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Article
Publication date: 1 March 1995

L.J. Sluys, M. Cauvern and R. De Borst

The dispersive behaviour of waves in softening problems is analysed.Attention is focused on the influence of the numerical scheme on thedispersion characteristics in the process…

96

Abstract

The dispersive behaviour of waves in softening problems is analysed. Attention is focused on the influence of the numerical scheme on the dispersion characteristics in the process of localization of deformation. Distinction has been made between softening models defined in a standard plasticity framework and in a gradient‐dependent plasticity theory. Waves in a standard softening plasticity continuum do not disperse but due to spatial discretization dispersion is introduced which results in a mesh size dependent length scale effect. On the other hand, wave propagation in a gradient‐dependent softening plasticity continuum is dispersive. By carrying out the dispersion analysis on the discretized system the influence of numerical dispersion on material dispersion can be quantified which enables us to determine the accuracy for the solution of the localization zone. For a modelling with and without the inclusion of strain gradients accuracy considerations with respect to mass discretization, finite element size, time integration scheme and time step have been carried out.

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Engineering Computations, vol. 12 no. 3
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 1 February 1993

R. DE BORST, L.J. SLUYS, H.‐B. MUHLHAUS and J. PAMIN

Classical continuum models, i.e. continuum models that do not incorporate an internal length scale, suffer from excessive mesh dependence when strain‐softening models are used in…

1893

Abstract

Classical continuum models, i.e. continuum models that do not incorporate an internal length scale, suffer from excessive mesh dependence when strain‐softening models are used in numerical analyses and cannot reproduce the size effect commonly observed in quasi‐brittle failure. In this contribution three different approaches will be scrutinized which may be used to remedy these two intimately related deficiencies of the classical theory, namely (i) the addition of higher‐order deformation gradients, (ii) the use of micropolar continuum models, and (iii) the addition of rate dependence. By means of a number of numerical simulations it will be investigated under which conditions these enriched continuum theories permit localization of deformation without losing ellipticity for static problems and hyperbolicity for dynamic problems. For the latter class of problems the crucial role of dispersion in wave propagation in strain‐softening media will also be highlighted.

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Engineering Computations, vol. 10 no. 2
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 1 February 2001

R. de Borst, G.N. Wells and L.J. Sluys

The formulation of finite elements with incompatible discontinuous modes is examined rigorously. Both weak and strong discontinuities are considered. Starting from a careful…

486

Abstract

The formulation of finite elements with incompatible discontinuous modes is examined rigorously. Both weak and strong discontinuities are considered. Starting from a careful elaboration of the kinematics for both types of discontinuities a comprehensive finite element formulation is derived based on a three‐field variational statement. Similarities and differences are highlighted between the various formulations which ensue.

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Engineering Computations, vol. 18 no. 1/2
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 6 September 2021

Bruna Caroline Campos, Felicio Bruzzi Barros and Samuel Silva Penna

The aim of this paper is to present a novel data transfer technique to simulate, by G/XFEM, a cohesive crack propagation coupled with a smeared damage model. The efficiency of…

100

Abstract

Purpose

The aim of this paper is to present a novel data transfer technique to simulate, by G/XFEM, a cohesive crack propagation coupled with a smeared damage model. The efficiency of this technique is evaluated in terms of processing time, number of Newton–Raphson iterations and accuracy of structural response.

Design/methodology/approach

The cohesive crack is represented by the G/XFEM enrichment strategy. The elements crossed by the crack are divided into triangular cells. The smeared crack model is used to describe the material behavior. In the nonlinear solution of the problem, state variables associated with the original numerical integration points need to be transferred to new points created with the triangular subdivision. A nonlocal strategy is tailored to transfer the scalar and tensor variables of the constitutive model. The performance of this technique is numerically evaluated.

Findings

When compared with standard Gauss quadrature integration scheme, the proposed strategy may deliver a slightly superior computational efficiency in terms of processing time. The weighting function parameter used in the nonlocal transfer strategy plays an important role. The equilibrium state in the interactive-incremental solution process is not severely penalized and is readily recovered. The advantages of such proposed technique tend to be even more pronounced in more complex and finer meshes.

Originality/value

This work presents a novel data transfer technique based on the ideas of the nonlocal formulation of the state variables and specially tailored to the simulation of cohesive crack propagation in materials governed by the smeared crack constitutive model.

