scholarly journals The Generalized Constitutive Law in Nonlinear Structural Analysis of Steel Frames

2021 ◽  
Author(s):  
Damian Mrówczyński ◽  
Tomasz Gajewski ◽  
Tomasz Garbowski
Keyword(s):  
Reference Model ◽  
Constitutive Models ◽  
Shear Stiffness ◽  
Beam Element ◽  
Linear Analysis ◽  
Constitutive Law ◽  
Complex Materials ◽  
Shear Forces ◽  
Beam Structures ◽  
Numerical Examples

The article presents a modified finite element (FE) based algorithm for nonlinear analysis of 2D beam structures, which takes into account the influence of the shear forces. The method proposed enables using complex materials with nonlinearities without the need of implementing advanced constitutive models in FE routines. It can be directly integrated with commonly available FE software for linear analysis of beam structures, so its functionality can be easily extended also with material nonlinearities. The presented approach adopts the generalized constitutive law algorithm to iteratively modify the stiffness of beam element. To address an influence of a shear stiffness, a Timoshenko beam element was used. The methodology was implemented and its performance was verified on several numerical examples. For validation, the displacements and the ultimate loads were compared with the values from a commercial FE software. The results shown a good correlation between the reference model and the method proposed.

scholarly journals Application of the Generalized Nonlinear Constitutive Law in 2D Shear Flexible Beam Structures

2021 ◽  
Author(s):  
Damian Mrówczyński ◽  
Tomasz Gajewski ◽  
Tomasz Garbowski
Keyword(s):  
Finite Element ◽  
Cross Sections ◽  
Reference Model ◽  
Constitutive Models ◽  
Constitutive Law ◽  
Flexible Beam ◽  
Beam Model ◽  
Beam Structures ◽  
Nodal Displacements ◽  
Nonlinear Constitutive Law

The paper presents a modified finite element method for nonlinear analysis of 2D beam structures. To take into account the influence of the shear flexibility, a Timoshenko beam element was adopted. The algorithm proposed enables using complex material laws without the need of implementing advanced constitutive models in finite element routines. The method is easy to implement in commonly available CAE software for linear analysis of beam structures. It allows to extend the functionality of these programs with material nonlinearities. By using the structure deformations, computed from the nodal displacements, and the presented here generalized nonlinear constitutive law, it is possible to iteratively reduce the bending, tensile and shear stiffnesses of the structures. By applying a beam model with a multi layered cross-section and generalized stresses and strains to obtain a representative constitutive law, it is easy to model not only the complex multi-material cross-sections, but also the advanced nonlinear constitutive laws (e.g. material softening in tension). The proposed method was implemented in the MATLAB environment, its performance was shown on the several numerical examples. The cross-sections such us a steel I-beam and a steel I-beam with a concrete encasement for different slenderness ratios were considered here. To verify the accuracy of the computations, all results are compared with the ones received from a commercial CAE software. The comparison reveals a good correlation between the reference model and the method proposed.

scholarly journals Damage Mechanisms Of Filled Siloxanes For Predictive Multiscale Modeling Of Aging Behavior

2002 ◽  
Vol 731 ◽  
Author(s):  
Bryan Balazs ◽  
Robert Maxwell ◽  
Steve deTeresa ◽  
Long Dinh ◽  
Rick Gee
Keyword(s):  
Predictive Models ◽  
Constitutive Models ◽  
Complex Materials ◽  
Aging Behavior ◽  
Component Level ◽  
Element Analysis ◽  
Damage Mechanisms ◽  
Silica Filler ◽  
Direct Measurements ◽  
Polymer Interaction

