Wyniki wyszukiwania - BazTech

1

Performance of isotropic constitutive laws in simulating failure mechanisms in scaled RC beams

Marzec I., Bobiński J.

Archives of Mechanics

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2020

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Vol. 72, nr 3

193--215

EN

Results of numerical calculations of reinforced concrete (RC) beams are presented. Based on experimental results on longitudinally reinforced specimens of different sizes and shapes are investigated. Four different continuum constitutive laws with isotropic softening are used: one defined within continuum damage mechanics, an elasto-plastic with the Rankine criterion in tension and the Drucker–Prager criterion in compression, a formulation coupling elasto-plasticity and damage mechanics and the concrete damaged plasticity (CDP) model implemented in Abaqus. In a softening regime, a non-local theory of integral format is applied to the first three constitutive laws. A fracture energy approach is utilised in CDP model. An ability to reproduce different failure mechanisms observed in experiments for each constitutive model is analysed. A comparison of force-displacement curves and crack patterns between numerical and experimental outcomes is performed.

2

Computational modelling of concrete behaviour under static and dynamic conditions

Marzec I., Tejchman J.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2013

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Vol. 61, nr 1

85-96

EN

The paper presents results of FE simulations of the concrete behaviour under quasi-static and dynamic loading. For quasi-static cyclic analyses, an enhanced coupled elasto-plastic-damage constitutive model has been used. To take the effect of the loading velocity into account, viscous and inertial terms have been also included. To ensure the mesh-independence and to properly reproduce strain localization in the entire range of strain rates, a constitutive formulation has been enhanced by a characteristic length of micro-structure by means of a non-local theory. Numerical results have been compared with some corresponding laboratory tests.

3

Variational formulation for buckling of multi-walled carbon nanotubes modelled as nonlocal Timoshenko beams

Adali S.

Journal of Theoretical and Applied Mechanics

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2012

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Vol. 50 nr 1

321-333

EN

Variational formulation for multi-walled carbon nanotubes subject to buckling is derived by the semi-inverse method with governing equations based on the nonlocal Timoshenko beam theory which takes small scale effects and shear deformation into account. The nonlocal theory improves the range and applicability of the physical model by modelling the nano-scale phenomenon more accurately. The natural and geometric boundary conditions are derived, which lead to a set of coupled boundary conditions for multi-walled nanotubes as opposed to uncoupled boundary conditions in the case of simply supported and clamped boundaries and also in the case of a local theory. The variational principle and the corresponding Rayleigh quotient facilitate the application of approximate and numerical methods of solution.

PL

W pracy przedyskutowano wariacyjne sformułowanie zagadnienia wyboczenia wielościennych nanorurek węglowych wyprowadzone metodą pół-odwrotną z równaniami konstytutywnymi opartymi na nielokalnej teorii belki Timoszenki uwzględniającej efekty małoskalowe i odkształcenia postaciowe. Teoria nielokalna rozszerza zakres stosowalności modelu fizycznego belki poprzez dokładniejsze odwzorowanie zjawisk nanoskalowych. Wprowadzono naturalne i geometryczne warunki brzegowe dla wielościennych nanorurek, które ostatecznie ujęto jako warunki brzegowe sprzężone, w odróżnieniu do warunków rozprzężonych w przypadku prostego podparcia lub zamurowania brzegów oraz zastosowania teorii lokalnej. Wykazano, że wykorzystane zasady wariacyjne i wynikający iloraz Rayleigha podnoszą wydajność przybliżonych metod numerycznych.

4

Enhanced coupled elasto-plastic-damage models to describe concrete behaviour in cyclic laboratory tests: comparison and improvement

Marzec I., Tejchman J.

Archives of Mechanics

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2012

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Vol. 64, nr 3

227-227

EN

The paper presents two-dimensional FE simulation results of the concrete behaviour under quasi-static cyclic loading using different enhanced coupled elasto-plastic-damage continuum models. Attention is paid to strain localization and stiffness degradation under tensile bending failure. To ensure the mesh-independence, to properly reproduce strain localization and to capture a deterministic size effect, all constitutive models include a characteristic length of micro-structure by means of a non-local theory. Numerical results are compared with corresponding cyclic laboratory tests on concrete specimens under bending. Advantages and disadvantages of coupled models used are outlined. In addition, numerical aspects of implementation and non-local averaging of coupled models are discussed. Finally, a new improved model is proposed to describe strain localization simultaneously under both tension and compression.

5

Variational principles and natural boundary conditions for multilayered orthotropic graphene sheets undergoing vibrations and based on nonlocal elastic theory

Adali S.