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Article
Publication date: 28 October 2013

Mojtaba Talebian, Rafid Al-Khoury and Lambertus J. Sluys

This paper aims to present a computationally efficient finite element model for the simulation of isothermal immiscible two-phase flow in a rigid porous media with a particular…

214

Abstract

Purpose

This paper aims to present a computationally efficient finite element model for the simulation of isothermal immiscible two-phase flow in a rigid porous media with a particular application to CO2 sequestration in underground formations. Focus is placed on developing a numerical procedure, which is effectively mesh-independent and suitable to problems at regional scales.

Design/methodology/approach

The averaging theory is utilized to describe the governing equations of the involved unsaturated multiphase flow. The level-set (LS) method and the extended finite element method (XFEM) are utilized to simulate flow of the CO2 plume. The LS is employed to trace the plume front. A streamline upwind Petrov-Galerkin method is adopted to stabilize possible occurrence of spurious oscillations due to advection. The XFEM is utilized to model the high gradient in the saturation field front, where the LS function is used for enhancing the weighting and the shape functions.

Findings

The capability of the proposed model and its features are evaluated by numerical examples, demonstrating its accuracy, stability and convergence, as well as its advantages over standard and upwind techniques. The study showed that a good combination between a mathematical model and a numerical model enables the simulation of complicated processes occurring in complicated and large geometry using minimal computational efforts.

Originality/value

A new computational model for two-phase flow in porous media is introduced with basic requirements for accuracy, stability, and convergence, which are met using relatively coarse meshes.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 23 no. 8
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 3 July 2017

Arman Shojaei, Mirco Zaccariotto and Ugo Galvanetto

The paper aims to use a switching technique which allows to couple a nonlocal bond-based Peridynamic approach to the Meshless Local Exponential Basis Functions (MLEBF) method…

655

Abstract

Purpose

The paper aims to use a switching technique which allows to couple a nonlocal bond-based Peridynamic approach to the Meshless Local Exponential Basis Functions (MLEBF) method, based on classical continuum mechanics, to solve planar problems.

Design/methodology/approach

The coupling has been achieved in a completely meshless scheme. The domain is divided in three zones: one in which only Peridynamics is applied, one in which only the meshless method is applied and a transition zone where a gradual transition between the two approaches takes place.

Findings

The new coupling technique generates overall grids that are not affected by ghost forces. Moreover, the use of the meshless approach can be limited to a narrow boundary region of the domain, and in this way, it can be used to remove the “surface effect” from the Peridynamic solution applied to all internal points.

Originality/value

The current study paves the road for future studies on dynamic and static crack propagation problems.

Details

Engineering Computations, vol. 34 no. 5
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 20 April 2015

Xiaodong Zhang and Tinh Quoc Bui

– The purpose of this paper is to achieve numerical simulation of cohesive crack growth in concrete structures.

930

Abstract

Purpose

The purpose of this paper is to achieve numerical simulation of cohesive crack growth in concrete structures.

Design/methodology/approach

The extended finite element method (XFEM) using four-node quadrilateral element associated with the fictitious cohesive crack model is used. A mixed-mode traction-separation law is assumed for the cohesive crack in the fracture process zone (FPZ). Enrichments are considered for both partly and fully cracked elements, and it thus makes the evolution of crack to any location inside the element possible. In all. two new solution procedures based on Newton-Raphson method, which differ from the approach suggested by Zi and Belytschko (2003), are presented to solve the nonlinear system of equations. The present formulation results in a symmetric tangent matrix, conveniently in finite element implementation and programming.

Findings

The inconvenience in solving the inversion of an unsymmetrical Jacobian matrix encountered in the existing approach is avoided. Numerical results evidently confirm the accuracy of the proposed approach. It is concluded that the developed XFEM approach is especially suitable in simulating cohesive crack growth in concrete structures.

Research limitations/implications

Multiple cracks and crack growth in reinforced concretes should be considered in further studies.

Practical implications

The research paper presents a very useful and accurate numerical method for engineering application problems that has ability to numerically simulate the cohesive crack growth of concrete structures.

Originality/value

The research paper provides a new numerical approach using two new solution procedures in solving nonlinear system of equations for cohesive crack growth in concrete structures that is very convenient in programming and implementation.

Details

Engineering Computations, vol. 32 no. 2
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 27 January 2021

Angel Rawat, Raghu Piska, A. Rajagopal and Mokarram Hossain

This paper aims to present a nonlocal gradient plasticity damage model to demonstrate the crack pattern of a body, in an elastic and plastic state, in terms of damage law. The…

244

Abstract

Purpose

This paper aims to present a nonlocal gradient plasticity damage model to demonstrate the crack pattern of a body, in an elastic and plastic state, in terms of damage law. The main objective of this paper is to reconsider the nonlocal theory by including the material in-homogeneity caused by damage and plasticity. The nonlocal nature of the strain field provides a regularization to overcome the analytical and computational problems induced by softening constitutive laws. Such an approach requires C1 continuous approximation. This is achieved by using an isogeometric approximation (IGA). Numerical examples in one and two dimensions are presented.

