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1 – 10 of over 2000Fabio 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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H.W. Zhang, M. Wang, X.W. Zhang and X. Guo
An improved mathematical programming method for numerical simulation of cloth wrinkling is investigated.
Abstract
Purpose
An improved mathematical programming method for numerical simulation of cloth wrinkling is investigated.
Design/methodology/approach
Cloth is modeled as the network of bars (called bar network) or membrane elements with a special nonlinear mechanical constitutive law in the finite element analysis.
Findings
Compared with conventional numerical methods, the proposed method does not depend on stress iteration, but on the base exchanges in the solution of a standard quadratic programming problem. Thus, the new method presents very good convergence behavior and accurate predictions of wrinkling patterns and stress distributions of cloths. Numerical results demonstrate the validity and the efficiency of the proposed method.
Originality/value
From the engineering point of view, accurate numerical methods are required in wrinkling analysis of cloth deformation. The algorithm developed here also can be applied into fields such as large deformation under wind load and dynamic behaviors of cloths.
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The aim of this paper is to develop a suitable artificial neural network (ANN) model that fits best in predicting the experimental flow stress values to the closet proximity for…
Abstract
Purpose
The aim of this paper is to develop a suitable artificial neural network (ANN) model that fits best in predicting the experimental flow stress values to the closet proximity for mechanically alloyed Al6063/0.75Al2O3/0.75Y2O3 hybrid nanocomposite.
Design/methodology/approach
The ANN model is implemented on neural network toolbox of MATLAB® using feed‐forward back propagation network and logsig functions. A set of 80 training data and 20 testing data were used in the ANN model. The layout of the network is arranged with three input parameters that include temperature, strain and strain rate, one hidden layer with 22 neurons and one output parameter consisting of flow stress. Flow stress was also predicted using Arrhenius constitutive model.
Findings
Based on the comparison of the predicted results using ANN model and Arrhenius constitutive model, it was observed that the ANN model has higher accuracy and could be used to estimate the flow stress values during hot deformation of Al6063/0.75Al2O3/0.75Y2O3 hybrid nanocomposite.
Originality/value
The ANN trained with feed forward back propagation algorithm developed, presents the excellent performance of flow stress prediction of Al6063/0.75Al2O3/0.75Y2O3 hybrid nanocomposite with minimum error rates.
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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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Miroslav 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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A.R. Khoei, A. Bakhshiani and M. Mofid
In this paper, a new rate type endochronic constitutive model is introduced to describe deformations in the finite strain range. A new material dependent objective rate of Cauchy…
Abstract
In this paper, a new rate type endochronic constitutive model is introduced to describe deformations in the finite strain range. A new material dependent objective rate of Cauchy stress is suggested based on the general form of spin tensors, defining objective stress rates. The endochronic constitutive equations are extended using the concept of corotational stress rates and additive decomposition of deformation rate. The constitutive relations are specialized for thin‐walled tubes under torsion and a procedure for solving the ordinary differential equations for cases of simple and pure torsion is developed. The axial effects for various materials, subjected to simple and pure torsion, are simulated and compared with experimental data. The results clearly indicate that the new combined rate endochronic model can be effectively used to describe the behavior of material in the finite strain range.
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D. Peric´ and W. Dettmer
This work is concerned with the computational modelling of non‐linear solid material behaviour in the finite strain regime. Based on the recent computational formulations for…
Abstract
This work is concerned with the computational modelling of non‐linear solid material behaviour in the finite strain regime. Based on the recent computational formulations for modelling of inelastic material behaviour, a generalized material model is presented for inelastic materials incorporating classical elastic, viscoelastic, plastic and viscoplastic material description, all operating in the finite strain regime. The underlying rheological model corresponds to the combined action of several rheological components, such as Hooke, Maxwell and Prandtl elements, arranged in parallel. This work summarizes the theoretical basis of the material model and presents the computational treatment in the framework of a finite element solution procedure. Numerical examples are provided to illustrate the scope of the described computational strategy.
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S.M. Giusti, P.J. Blanco, E.A. de Souza Netoo and R.A. Feijóo
The purpose of this paper is to assess the Gurson yield criterion for porous ductile metals.
Abstract
Purpose
The purpose of this paper is to assess the Gurson yield criterion for porous ductile metals.
Design/methodology/approach
A finite element procedure is used within a purely kinematical multi‐scale constitutive modelling framework to determine estimates of extremal overall yield surfaces. The RVEs analysed consist of an elastic‐perfectly plastic von Mises type matrix under plane strain conditions containing a single centered circular hole. Macroscopic yield surface estimates are obtained under three different RVE kinematical assumptions: linear boundary displacements (an upper bound); periodic boundary displacement fluctuations (corresponding to periodically perforated media); and, minimum constraint or uniform boundary traction (a lower bound).
Findings
The Gurson criterion predictions fall within the bounds obtained under relatively high void ratios – when the bounds lie farther apart. Under lower void ratios, when the bounds lie close together, the Gurson predictions of yield strength lie slightly above the computed upper bounds in regions of intermediate to high stress triaxiality. A modification to the original Gurson yield function is proposed that can capture the computed estimates under the three RVE kinematical constraints considered.
Originality/value
Assesses the accuracy of the Gurson criterion by means of a fully computational multi‐scale approach to constitutive modelling. Provides an alternative criterion for porous plastic media which encompasses the common microscopic kinematical constraints adopted in this context.
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Michel Bellet, Olivier Jaouen and Isabelle Poitrault
The present paper addresses the computer modelling of pipe formation in metal castings.
Abstract
Purpose
The present paper addresses the computer modelling of pipe formation in metal castings.
Design/methodology/approach
As a preliminary, a brief review of the current state‐of‐the‐art in pipe shrinkage computation is presented. Then, in first part, the constitutive equations that have to be considered in thermomechanical computations are presented, followed by the main lines of the mechanical finite element resolution. A detailed presentation of an original arbitrary Lagrangian‐Eulerian (ALE) formulation is given, explaining the connection between the Lagrangian and the quasi Eulerian zones, and the treatment of free surfaces.
Findings
Whereas most existing methods are based on thermal considerations only, it is demonstrated in the current paper that this typical evolution of the free surface, originated by shrinkage at solidification front and compensating feeding liquid flow, can be effectively approached by a thermomechanical finite element analysis.
Research limitations/implications
Future work should deal with the following points: identification of thermo‐physical and rheological data, automatic and adaptive mesh refinement, calculation of the coupled deformation of mold components, development of a two‐phase solid/liquid formulation.
Practical implications
An example of industrial application is given. The proposed method has been implemented in the commercial software THERCAST® dedicated to casting simulation.
Originality/value
The proposed numerical methods provide a comprehensive approach, capable of modelling concurrently all the main phenomena participating in pipe formation.
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Many industrial analyses require the resolution of complex nonlinear problems. For such calculations, error‐controlled adaptive strategies must be used to improve the quality of…
Abstract
Many industrial analyses require the resolution of complex nonlinear problems. For such calculations, error‐controlled adaptive strategies must be used to improve the quality of the results. In this paper, adaptive strategies for nonlinear calculations in plasticity based on an enhanced error on the constitutive relation are presented. We focus on the adaptivity of the mesh and of the time discretization.
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