Journal of Theoretical and Applied Mechanics

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2011

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Vol. 49 nr 3

621-639

EN

Variational principles are derived for multilayered orthotropic graphene sheets undergoing transverse vibrations based on the nonlocal elastic theory of orthotropic plates which provide a continuum model for graphene sheets. The variational formulation allows the derivation of natural boundary conditions which are expressed in the form of a set of coupled equations for multilayered sheets as opposed to uncoupled boundary conditions applicable to simply supported and clamped boundaries and also in the case of a formulation based on the local (classical) elasticity theory. For the free vibrations case, the Rayleigh quotient is derived. The methods for the variational formulation use techniques of calculus of variations and the semi-inverse method for deriving variational integrals. Variational formulations provide the basis for a number of approximate and numerical methods of solutions and improve the understanding of the physical phenomena.

PL

W pracy zajęto się problemem drgań poprzecznych ortotropowych paneli grafenowych, dla których sformułowano zasady wariacyjne na podstawie nielokalnej teorii sprężystości, co pozwoliło na budowę ciągłego modelu takich struktur. Formuła wariacyjna umożliwiła konstrukcję naturalnych warunków brzegowych wyrażonych zbiorem sprzężonych równań opisujących grafenowe panele wielowarstwowe w odróżnieniu od rozprzężonych warunków brzegowych stosowanych jedynie do zamocowań typu swobodne podparcie lub zamurowanie, jednocześnie przy zastosowaniu lokalnej (klasycznej) teorii sprężystości. Dla przypadku drgań swobodnych wyznaczono iloraz Rayleigha układu z grafenu. W prezentowanym sformułowaniu użyto odpowiednich technik obliczania funkcjonałów i półodwrotnej metody wyznaczania całek. Wykazano, że postać wariacyjna stanowi podstawę dla numerycznych metod poszukiwania przybliżonych rozwiązań i pogłębia zrozumienie zachodzących zjawisk fizycznych w takich układach.

6

Electromagnetic solids with irreversible process of local mass displacement

Kondrat V., Hrytsyna O.

Archives of Mechanics

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2011

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Vol. 63, nr 3

255-255

EN

The non-local model of electromagnetothermomechanics for polarized nonferromagnetic solids is proposed. It takes into account the process of local mass displacement due to structural changes of a physically small element of a body. An approach which takes into account possible irreversibility of the local mass displacement is also proposed. On this basis, we have obtained the rheological constitutive relations for the vectors of the mass displacement and for the polarization. The proposed model allows to study the surface charge kinetics and the formation of near-surface inhomogeneities of the stress-strained state as well as the electric polarization, surface tension and disjoining pressure.

7

Modeling of strain localization in quasi-brittle materials with a coupled elasto-plastic-damage model

Bobiński J., Tejchman J.

Journal of Theoretical and Applied Mechanics

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2006

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Vol. 44 nr 4

767-782

EN

The paper presents results of numerical simulations of strain localization in quasi-brittle materials (like concrete) under plane strain conditions. To model the material behaviour, an isotropic elasto-plastic-damage model combining elasto-plasticity and scalar damage was used. An elasto-plastic constitutive law using a Drucker-Prager yield surface (in compression) and Rankine yield surface (in tension) was defined. A modified failure criterion by Rankine for the equivalent strain using an exponential evolution law was assumed within damage mechanics. To obtain mesh-independent results of strain localization, the model was enhanced by non-local terms in the softening regime. A four-point bending test of a concrete beam with a single notch was numerically simulated using the finite element method. FE-results were compared with laboratory experiments.

PL

W artykule przedstawiono wyniki symulacji numerycznych lokalizacji odkształceń w materiałach quasi-kruchych (jak beton) w płaskim stanie odkształcenia. Do opisu materiału przyjęto izotropowy model sprężysto-plastyczno-zniszczeniowy uwzględniający prawo sprężysto-plastyczne ze skalarną degradacją sztywności. W przypadku prawa sprężysto-plastycznego przyjęto kryterium plastyczności Druckera-Pragera w ściskaniu i kryterium plastyczności Rankine'a w rozciąganiu. Degradację sprężystą opisano z wykorzystaniem definicji odkształcenia zastępczego wegług warunku Rankine'a i wykładniczym prawem ewolucji. W celu otrzymania wyników niezależnych od siatki elementów skończonych, w obszarze osłabienia przyjęto teorię nielokalną. Przedstawiono wyniki symulacji numerycznych dla belki betonowej z nacięciem obciążonej dwoma siłami skupionymi. Wyniki numeryczne porównane z wynikami doświadczalnymi.

