• Transactions of Materials Processing
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• v.9 no.1
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• pp.59-65
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• 2000

Most studies of failure analysis in ductile metals have been based on the classical plasticity theory using the local constitutive relations. These frequently yields a physically unrealistic solution, in which a numerical prediction of the onset of a deformation localization shows an inherent mesh-size sensitivity. A one way to remedy the spurious mesh sensitivity resulted in the unreasonable results is to incorporate the non-local plasticity into the simulation model, which introduce an internal (material) length-scale parameter into the classical constitutive relations. In this paper, a non-local version of the modified Gurson constitutive relation has been introduced into the finite element formulation of the simulation for plane strain compression of the visco elastic-plastic void material. By introducing the non-local constitutive relations we could successfully removed the inherent mesh-size sensitivity for the prediction of the deformation localization. The effects of non-local constitutive relation are discussed in terms of the load-stroke curve and the strain distributions accross the shear band.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2001.05a
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• pp.205-208
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• 2001

Localized shear band is investigated through the analysis of one-dimensional model for simple shearing deformation of thermally rate dependent material. Generally mesh size or interval of nodes play an important role in determining the overall flow behavior of the material. In order to observe these size effects we adapted non-local theory by including higher order strain gradients of the equivalent strain into the constitutive equation for the flow stress. for the ease of convergence and numerical stability the inplicit finite difference scheme is employed.

• Advances in nano research
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• v.8 no.1
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• pp.37-47
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• 2020

This work focuses on the behavior of non-local shear deformation beam theory for the vibration of functionally graded (FG) nanobeams with porosities that may occur inside the functionally graded materials (FG) during their fabrication, using the non-local differential constitutive relations of Eringen. For this purpose, the developed theory accounts for the higher-order variation of transverse shear strain through the depth of the nanobeam. The material properties of the FG nanobeam are assumed to vary in the thickness direction. The equations of motion are derived from Hamilton's principle. Analytical solutions are presented for a simply supported FG nanobeam with porosities. The validity of this theory is verified by comparing some of the present results with other higher-order theories reported in the literature, the influence of material parameters, the volume fraction of porosity and the thickness ratio on the behavior mechanical P-FGM beam are represented by numerical examples.

• Computers and Concrete
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• v.15 no.4
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• pp.515-545
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• 2015

The paper presents results of FE simulations of the strain-rate sensitive concrete behaviour under dynamic loading at the macroscopic level. To take the loading velocity effect into account, viscosity, stress modifications and inertial effects were included into a rate-independent elasto-plastic formulation. In addition, a decrease of the material stiffness was considered for a very high loading velocity to simulate fragmentation. In order to ensure the mesh-independence and to properly reproduce strain localization in the entire range of loading velocities, a constitutive formulation was enhanced by a characteristic length of micro-structure using a non-local theory. Numerical results were compared with corresponding laboratory tests and available analytical formulae.

• Computers and Concrete
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• v.20 no.6
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• pp.689-704
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• 2017

The paper presents experimental and numerical investigations of prefabricated composite structural building reinforced concrete slabs with the insulating material for a residential building construction. The building slabs were composed of concrete and expanded polystyrene. In experiments, the slabs in the full-scale 1:1 were subjected to vertical concentrated loads and failed along a diagonal shear crack. The experiments were numerically evaluated using the finite element method based on two different constitutive continuum models for concrete. First, an elasto-plastic model with the Drucker-Prager criterion defined in compression and with the Rankine criterion defined in tension was used. Second, a coupled elasto-plastic-damage formulation based on the strain equivalence hypothesis was used. In order to describe strain localization in concrete, both models were enhanced in the softening regime by a characteristic length of micro-structure by means of a non-local theory. Attention was paid to the formation of critical diagonal shear crack which was a failure precursor.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2011.11a
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• pp.528-535
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• 2011

In the present, the formation of shear band under a simple shear deformation is investigated using a rate-independent elastic-plastic constitutive relations. Moreover, the strain gradient terms are incorporated to obtain a non-local plastic constitutive relation, which in turn represented using combined two-back stress hardening model. Then, the continuum damage model is also included to the proposed model. The post-localization behavior are studied by introducing a small imperfection in a work piece. The strain gradient affects the shear localization significantly such that the intensity of shear band decreases as the strain gradient coefficient increases when the J2 flow theory is employed.

