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1 – 10 of over 1000Miroslav Halilovic, Bojan Starman, Marko Vrh and Boris Stok
The purpose of this study, which is designed for the implementation of models in the implicit finite element framework, is to propose a robust, stable and efficient explicit…
Abstract
Purpose
The purpose of this study, which is designed for the implementation of models in the implicit finite element framework, is to propose a robust, stable and efficient explicit integration algorithm for rate-independent elasto-plastic constitutive models.
Design/methodology/approach
The proposed automatic substepping algorithm is founded on an explicit integration scheme. The estimation of the maximal subincrement size is based on the stability analysis.
Findings
In contrast to other explicit substepping schemes, the algorithm is self-correcting by definition and generates no cumulative drift. Although the integration proceeds with maximal possible subincrements, high level of accuracy is attained. Algorithmic tangent stiffness is calculated in explicit form and optionally no analytical second-order derivatives are needed.
Research limitations/implications
The algorithm is convenient for elasto-plastic constitutive models, described with an algebraic constraint and a set of differential equations. This covers a large family of materials in the field of metal plasticity, damage mechanics, etc. However, it cannot be directly used for a general material model, because the presented algorithm is convenient for solving a set of equations of a particular type.
Practical implications
The estimation of the maximal stable subincrement size is computationally cheap. All expressions in the algorithm are in explicit form, thus the implementation is simple and straightforward. The overall performance of the approach (i.e. accuracy, time consumption) is fully comparable with a default (built-in) ABAQUS/Standard algorithm.
Originality/value
The estimated maximal subincrement size enables the algorithm to be stable by definition. Subincrements are much larger than those in conventional substepping algorithms. No error control, error correction or local iterations are required even in the case of large increments.
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Fabio De Angelis and Robert L. Taylor
The purpose of this paper is to present an efficient return mapping algorithm for elastoplastic constitutive problems of ductile metals with an exact closed form solution of the…
Abstract
Purpose
The purpose of this paper is to present an efficient return mapping algorithm for elastoplastic constitutive problems of ductile metals with an exact closed form solution of the local constitutive problem in the small strain regime. A Newton Raphson iterative method is adopted for the solution of the boundary value problem.
Design/methodology/approach
An efficient return mapping algorithm is illustrated which is based on an elastic predictor and a plastic corrector scheme resulting in an implicit and accurate numerical integration method. Nonlinear kinematic hardening rules and linear isotropic hardening rules are used to describe the components of the hardening variables. In the adopted algorithmic approach the solution of the local constitutive equations reduces to only one straightforward nonlinear scalar equation.
Findings
The presented algorithmic scheme naturally leads to a particularly simple form of the nonlinear scalar equation which ultimately scales down to an algebraic (polynomial) equation with a single variable. The straightforwardness of the present approach allows to find the analytical solution of the algebraic equation in a closed form. Further, the consistent tangent operator is derived as associated with the proposed algorithmic scheme and it is shown that the proposed computational procedure ensures a quadratic rate of asymptotic convergence when used with a Newton Raphson iterative method for the global solution procedure.
Originality/value
In the present approach the solution of the algebraic nonlinear equation is found in a closed form and accordingly no iterative method is required to solve the problem of the local constitutive equations. The computational procedure ensures a quadratic rate of asymptotic convergence for the global solution procedure typical of computationally efficient solution schemes. In the paper it is shown that the proposed algorithmic scheme provides an efficient and robust computational solution procedure for elastoplasticity boundary value problems. Numerical examples and computational results are reported which illustrate the effectiveness and robustness of the adopted integration algorithm for the finite element analysis of elastoplastic structures also under elaborate loading conditions.
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Nicolas Renon, Pierre Montmitonnet and Patrick Laborde
Purpose – The aim of this work is to provide a global 3D finite element (FE) model devoted to the modelling of superficial soil ploughing in the large deformation range and for a…
Abstract
Purpose – The aim of this work is to provide a global 3D finite element (FE) model devoted to the modelling of superficial soil ploughing in the large deformation range and for a vast class of soil treatment tools. Design/methodology/approach – We introduced soil constitutive equation in a FE software initially designed for the metal forming. We performed the numerical integration of the non‐linear ploughing problem. Non‐linearities encountered by the problem can be summed up: as soil constitutive equation (idealized with non‐associated compressible plastic law), unilateral frictional contact conditions (with a rigid body), geometrical non‐linearities (the ploughing tool) and large deformation range. To handle such difficulties we performed several numerical methods as implicit temporal scheme, Newton‐Raphson, non‐symmetric iterative solver, as well as proper approximation on stress and strain measures. Findings – Main results deal with the validation of the integration of the non‐linear constitutive equation in the code and a parametric study of the ploughing process. The influence of tool geometric parameters on the soil deformation modes and on the force experienced on the tools had been point out. As well, the influence of soil characteristics as compressibility had been analyzed. Research limitations/implications – This research is devoted to perform a numerical model applicable for a large range of soil treatment tools and for a large class of soil. However, taking into account all kind of soil is utopist. So limitations met are essentially related to the limit of the accuracy of the elasto‐plastic idealization for the soil. Practical implications – In practice the numerical model exposed in the paper can clearly help to improve and optimize any process involving superficial soil submitted to the mechanical action of a rigid body. Originality/value – The original value of the paper is to provide a global and an applicable numerical model able to take into account the main topics related to the ploughing of superficial soils. Industrials in geotechnics, in agriculture or in military purposes can benefit in using such numerical model.
