalization of this law involving fractional derivatives. Numerical simulations suggest that hypertension could contribute to microaneurysmal formation.

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Fractional viscoplasticity

Cited by 118 publications

References 19 publications

Comparative experimental study of dynamic compressive strength of mortar with glass and basalt fibres

Comparative experimental study of dynamic compressive strength of mortar with glass and basalt fibres

Fractional-order uniaxial visco-elasto-plastic models for structural analysis

Poiseuille Flow of a Non-Local Non-Newtonian Fluid with Wall Slip: A First Step in Modeling Cerebral Microaneurysms

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