AbstractPredictions of component performance versus lifetime are often risky for complex materials in which there may be many underlying aging or degradation mechanisms. In order to develop more accurate predictive models for silica-filled siloxane foam components, we are studying damage mechanisms over a broad range of size domains, linked together through several modeling efforts. Atomistic and molecular dynamic modeling has elucidated the chemistry of the silica filler to polymer interaction, as this interaction plays a key role in this material's aging behavior. This modeling work has been supported by experimental data on the removal of water from the silica surface, the effect of the surrounding polymer on this desiccation, and on the subsequent change in the mechanical properties of the system. Solid State NMR efforts have characterized the evolution of the polymer and filler dynamics as the material is damaged through irradiation or desiccation. These damage signatures have been confirmed by direct measurements of changes in polymer crosslink density and filler interaction as measured by solvent swelling, and by mechanical property tests. Data from the changes at these molecular levels are simultaneously feeding the development of age-aware constitutive models for polymer behavior. In addition, the microstructure of the foam, including while under load, has been determined by Computed Tomography, and these data are being introduced into Finite Element Analysis codes to allow component level models. All of these techniques are directed towards the incorporation of molecular and microstructural aging signatures into predictive models for overall component performance.

scholarly journals Multiple Tensor Train Approximation of Parametric Constitutive Equations in Elasto-Viscoplasticity

2019 ◽  
Vol 24 (1) ◽  
pp. 17
Author(s):  
Clément Olivier ◽  
David Ryckelynck ◽  
Julien Cortial
Keyword(s):  
Constitutive Equations ◽  
Surrogate Model ◽  
Reference Model ◽  
Data Representation ◽  
Differential Algebraic Equations ◽  
Constitutive Law ◽  
Algebraic Equations ◽  
Tensor Representation ◽  
Novel Approach ◽  
Parametric Studies

This work presents a novel approach to construct surrogate models of parametric differential algebraic equations based on a tensor representation of the solutions. The procedure consists of building simultaneously an approximation given in tensor-train format, for every output of the reference model. A parsimonious exploration of the parameter space coupled with a compact data representation allows alleviating the curse of dimensionality. The approach is thus appropriate when many parameters with large domains of variation are involved. The numerical results obtained for a nonlinear elasto-viscoplastic constitutive law show that the constructed surrogate model is sufficiently accurate to enable parametric studies such as the calibration of material coefficients.

On instability of constitutive models for isotropic elastic-perfectly plastic material behaviour at finite deformations

2020 ◽  
pp. 095440622092068
Author(s):  
Marina Trajković-Milenković ◽  
Otto T Bruhns ◽  
Andrija Zorić
Keyword(s):  
Plastic Material ◽  
Constitutive Relations ◽  
Relevant Literature ◽  
Constitutive Models ◽  
Constitutive Law ◽  
Elastoplastic Deformations ◽  
Perfectly Plastic ◽  
User Subroutine ◽  
Shear Problem ◽  
Elastic Perfectly Plastic

The main goal of this work is to test the possibility of a newly introduced constitutive law to model the behaviour of the isotropic elastic-perfectly plastic material which is exposed to large elastoplastic deformations. The proposed constitutive relation is based on the hypo-elastic relation and the inelastic INTERATOM model. The verification of the model is done by its implementation into the commercial software ABAQUS/Standard via the user subroutine UMAT. For that purpose, the large simple shear problem is studied where selected objective corotational rates, i.e. the logarithmic rate, the Jaumann rate and the Green-Naghdi rate, are individually implemented in the aforementioned constitutive relations. The obtained results are compared mutually and with the relevant literature. The proposed constitutive model is also used to test the behaviour of the part of a real engineering structure, i.e. a seismic isolator, in order to obtain the correct input data for further analysis of superstructure behaviour due to seismic excitation.