Design/methodology/approach

In this work, the authors propose a nonlocal elastic plastic damage model. The nonlocal nature of the strain field provides a regularization to overcome the analytical and computational problems induced by softening constitutive laws. An additive decomposition of strains in to elastic and inelastic or plastic part is considered. To obtain stable damage, a higher gradient order is considered for an integral equation, which is obtained by the Taylor series expansion of the local inelastic strain around the point under consideration. The higher-order continuity of nonuniform rational B-splines (NURBS) functions used in isogeometric analysis are adopted here to implement in a numerical scheme. To demonstrate the validity of the proposed model, numerical examples in one and two dimensions are presented.

Findings

The proposed nonlocal elastic plastic damage model is able to predict the damage in an accurate manner. The numerical results are mesh independent. The nonlocal terms add a regularization to the model especially for strain softening type of materials. The consideration of nonlocality in inelastic strains is more meaningful to the physics of damage. The use of IGA framework and NURBS basis functions add to the nonlocal nature in approximations of the field variables.

Research limitations/implications

The method can be extended to 3D. The model does not consider the effect of temperature and the dissipation of energy due to temperature. The method needs to be implemented for more real practical problems and compare with experimental work. This is an ongoing work.

Practical implications

The nonlocal models are suitable for predicting damage in quasi brittle materials. The use of elastic plastic theories allows to capture the inelastic deformations more accurately.

Social implications

The nonlocal models are suitable for predicting damage in quasi brittle materials. The use of elastic plastic theories allows to capture the inelastic deformations more accurately.

Originality/value

The present work includes the formulation and implementation of a nonlocal damage plasticity model using an isogeometric discretization, which is the novel contribution of this paper. An implicit gradient enhancement is considered to the inelastic strain. During inelastic deformations, the proposed strain tensor partitioning allows the use of a distinct potential surface and distinct failure criterion for both damage and plasticity models. The use of NURBS basis functions adds to more nonlocality in the approximation.

Details

Engineering Computations, vol. 38 no. 6
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 2 January 2009

D. Brancherie and A. Ibrahimbegovic

The purpose of this paper is to present a finite element model capable of describing both the diffuse damage mechanism which develops first during the loading of massive brittle…

542

Abstract

Purpose

The purpose of this paper is to present a finite element model capable of describing both the diffuse damage mechanism which develops first during the loading of massive brittle structures and the failure process, essentially due to the propagation of a macro‐crack responsible for the softening behaviour of the structure. The theoretical developments for such a model are presented, considering an isotropic damage model for the continuum and a Coulomb‐type criterion for the localized part.

Design/methodology/approach

This is achieved by activating subsequently diffuse and localized damage mechanisms. Localized phenomena are taken into account by means of the introduction of a displacement discontinuity at the element level.

Findings

It was found that, with such an approach, the final crack direction is predicted quite well, in fact much better than the prediction made by the fracture mechanics type of models considering combination of only elastic response and softening.

Originality/value

The presented model has the potential to describe complex damage phenomena in a cyclic and/or non‐proportional loading program, such as crack closing and re‐opening, cohesive resistance deterioration due to tangential sliding, by using only a few parameters compared to the traditional models for cyclic loading.

Details

Engineering Computations, vol. 26 no. 1/2
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 1 July 2005

Guillaume Hervé, Fabrice Gatuingt and Adnan Ibrahimbegović

To provide an efficient and robust constitutive equations for concrete ion application to high rate dynamics.

1082

Abstract

Purpose

To provide an efficient and robust constitutive equations for concrete ion application to high rate dynamics.

Design/methodology/approach

Develops an explicit‐implicit integration scheme for a concrete model. This robust integration scheme ensures computational efficiency. Comparison between simulations of impact of equivalent aircraft engine projectiles and the tests carried out in Sandia laboratory also demonstrate its efficiency.

Findings

Shows that modeling transient high rate dynamic behavior of concrete is very important to take into account for design concrete structures in the cases of dynamic loading conditions, such as an impact on the structure.

Originality/value

Proposes an original integration scheme for a coupled rate dependent damage plasticity model. Also provides a detailed consideration of the numerical stability of this kind of scheme for rate‐dependent damage model.

Details

Engineering Computations, vol. 22 no. 5/6
Type: Research Article
ISSN: 0264-4401

Keywords

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