8

Modelling of concrete behaviour with a non-local continuum damage approach

Bobiński J., Tejchman J.

Archives of Hydro-Engineering and Environmental Mechanics

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2005

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Vol. 52, nr 3

243-263

EN

The paper presents FE-results on the behaviour of concrete under plane strain conditions. The material was modelled using a simple isotropic damage continuum model. The model was enriched by non-local terms to avoid a pathological mesh-sensitivity and to obtain a well-posed rate boundary value problem. The constitutive model was used to simulate localization of deformation in 3 benchmark problems: a double-edge notched specimen under uniaxial tension and a notched beam under three- and four-point bending. Attention was laid on the effect of a characteristic length on the load-displacement curves and strain localization. The FE-results were compared with experiments and other numerical studies.

9

Nonlocal theoretical analysis of the dynamic behavior of two Griffith cracks in a piezoelectric strip

Sun Y. G., Zhou Z. G.

Archives of Mechanics

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2004

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Vol. 56, nr 4

271-291

EN

The dynamic behavior of two Griffith cracks in a strip made of piezoelectric materials under anti-plane shear waves is investigated by means of the non-local theory for impermeable crack surface conditions. A one-dimensional non-local kernel is used instead of a two-dimensional one for the anti-plane dynamic problem to obtain the stress and the electric displacement near the crack tips. By utilizing the Fourier transform, the problem can be solved by means of two pairs of triple integral equations. These equations are solved using the Schmidt method. Contrary to the classical solution, it is found that no stress and electric displacement singularity are present at the crack tip. This is shown to be consistent with the physical nature.

10

Non-local coupling of viscoplasticity and anisotropic viscodamage for impact problems using the gradient theory

Voyiadjis G. Z., Abu Al-Rub R. K., Palazotto A. N.

Archives of Mechanics

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2003

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Vol. 55, nr 1

39-89

EN

A general framework for the analysis of heterogeneous media that assesses a strong coupling between viscoplasticity and anisotropic viscodamage evolution is formulated for-impact related problems within the framework of thermodynamic laws and nonlinear continuum mechanics. The proposed formulations include thermo-elasto-viscoplastici- ty with anisotropic thermo-elasto-viscodamage, a dynamic yield criterion of a von Mises type and a dynamic viscodamage criterion, the associated flow rules, non-linear strain hardening, strain-rate hardening, and temperature softening. The constitutive equations for the damaged material are written according to the principle of strain energy equivalence between the virgin material and the damaged material. That is, the damaged material is modeled using the constitutive laws of the effective undamaged material in which the nominal stresses are replaced by the effective stresses. The evolution laws are impeded in a finite deformation framework based on the multiplicative decomposition of the deformation gradient into elastic, viscoplastic, and viscodamage parts. Since the material macroscopic thermomechanical response under high-impact loading is governed by different physical mechanisms on the macroscale level, the proposed three-dimensional kinematical model is introduced with manifold structure accounting for discontinuous fields of dislocation interactions (plastic hardening), and crack and void interactions (damage hardening). The non-local theory of viscoplasticity and viscodamage that incorporates macroscale interstate variables and their higher-order gradients is used here to describe the change in the internal structure and in order to investigate the size effect of statistical inhomogeneity of the evolution-related viscoplasticity and viscodamage hardening variables. The gradients are introduced here in the hardening internal state variables and are considered to be independent of their local counterparts. It also incorporates the thermomechanical coupling effects as well as the internal dissipative effects through the rate-type covariance constitutive structure with a finite set of internal state variables. The model presented in this paper can be considered as a framework, which enables one to derive various non-local and gradient viscoplasticity and viscodamage theories by introducing simplifying assumptions.

11

A Non-local elasto-plastic model to describe localisations of deformation in concrete

Bobiński J., Tejchman J.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

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2002

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Vol. 6, No 3

437-446

EN

The paper presents numerical simulations of behaviour of concrete elements subjected to uniaxial compression for plane strain. FE-calculations are performed with two different elasto-plastic constitutive laws for concrete. Numerical results obtained suffer from mesh sensivity due to the presence of material softening. To obtain a well-posed boundary problem and a mesh independent solution, conventional constitutive laws with softening require an extension (called regularisation) to describe properly the localisations of deformations. In this paper elasto-plastic constitutive laws are extended by non-local strain terms. Owing to them, localisations of deformations are realistically captured.