Formulation of a three-dimensional shear-flexible bimaterial beam element with constant curvature

2014 ◽  
Vol 229 (15) ◽  
pp. 2687-2705 ◽  
Author(s):  
Eugenio Dragoni ◽  
William J Bagaria
Keyword(s):  
Large Scale ◽  
Three Dimensional ◽  
Beam Element ◽  
Curvature Radius ◽  
Test Case ◽  
Torsional Stress ◽  
Shear Forces ◽  
Beam Curvature ◽  
Numerical Predictions ◽  
Curved Beam Element

This paper presents the closed-form formulation for a three-dimensional curved beam element with round bimaterial section. The formulation includes the effects of shear forces on displacements and stresses and of the beam curvature on the distribution of bending and torsional stress over the cross section. The element is coherent with the well-known theory for straight beams, which is obtained exactly as the curvature radius becomes infinite. The numerical predictions for a test case compare favourably with published analytical and experimental results and with the outcome of a purposely developed, large-scale FE brick model.

Research and Applications of a Plane Embedded Combined Element Model Considering Bond and Slip

2013 ◽  
Vol 275-277 ◽  
pp. 1296-1301
Author(s):  
Ji Wei Wang ◽  
Qin Qin Qiao ◽  
Fei Leng
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Shear Deformation ◽  
Element Model ◽  
Beam Element ◽  
Shape Functions ◽  
Element Analysis ◽  
Bond Slip ◽  
Numerical Examples ◽  
Nodal Force

It is one of the most important issues for finite element analysis of lining structures that how to describe anchor rod reasonably and effectively and simulate the interaction between rod and concrete or rock. Virtual nodes are constructed in concrete/rock element at the ends of anchor rod and bond-slip element is set between virtual nodes and beam element which describes anchor rod. An embedded combined element with bond slip and shear deformation is established through the transformation of nodal force at nodes of bond-slip element to those of concrete/rock element via shape functions. The element is convenient for meshing element because the location and direction of anchor rod are not necessary to be considered. Meanwhile, the element has the advantage of low computing cost. Finally, the validity and efficiency are verified by numerical examples.

A New Constitutive Model for the Compressibility of Elastomers at Finite Deformations

2001 ◽  
Vol 74 (4) ◽  
pp. 541-559 ◽  
Author(s):  
Jeffrey E. Bischoff ◽  
Ellen M. Arruda ◽  
Karl Grosh
Keyword(s):  
Uniaxial Tension ◽  
Volume Change ◽  
Constitutive Models ◽  
Hydrostatic Compression ◽  
Constitutive Law ◽  
Elastic Behavior ◽  
Compression Tests ◽  
Volume Response ◽  
Using Data ◽  
Nonlinear Elastic

Abstract Although traditional constitutive models for rubbery elastic materials are incompressible, many materials that demonstrate nonlinear elastic behavior are somewhat compressible. Clearly important in hydrostatic deformations, compressibility can also significantly affect the response of elastomers in applications for which several boundaries are rigidly fixed, such as bushings, or triaxial states of stress are realized. Compressibility is also important for convergence of finite element simulations in which a rubbery elastic constitutive law is in use. Volume changes that reflect compressibility have been observed historically in both uniaxial tension and hydrostatic compression tests; however, there appear to be no data obtained from both types of tests on the same material by which to validate a compressible hyperelastic law. In this paper, we propose a new compressible hyperelastic constitutive law for elastomers and other rubbery materials in which entropy and internal energy changes contribute to the volume change. Using data from the literature, we show that this law is capable of reproducing both the pressure—volume response of elastomers in hydrostatic compression, as well as the stress—stretch and volume change—stretch data of elastomers in uniaxial tension.

Nonlinear Incompressible Finite Element for Simulating Loading of Cardiac Tissue—Part II: Three Dimensional Formulation for Thick Ventricular Wall Segments

1988 ◽  
Vol 110 (1) ◽  
pp. 62-68 ◽  
Author(s):  
A. Horowitz ◽  
I. Sheinman ◽  
Y. Lanir
Keyword(s):  
Finite Element ◽  
Cardiac Tissue ◽  
Large Deformations ◽  
Three Dimensional ◽  
Shear Stiffness ◽  
Cardiac Mechanics ◽  
Nonlinear Finite Element ◽  
Constitutive Law ◽  
Ventricular Wall ◽  
Collagenous Matrix

