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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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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Deniz D. Somer, D Peric, Eduardo Alberto de Souza Neto and Wulf G Dettmer
The purpose of this paper is to present knowledge in estimating yield surfaces of heterogeneous media by use of homogenization, especially where the macroscopic behaviour is…
Abstract
Purpose
The purpose of this paper is to present knowledge in estimating yield surfaces of heterogeneous media by use of homogenization, especially where the macroscopic behaviour is driven by weak interfaces between phase constituents.
Design/methodology/approach
A computational homogenization procedure is used to determine the yield surface of a Representative Volume Element (RVE) that contains a fully debonded inclusion embedded within ideally plastic matrix, whereby the interface is modelled by a Coulomb type friction law.
Findings
The macroscopic behaviour of the RVE is shown to coincide an RVE with a hole for expanding loads, whereas for compressive loads, it was shown to approach an RVE with a fully bonded inclusion.
Originality/value
The present paper builds on Gurson’s work in estimating macroscopic yield surfaces of heterogeneous materials. The work is novel in the sense that there had been no previous publications discussing influence of weak interfaces on yield surfaces.
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This work is concerned with computational modelling of viscoplastic fluids. The flows considered are assumed to be incompressible, while the viscoplastic laws are obtained by…
Abstract
This work is concerned with computational modelling of viscoplastic fluids. The flows considered are assumed to be incompressible, while the viscoplastic laws are obtained by incorporating a yield stress below which the fluid is assumed to remain non‐deformable. The Bingham fluid is chosen as a model problem and is considered in detail in the text. The finite element formulation adopted in this work is based on a version of the stabilised finite element method, known as the Galerkin/least‐squares method, originally developed by Hughes and co‐workers. This methodology allows use of low and equal order interpolation of the pressure and velocity fields, thus providing an efficient finite element framework. The Newton‐Raphson method has been chosen for solution of the incremental non‐linear problem arising through the temporal discretisation of the evolution problem. Numerical examples are provided to illustrate the main features of the described methodology.
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K. Han, D. Peric´, D.R.J. Owen and J. Yu
Following earlier work on the combined finite/discrete element simulation of shot peening process in 2D case, 3D representation of the problem is established with respect to DE…
Abstract
Following earlier work on the combined finite/discrete element simulation of shot peening process in 2D case, 3D representation of the problem is established with respect to DE modelling and contact interaction laws. An important relevant computational issue regarding the critical time step is carefully studied, and a new time stepping scheme that can ensure both short and long term stability of the contact models is developed. Numerical tests are performed to evaluate the proposed normal and frictional contact interaction laws with various model parameters. The influences of single and multiple shot impact, as well as element sizes are also numerically investigated. The established contact interaction laws can also be applied to other multi‐body dynamic simulations.
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K. Han, D.R.J. Owen and D. Peric
Because of the unrealistic demand of computer resources in terms of memory and CPU times for the direct numerical simulation of practical peen forming processes, a two‐stage…
Abstract
Because of the unrealistic demand of computer resources in terms of memory and CPU times for the direct numerical simulation of practical peen forming processes, a two‐stage combined finite/discrete element and explicit/implicit solution strategy is proposed in this paper. The procedure involves, at the first stage, the identification of the residual stress/strain profile under particular peening conditions by employing the combined finite/discrete approach on a small scale sample problem, and then at the second stage, the application of this profile to the entire workpiece to obtain the final deformation and stress distribution using an implicit static analysis. The motivation behind the simulation strategy and the relevant computational and implementation issues are discussed. The numerical example demonstrates the ability of the proposed scheme to simulate a peen forming process.
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Ramin Moshfegh, Xiangdong Li and Larsgunnar Nilsson
Two mesh refinement indicators based on the gradients of effective stress (GSIG) and effective plastic strain (GEPS), respectively, are proposed for adaptive finite element…
Abstract
Two mesh refinement indicators based on the gradients of effective stress (GSIG) and effective plastic strain (GEPS), respectively, are proposed for adaptive finite element analysis of the large deformation, quasi‐static or dynamic response of shell structures. The mesh refinement indicators are based on equi‐distributing the variation of stresses or plastic strains over the elements of the mesh. A program module is developed and implemented in the non‐linear explicit finite element code LS‐DYNA. This module provides element‐wise refinement evaluations so that selective mesh refinements are carried out in regions of the mesh where the values of local indicators exceed a user‐specified tolerance. The FE model of a conventional deep drawing process is used as a numerical model, including both material and geometrical non‐linearities, in order to demonstrate the versatility of the two refinement indicators. Four different refinement indicators, based on angle change, thickness change, GSIG and GEPS, are applied in this investigation. The numerical results are compared with experimental results regarding the thickness distribution versus cup height, cup height variation versus circumference angle, effective plastic strain in the deformed sheet and punch force. It is shown that the proposed indicators can identify finite elements which have high gradients of effective stress or effective plastic strain so that the mesh is refined in the regions undergoing the most severe deformations and the numerical results are improved.
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This paper gives a review of the finite element techniques (FE)applied in the area of material processing. The latest trends in metalforming, non‐metal forming and powder…
Abstract
This paper gives a review of the finite element techniques (FE) applied in the area of material processing. The latest trends in metal forming, non‐metal forming and powder metallurgy are briefly discussed. The range of applications of finite elements on the subjects is extremely wide and cannot be presented in a single paper; therefore the aim of the paper is to give FE users only an encyclopaedic view of the different possibilities that exist today in the various fields mentioned above. An appendix included at the end of the paper presents a bibliography on finite element applications in material processing for the last five years, and more than 1100 references are listed.
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Izian Abd. Karim, Chun Hean Lee, Antonio J. Gil and Javier Bonet
– The purpose of this paper is to present a new stabilised low-order finite element methodology for large strain fast dynamics.
Abstract
Purpose
The purpose of this paper is to present a new stabilised low-order finite element methodology for large strain fast dynamics.
Design/methodology/approach
The numerical technique describing the motion is formulated upon the mixed set of first-order hyperbolic conservation laws already presented by Lee et al. (2013) where the main variables are the linear momentum, the deformation gradient tensor and the total energy. The mixed formulation is discretised using the standard explicit two-step Taylor-Galerkin (2TG) approach, which has been successfully employed in computational fluid dynamics (CFD). Unfortunately, the results display non-physical spurious (or hourglassing) modes, leading to the breakdown of the numerical scheme. For this reason, the 2TG methodology is further improved by means of two ingredients, namely a curl-free projection of the deformation gradient tensor and the inclusion of an additional stiffness stabilisation term.
Findings
A series of numerical examples are carried out drawing key comparisons between the proposed formulation and some other recently published numerical techniques.
Originality/value
Both velocities (or displacements) and stresses display the same rate of convergence, which proves ideal in the case of industrial applications where low-order discretisations tend to be preferred. The enhancements introduced in this paper enable the use of linear triangular (or bilinear quadrilateral) elements in two dimensional nearly incompressible dynamics applications without locking difficulties. In addition, an artificial viscosity term has been added into the formulation to eliminate the appearance of spurious oscillations in the vicinity of sharp spatial gradients induced by shocks.