Elasto-plastic Law Research Articles

Modelling of cutting tool – soil interaction – part I: contact behaviour

The unknown interaction of the cutting tools with geological settings represents an interesting problem for the excavation machinery industry. To simplify the non-linear aspects involved in the numerical analysis of such phenomena a strategy for an accurate soil modelling has to be defined. A possible approach is the discrete one, by considering the soil as an assembly of rigid spheres. In this work this strategy is adopted. The basic idea is to concentrate at the contact level between the spheres the real mechanical behaviour of the soil. For this purpose suitable contact models have been developed, where specific elasto-plastic laws have been implemented in the node-to-segment contact formulation. The framework for the plastic behaviour consists of a failure criterion, a one-dimensional, rate-independent elasto-plastic flow rule for the normal and the tangential force and a non-linear yield criterion. The final aim of this paper is to develop mechanical models to study the behaviour of stiff soils and rocks under different loading conditions.

Localization analysis in softening RC frame structures

AbstractThis paper discusses the sensitivity of softening reinforced concrete frame structures to the changes in input ground motion and investigates the possibility of localizations for this type of structure in static and dynamic analysis. A finite element model is used in which the sections resisting force are calculated using a proposed differential hysteretic model. This model is especially developed for modelling softening behaviour under cyclic loading. To obtain parameters of the differential model the moment–curvature of each section is evaluated using a microplane constitutive law for concrete and bi‐linear elasto‐plastic law for reinforcements. The capability of the procedure is verified by comparing results with available experimental data at element level, which shows good accuracy of the procedure. The effect of possible changes in ground motion is assessed using a non‐stationary Kanai–Tajimi process. This process is used to generate ground motions with approximately the same amplitude and frequency content evolution as those of base ground motion. The possibility of localization in static and dynamic loading is investigated using two structures. A measure for the possibility of localization in code‐designed structures is obtained. This study indicates that localization may occur in ordinary moment‐resisting structures located in high seismic zones. Localization may result in substantial drift in global response and instability due to P–δ effect. Also, it is shown that the structure becomes very sensitive to the input ground motion. It is concluded that allowance by some design codes of the use of ordinary moment‐resisting frames in regions with high seismicity should be revised or improvements should be made in the detailing requirements at critical sections of these structures. Copyright © 2002 John Wiley & Sons, Ltd.

Two-dimensional bilinear oscillator: group-preserving scheme and steady-state motion under harmonic loading

We study the dynamic behavior of a single-mass, two-degree-of-freedom bilinear oscillator, whose restoring force obeys a bilinear elastoplastic law. For the purpose of calculation we develop a group-preserving scheme utilizing the internal symmetry group of the model in the plastic phase so as to satisfy the yield condition exactly at each time step. Then the oscillator is subjected to biaxial harmonic excitations, and the responses are displayed. Based on circular motion assumption and harmonic balance method, the closed-form formulae to estimate the steady-state responses are derived, which are then compared with the results calculated by the group-preserving scheme. The accuracy of the formulae is thus confirmed. Simple formulae to select minimum driving force amplitudes or maximum yield forces which cause the bilinear oscillator steadily oscillating in the plastic phase are derived. For the benefit of engineers’ use we also derive closed-form formulae to decide the force ratios required to sustain the user-specified dissipation per cycle.

Localization Analysis of Reinforced Concrete Members with Softening Behavior

This paper presents a method of analysis for evaluating the softening behavior of reinforced concrete (RC) members. To obtain mesh objective results, a nonlocal fiber element model is introduced. The resisting force of each section, in the nonlocal fiber element model, is calculated using a proposed differential hysteretic model, which is especially developed for modeling softening behavior under cyclic loading. The section hysteretic response is determined using microplane constitutive law for concrete and bilinear elastoplastic law for reinforcements. The calculated hysteretic behavior of sections is employed to scale the parameters of the differential hysteretic model. The proposed method is verified by the available experimental results. Close agreements between the numerical and experimental results are obtained. The method provides insight to the procedure of flexural localization. Also, due to computational efficiency of the method, it is possible to extend its use for analyzing RC frames with soft...

Elastoplastic truss design using a displacement based optimization

A displacement based optimization (DBO) method is applied to truss design problems with material nonlinearities, to explore feasibility and verify efficiency of the method as compared to traditional structural optimization. Minimum-weight truss sizing problems with various path-independent elastoplastic laws, including elastic perfectly plastic, linear strain hardening, and Ramberg–Osgood models, are investigated. This type of material nonlinearity allows us to naturally extend the linear elastic truss sizing in the DBO setting to nonlinear problems. To implement the methodology a computer program that uses the commercially available optimizer DOT by VR&D and IMSL Linear Programming solver by Visual Numerics is developed. Several test problems are successfully solved using the DBO approach and solutions are compared to those available in the literature, demonstrating significant reduction of computational time in comparison to the traditional structural optimization method. In particular, the DBO approach is found to be suitable for truss topology design since the method allows member areas to have cross-sectional areas equal to zero exactly.