• Computers and Concrete
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• v.12 no.5
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• pp.585-612
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• 2013

The paper presents quasi-static numerical simulations of the behaviour of short reinforced concrete beams without shear reinforcement under mixed shear-tension failure using the FEM and four various constitutive continuum models for concrete. First, an isotropic elasto-plastic model with a Drucker-Prager criterion defined in compression and with a Rankine criterion defined in tension was used. Next, an anisotropic smeared crack and isotropic damage model were applied. Finally, an elasto-plastic-damage model was used. To ensure mesh-independent FE results, to describe strain localization in concrete and to capture a deterministic size effect, all models were enhanced in a softening regime by a characteristic length of micro-structure by means of a non-local theory. Bond-slip between concrete and reinforcement was considered. The numerical results were directly compared with the corresponding laboratory tests performed by Walraven and Lehwalter (1994). The advantages and disadvantages of enhanced models to model the reinforced concrete behaviour were outlined.

• Journal of Communications and Networks
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• v.6 no.3
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• pp.197-202
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• 2004

This work presents a stability analysis of the synchronous state for one-way master-slave time distribution networks with single star topology. Using bifurcation theory, the dynamical behavior of second-order phase-locked loops employed to extract the synchronous state in each node is analyzed in function of the constitutive parameters. Two usual inputs, the step and the ramp phase perturbations, are supposed to appear in the master node and, in each case, the existence and the stability of the synchronous state are studied. For parameter combinations resulting in non-hyperbolic synchronous states the linear approximation does not provide any information, even about the local behavior of the system. In this case, the center manifold theorem permits the construction of an equivalent vector field representing the asymptotic behavior of the original system in a local neighborhood of these points. Thus, the local stability can be determined.

• Structural Engineering and Mechanics
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• v.87 no.6
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• pp.529-540
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• 2023

A novel laminated-hybrid-composite-beam (LHCB) of glass-epoxy infused with flyash and graphene is constructed for this study. The conventional mixture-rule and constitutive-relationship are modified to incorporate filler and lamina orientation. Eringen's non-local-theory is used to include the filler effect. Hamilton's principle based on fifth-order-layer-wise-shear-deformation-theory is applied to formulate the equation of motion. The analogous shear-spring-models for LHCB with multiple-cracks are employed in finite-element-analysis (FEA). Modal-experimentations are conducted (B&K-analyser) and the findings are compared with theoretical and FEA results. In terms of dimensionless relative-natural-frequencies (RNF), the dynamic-response in cantilevered support is investigated for various relative-crack-severities (RCSs) and relative-crack-positions (RCPs). The increase of RCS increases local-flexibility in LHCB thus reductions in RNFs are observed. RCP is found to play an important role, cracks present near the end-support cause an abrupt drop in RNFs. Further, multiple cracks are observed to enhance the nonlinearity of LHCB strength. Introduction of the first to third crack in an intact LHCB results drop of RNFs by 8%, 10%, and 11.5% correspondingly. Also, it is demonstrated that the RNF varies because of the lamina-orientation, and filler addition. For 0° lamina-orientation the RNF is maximum. Similarly, it is studied that the addition of graphene reduces weight and increases the stiffness of LHCB in contrast to the addition of flyash. Additionally, the response of LHCB to moving mass is accessed by appropriately modifying the numerical programs, and it is noted that the successive introduction of the first to ninth crack results in an approximately 40% to 120% increase in the dynamic-amplitude-ratio.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.32 no.1
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• pp.37-44
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• 2019

A bond-based peridynamic model has been reported dynamic fracture characteristic of brittle materials through a simple constitutive model. In the model, each bond is assumed to be a simple spring operating independently. As a result, this simple bond interaction modeling restricts the material behavior having a fixed Poisson's ratio of 1/4 and not being capable of expressing shear deformation. We consider a state-based peridynamics as a generalized peridynamic model. Constitutive models in the state-based peridynamics are corresponding to those in continuum theory. In state-based peridynamics, thus, the response of a material particle depends collectively on deformation of all bonds connected to other particles. So, a state-based peridynamic theory can represent the volume and shear changes of the material. In this paper, the perfect plasticity is considered to express plastic deformation of material by the state-based peridynamic constitutive model with perfect plastic flow rule. The elastic-plastic behavior of the material is verified through the stress-strain curves of the flat plate example. Furthermore, we simulate the high-speed impact on 3D granite model with a nonlocal contact modeling. It is observed that the damage patterns obtained by peridynamics are similar to experimental observations.