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Divyanshu Kumar Lal and Arghya Das
Semi-implicit type cutting plane method (CPM) and fully implicit type closest point projection method (CPPM) are the two most widely used frameworks for numerical stress…
Abstract
Purpose
Semi-implicit type cutting plane method (CPM) and fully implicit type closest point projection method (CPPM) are the two most widely used frameworks for numerical stress integration. CPM is simple, easy to implement and accurate up to first order. CPPM is unconditionally stable and accurate up to second order though the formulation is complex. Therefore, this study aims to develop a less complex and accurate stress integration method for complex constitutive models.
Design/methodology/approach
Two integration techniques are formulated using the midpoint and Romberg method by modifying CPM. The algorithms are implemented for three different classes of soil constitutive model. The efficiency of the algorithms is judged via stress point analysis and solving a boundary value problem.
Findings
Stress point analysis indicates that the proposed algorithms are stable even with a large step size. In addition, numerical analysis for solving boundary value problem demonstrates a significant reduction in central processing unit (CPU) time with the use of the semi-implicit-type midpoint algorithm.
Originality/value
Traditionally, midpoint and Romberg algorithms are formulated from explicit integration techniques, whereas the present study uses a semi-implicit approach to enhance stability. In addition, the proposed stress integration algorithms provide an efficient means to solve boundary value problems pertaining to geotechnical engineering.
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N.N.S. Yapage and D.S. Liyanapathirana
Several constitutive models are available in the literature to describe the mechanical behaviour of cement stabilized soils. However, difficulties in implementing such models…
Abstract
Purpose
Several constitutive models are available in the literature to describe the mechanical behaviour of cement stabilized soils. However, difficulties in implementing such models within commercial finite element programs have hindered their application to solve related boundary value problems. Therefore, the aim of this study is to implement a constitutive model, which has the capability to simulate cement stabilized soil behaviour, into the finite element program ABAQUS through the user material subroutine UMAT.
Design/methodology/approach
After a detailed review of existing constitutive models for cement stabilized soils, a model based on the elasto‐plastic theory and the extended critical state concept with an associated flow rule is selected for the finite element implementation. A semi‐implicit integration method (cutting plane algorithm) with a continuum elasto‐plastic modulus and path dependent stress prediction strategy has been used in the implementation. The performance of the new finite element formulation of the constitutive model is verified by simulating triaxial test data using the finite element program with the new implementation and predictions from constitutive equations as well as experimental data.
Findings
The paper provides the implementation procedure of the constitutive model into ABAQUS but this method is useful for the implementation of any other constitutive model into ABAQUS or any other finite element program. Simulated results for the volumetric deformation of cement stabilized soils show that the cement stabilized soils do not obey the associated flow rule at high confining pressures. The parametric study shows that the influence of cementation increases the brittle nature and the bearing capacity of treated clay. In addition the results show that proposed finite element implementation has the ability to illustrate key features of the cement stabilized clay.
Originality/value
This paper presents an implementation of an elasto‐plastic constitutive model, based on the extended critical state concept, for cement stabilized soils into a finite element programme, which has been identified as an important and challenging topic in computational geomechanics. This implementation is useful in solving boundary value problems in geomechanics involving cement stabilized soils, incorporating key characteristics of these soils.
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Mohammad Rezaiee‐Pajand, Cyrus Nasirai and Mehrzad Sharifian
The purpose of this paper is to present a new effective integration method for cyclic plasticity models.
Abstract
Purpose
The purpose of this paper is to present a new effective integration method for cyclic plasticity models.
Design/methodology/approach
By defining an integrating factor and an augmented stress vector, the system of differential equations of the constitutive model is converted into a nonlinear dynamical system, which could be solved by an exponential map algorithm.
Findings
The numerical tests show the robustness and high efficiency of the proposed integration scheme.
Research limitations/implications
The von‐Mises yield criterion in the regime of small deformation is assumed. In addition, the model obeys a general nonlinear kinematic hardening and an exponential isotropic hardening.
Practical implications
Integrating the constitutive equations in order to update the material state is one of the most important steps in a nonlinear finite element analysis. The accuracy of the integration method could directly influence the result of the elastoplastic analyses.
Originality/value
The paper deals with integrating the constitutive equations in a nonlinear finite element analysis. This subject could be interesting for the academy as well as industry. The proposed exponential‐based integration method is more efficient than the classical strategies.