Numerical damage models using a structural approach: application in bones and ligaments

The purpose of the present study was to apply knowledge of structural properties to perform numerical simulations with models of bones and knee ligaments exposed to dynamic tensile loading leading to tissue damage. Compact bones and knee ligaments exhibit the same geometrical pattern in their different levels of structural hierarchy from the tropocollagen molecule to the fibre. Nevertheless, their mechanical behaviours differ considerably at the fibril level. These differences are due to the contribution of the joints in the microfibril-fibril-fibre assembly and to the mechanical properties of the structural components. Two finite element models of the fibrous bone and ligament structure were used to describe damage in terms of elastoplastic laws or joint decohesion processes.

3D Finite-Element Simulation of a Square Silo with Flexible Walls

Most of the studies that have been published to evaluate stresses on silo walls during filling or discharge stages are based on a rigid wall assumption. In a 2D approach, the wall flexibility can be approximately modeled by using a corrective factor applied to the whole pressure distribution. It has been shown that such models are in agreement with experimental measurements on circular silos. But in square or rectangular silos, the variation of the stiffness of the wall due to vertical or horizontal stiffeners produces nonuniform wall deformations that are not taken into account in the previous axisymmetric 2D model. The aim of this paper is to present a full 3D modeling of the filling and discharge stages using a nonlinear finite-element method. The bulk material behavior is based on an elastoplastic law. Contact elements using a Mohr-Coulomb criterion simulate the interaction between the wall and the bulk material, and the flexibility of the silo structure is modeled with beam and shell elements. A detailed analysis of the numerical results computed for a square silo filled with wheat and discharged through a central outlet is presented and discussed.

The deformation of the Egersund–Ogna anorthosite massif, south Norway: finite-element modelling of diapirism

This paper aims at testing the mechanical relevance of the petrological model of anorthosite massif diapiric emplacement. The Egersund–Ogna massif (S. Norway) is of particular interest because recent petrological and geochronological data constrain the initial geometry, emplacement conditions and timing (about 2 m.y.). The formation of this anorthosite massif is in agreement with the classical petrological model, in which accumulation of plagioclase takes place in a deep-seated magma chamber at the crust–mantle limit, from which masses of plagioclase separate and rise through the lower crust up to the final level of emplacement at mid-crustal depths. The Egersund–Ogna massif also displays a foliated inner margin, in which strain ellipsoids have been reconstructed by investigating at 51 sites the deformation of megacrysts of high-alumina orthopyroxene. Based on these petrological data, a model made up of one rigid layer (upper granitic crust) and three viscous layers (lower part of the granitic crust, noritic lower crust and anorthosite) has been built up. The upper crust behaviour is represented by an elastoplastic law and the viscous layers obey elastic-viscoplastic laws with Newtonian viscosity. An inverse density gradient is considered between the lower crust ( d=3.00) and the anorthosite ( d=2.75), the loading consisting only in gravity. The modelling is carried out under axisymmetrical conditions, using the LAGAMINE finite-element code coupled with an automatic re-meshing algorithm designed to deal with large strains in complex structures. The results show that, from a mechanical point of view, the diapirism model is a robust and consistent assumption for the emplacement of anorthosites, because realistic diapir and rim-syncline shapes are obtained. Moreover, the numerically obtained emplacement time (about 2.5 m.y.) is in agreement with the available geochronological data, and the computed strain field is coherent with field measurements, especially regarding the circumferential extension, which becomes the largest extension strain component in the expansion phase.

Path-dependent three-dimensional constitutive laws of reinforced concrete -formulation and experimental verifications-

A three-dimensional constitutive modeling for reinforced concrete is presented for finite element nonlinear analysis of reinforced concrete. The targets of interest to the authors are columns confined by lateral steel hoops, RC thin shells subjected to combined in-plane and out-of-plane actions and massive structures of three-dimensional (3D) extent in shear. The elasto-plastic and continuum fracture law is applied to pre-cracked solid concrete. For post cracking formulation, fixed multi-directional smeared crack model is adopted for RC domains of 3D geometry subjected to monotonic and reversed cyclic actions. The authors propose a new scheme of decomposing stress strain fields into sub-planes on which 2D constitutive laws can be applied. The proposed model for 3D reinforced concrete is experimentally verified in both member and structural levels under cyclic actions.