A three dimensional incompressible and geometrically as well as materially nonlinear finite element is formulated for future implementation in models of cardiac mechanics. The stress-strain relations in the finite element are derived from a recently proposed constitutive law which is based on the histological composition of the myocardium. The finite element is formulated for large deformations and considers incompressibility by introducing the hydrostatic pressure as an additional variable. The results of passive loading cases simulated by this element allow to analyze the mechanical properties of ventricular wall segments, the main of which are that the circumferential direction is stiffer than the longitudinal one, that its shear stiffness is considerably lower than its tensile and compressive stiffness, and that, due to its mechanically prominent role, the collagenous matrix may affect the myocardial perfusion.

scholarly journals NON-LINEAR ANALYSIS TO IMPROVE PUNCHING SHEAR STRENGTH IN FLAT SLAB USING Z-SHAPE SHEAR REINFORCEMENT

2019 ◽  
Vol 7 (1) ◽  
pp. 65-70
Author(s):  
Abdulnasser M. Abbas
Keyword(s):  
Shear Strength ◽  
Three Dimensional ◽  
Linear Analysis ◽  
Punching Shear ◽  
Stress Concentrations ◽  
Structural Behaviour ◽  
Shear Forces ◽  
Construction Time ◽  
Flat Slab ◽  
Non Linear

Currently, flat slabs become one of the widely used structures due to its architectural benefits such as uncomplicated formwork, flexibility and minimum construction time. However, these structures are relatively weak to resist the punching shear due to a considerable lowering in stiffness induced from the development of cracks that resulting from axial and seismic loads. Moreover, the punching failure is considered a brittle failure caused by the transferring of unbalanced moments and shear forces between the structural members. Unfortunately, this may cause a catastrophic collapse, especially in the region of the slab-column. Therefore, many experimental and theoretical studies were done to improve the punching strength of the flat slab. In the current work; a finite element three-dimensional non-linear analysis has simulated by ABAQUS tool to investigate the structural behaviour of flat slab. Two specimens have considered, the first is a flat slab reinforced by ordinary steel reinforcement. While in the second one, a Z-shape shear rebar improvement has been added to the slab-column connection. The proposed model has reflected a reasonable enhancement to the flat slab. The analysis considers different parameters such as punching shear forces, deformations, and stresses of Von-Mises. The outcomes indicate that punching shear strength is increased by approximately 11.1%, and the deflections are decreased by 77.3% when the Z-shape reinforcement is used. In the meantime, stress concentrations were reduced and move from the slab-column connection.

scholarly journals Energy dissipation for hereditary and energy conservation for non-local fractional wave equations

2020 ◽  
Vol 378 (2172) ◽  
pp. 20190295 ◽  
Author(s):  
Dušan Zorica ◽  
Ljubica Oparnica
Keyword(s):  
Energy Dissipation ◽  
Energy Conservation ◽  
Wave Equations ◽  
A Priori ◽  
Constitutive Models ◽  
Equation Of Motion ◽  
Constitutive Law ◽  
Energy Estimates ◽  
Fractional Wave Equations ◽  
Non Local

Using the method of a priori energy estimates, energy dissipation is proved for the class of hereditary fractional wave equations, obtained through the system of equations consisting of equation of motion, strain and fractional order constitutive models, that include the distributed-order constitutive law in which the integration is performed from zero to one generalizing all linear constitutive models of fractional and integer orders, as well as for the thermodynamically consistent fractional Burgers models, where the orders of fractional differentiation are up to the second order. In the case of non-local fractional wave equations, obtained using non-local constitutive models of Hooke- and Eringen-type in addition to the equation of motion and strain, a priori energy estimates yield the energy conservation, with the reinterpreted notion of the potential energy. This article is part of the theme issue ‘Advanced materials modelling via fractional calculus: challenges and perspectives’.

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