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E.A. De Souza Neto, Djordje Perić and D.R.J. Owen
This work addresses the computational aspects of a model forelastoplastic damage at finite strains. The model is a modification of apreviously established model for large strain…
Abstract
This work addresses the computational aspects of a model for elastoplastic damage at finite strains. The model is a modification of a previously established model for large strain elastoplasticity described by Perić et al. which is here extended to include isotropic damage and kinematic hardening. Within the computational scheme, the constitutive equations are numerically integrated by an algorithm based on operator split methodology (elastic predictor—plastic corrector). The Newton—Raphson method is used to solve the discretized evolution equations in the plastic corrector stage. A numerical assessment of accuracy and stability of the integration algorithm is carried out based on iso‐error maps. To improve the stability of the local N—R scheme, the standard elastic predictor is replaced by improvedinitial estimates ensuring convergence for large increments. Several possibilities are explored and their effect on the stability of the N—R scheme is investigated. The finite element method is used in the approximation of the incremental equilibrium problem and the resulting equations are solved by the standard Newton—Raphson procedure. Two numerical examples are presented. The results are compared with those obtained by the original elastoplastic model.
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Scott W. Sloan, Andrew J. Abbo and Daichao Sheng
Effective explicit algorithms for integrating complex elastoplastic constitutive models, such as those belonging to the Cam clay family, are described. These automatically divide…
Abstract
Effective explicit algorithms for integrating complex elastoplastic constitutive models, such as those belonging to the Cam clay family, are described. These automatically divide the applied strain increment into subincrements using an estimate of the local error and attempt to control the global integration error in the stresses. For a given scheme, the number of substeps used is a function of the error tolerance specified, the magnitude of the imposed strain increment, and the non‐linearity of the constitutive relations. The algorithms build on the work of Sloan in 1987 but include a number of important enhancements. The steps required to implement the integration schemes are described in detail and results are presented for a rigid footing resting on a layer of Tresca, Mohr‐Coulomb, modified Cam clay and generalised Cam clay soil. Explicit methods with automatic substepping and error control are shown to be reliable and efficient for these models. Moreover, for a given load path, they are able to control the global integration error in the stresses to lie near a specified tolerance. The methods described can be used for exceedingly complex constitutive laws, including those with a non‐linear elastic response inside the yield surface. This is because most of the code required to program them is independent of the precise form of the stress‐strain relations. In contrast, most of the implicit methods, such as the backward Euler return scheme, are difficult to implement for all but the simplest soil models.
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ADNAN IBRAHIMBEGOVIĆ and FRANÇOIS FREY
An efficient implementation of a constitutive model for reinforced concrete plates is discussed in this work. The constitutive model is set directly in terms of stress resultants…
Abstract
An efficient implementation of a constitutive model for reinforced concrete plates is discussed in this work. The constitutive model is set directly in terms of stress resultants and their energy conjugate strain measures, relating their total values. The latter simplification is justified by our primary goal being an evaluation of the limit load of a reinforced concrete plate. A concept of the ‘rotating crack model’ is utilized in proposing the constitutive model to relate the principal values of bending moments and the corresponding values of curvatures. Efficient implementation is provided by a very robust, but inexpensive plate element. The element is based on an assumed shear strain field and a set of incompatible bending modes, which provides that the non‐linear computations, pertinent to constitutive model, can be carried out locally, i.e. independently at each numerical integration point. Set of numerical examples is presented to demonstrate a very satisfying performance of the proposed model.
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Johan Clausen, Lars Damkilde and Lars Vabbersgaard Andersen
The purpose of this paper is to present several methods on how to deal with yield surface discontinuities. The explicit formulations, first presented by Koiter (1953), result in…
Abstract
Purpose
The purpose of this paper is to present several methods on how to deal with yield surface discontinuities. The explicit formulations, first presented by Koiter (1953), result in multisingular constitutive matrices which can cause numerical problems in elasto-plastic finite element calculations. These problems, however, are not documented in previous literature. In this paper an amendment to the Koiter formulation of the constitutive matrices for stress points located on discontinuities is proposed.
Design/methodology/approach
First, a review of existing methods of handling yield surface discontinuities is given. Examples of the numerical problems of the methods are presented. Next, an augmentation of the existing methods is proposed and its robustness is demonstrated through footing bearing capacity calculations that are usually considered “hard”.
Findings
Previous studies documented in the literature all present “easy” calculation examples, e.g. low friction angles and few elements. The amendments presented in this paper result in robust elasto-plastic computations, making the solution of “hard” problems possible without introducing approximations in the yield surfaces. Examples of “hard” problems are highly frictional soils and/or three-dimensional geometries.
Originality/value
The proposed method makes finite element calculations using yield criteria with corners and apices, e.g. Mohr-Coulomb and Hoek-Brown, much more robust and stable.
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