Stability of jointed rock masses evaluated by UDEC with an extended Saeb-Amadei constitutive law

This paper discusses the results of a numerical study which examines the influence of the choice of joint constitutive model on the stability of jointed rock masses. In the two-dimensional code of the Distinct Element Method used for this study, UDEC, the mechanical behaviour of rock joints is represented by an elasto-plastic law and the empirical continuous-yielding law. The modified version of the Saeb and Amadei non-linear model for rock joints subjected to monotonic and cyclic loading sequences as proposed by Souley et al. Int. J. Rock Mech. Min. Sci & Geomech. Abstr. 32, 101–109 (1995), is implemented in UDEC. Two simple examples provided a verification of the implemented model. These involved the monotonic normal compression of a joint and the direct shear test. The influence of joint constitutive law on the stability of an underground cavity was then examined for a specific joint network geometry. This analysis involved in situ low, medium, and high stress fields. Interpretation of the results shows that while stress magnitudes depend little on the type of constitutive law, the displacement field is, on the contrary, constitutive law dependent, particularly at high stress levels.

Influence of Clays on Borehole Stability : a Literature Survey Part One: Occurence of Drilling Problems. Physico-Chemical Description of Clays and of Their Interaction with Fluids

Influence of Clays on Borehole Stability : a Literature Survey Part One: Occurence of Drilling Problems. Physico-Chemical Description of Clays and of Their Interaction with Fluids

Algorithme de contraintes actives et contact unilatéral sans frottement

ABSTRACT We propose a method to take into account the unilateral contact problem based on an active set algorithm. This algorithm is developed inside the computation Code Aster. We first present a short bibliography on the subject. Then we develop the unilateral contact problem, the associated model and some theorems of uniqueness and convergence. The Kuhn Tucker theorem is then discussed in the context of minimization with constraints. The algorithm is presented by mean of a theoretical algorithm on which we demonstrate a convergence property and a computational algorithm with a discussion on the method. The validation of the obtained results is made by comparing the numerical results to analytical ones on a Hertz like problem. The last part is dedicated to the description of an industrial case with an elastoplastic law.

A simplified approach for sheet forming processes design

A new approach is developed to improve sheet forming parts and sheet forming processes design. In order to apply classical optimization methods, an energetic characterization of the global transformation of an elasto-plastic structure is proposed. After a brief review of thermostatics in elastoplastic laws, an energetic criterion is defined. With a geometrical definition of sheet forming processes, it is shown how to use this criterion to find the optimal displacement path between a flat blank and the part shape. Then, the classical assumptions of rigid-plastic behaviour and of thin shell geometry are introduced. Eventually, the criterion is used to define a formability criterion, for use at the preliminary design stage of parts. This paper concludes with numerical applications of the approach and analysis of formability criterion applications.

The optimum finite element grids around crack singularities in bilinear elastoplastic materials

In this paper, the effect of optimum finite element grids around crack tips in bilinear elastoplastic materials is addressed. The optimum meshes around singularities for elastic materials are proved to give also the best meshes for cases where bilinear elastoplastic laws are used to describe the overall material behavior. Plane-stress and plane-strain conditions under mode I tensile far-fields were examined in particular, giving very good results compared with the theoretical predictions and with other numerical solutions with standard finite element grids.

The response of a circular cylinder to a nuclear explosion

The theoretical foundation for a finite element analysis of the response of a clamped aluminum cylinder subjected to a nuclear burst environment is outlined. This includes non-linear strain-displacement relations as well as a linear isotropic hardening elastoplastic material law which obeys the von Mises yield criterion. The means of dealing with the thermal and blast loads are discussed. Finally the results of a numerical response study are presented: these include displacements, velocities, accelerations as well as stresses.

Numerical analysis of stone column supported foundations

In this paper, settlement and failure load of rafts resting on stone column reinforced soft clays are analyzed. The influence of the stone columns is assumed to be uniformly and homogeneously distributed throughout the reinforced region. It is also assumed that both columns and surrounding soil undergo the same total strains i.e. no slip occurs on the soil-column interface. A constitutive model is presented for an equivalent material. It combines different elasto-plastic laws, namely the Critical State model for clay and the Mohr-Coulomb criterion for gravel. Continuity of radial stresses is ensured by an additional pseudo-yield criterion. The model is incorporated in a finite element code and results for a circular footing are presented. The influence of dilatancy of the columns is highlighted together with the differences in the behaviour for columns situated at the centre or at the outer boundary of the footing. Flexible as well as rigid foundations are considered. It is emphasized that the finite element mesh is independent of the column spacing leading to considerable advantages in carrying out parametric studies.