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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…

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

Keywords

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…

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.

Article
Publication date: 17 October 2022

Nicolò Spiezia and Valentina Anna Lia Salomoni

This paper proposes a unified original general framework, designed to theoretically develop and to extremely easily implement elastoplastic constitutive laws defined in the so…

Abstract

Purpose

This paper proposes a unified original general framework, designed to theoretically develop and to extremely easily implement elastoplastic constitutive laws defined in the so called two-invariants space, both in small and finite strain regime.

Design/methodology/approach

A general return mapping algorithm is proposed, and particularly a standard procedure is developed to compute the two algorithmic tangent operators, required to solve the Newton–Raphson scheme at the local and global level and thus cast the elastoplastic algorithm within a FEM code.

Findings

This work demonstrates that the proposed procedure is fully general and can be applied whatever is the elastic law, the yield surface, the plastic potential function and the hardening law. Several numerical examples are reported, not only to demonstrate the accuracy and robustness of the algorithm, but also explain how to use this general algorithm also in other applications.

Originality/value

The proposed algorithm and its numerical implementation into a FEM code is new and original. The usefulness and the value of the algorithm is twofold: (1) it can be implemented in a small and finite strain simulation FEM code, in order to handle different types of constitutive laws in the same modular way, thus fully leveraging on modern object-oriented coding approach; (2) it can be used as a framework to develop (and then to implement) new constitutive models, since the researcher can simply define the relevant functions (and its main derivatives) and automatically get the numerical algorithm.

Details

Engineering Computations, vol. 39 no. 9
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 27 February 2020

Gianluca Mazzucco, Beatrice Pomaro, Giovanna Xotta, Carmelo E. Maiorana and Valentina A. Salomoni

The purpose of this paper is the numerical assessment of concrete behaviour close to failure, via the development of robust elastoplastic models inclusive of damage effects. If…

Abstract

Purpose

The purpose of this paper is the numerical assessment of concrete behaviour close to failure, via the development of robust elastoplastic models inclusive of damage effects. If mesoscale investigations are to be considered, the model must take into account the local confinement effects because of the presence of aggregate inclusions in the cement paste and, correspondingly, the possibility to account for local 3D stress states even under uniaxial compression. Additionally, to enhance the predictive capabilities of a mesoscale representation, the reconstructed geometry must accurately follow the real one.

Design/methodology/approach

The work provides a procedure that combines a 3D digital image technique with finite element (FE) modelling thus maintaining the original 3D morphology of the composite.

Findings

The potentialities of the proposed approach are discussed, giving new insights to a FE modelling (FEM)-based approach applied together with a computer-aided design. Coupled mechanisms of mechanical mismatch and confinement, characterizing the combined cement matrix-aggregates effect, are captured and highlighted via the numerical tests.

Originality/value

The novelty of this research work lies in the proposal of a digitally based methodology for a precise concrete reconstruction together with the adoption of an upgraded elastic–plastic damage model for the cement paste.

Details

Engineering Computations, vol. 37 no. 7
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 1 January 2004

Jaroslav Mackerle

This paper gives a bibliographical review of the finite element modelling and simulation of indentation testing from the theoretical as well as practical points of view. The…

2056

Abstract

This paper gives a bibliographical review of the finite element modelling and simulation of indentation testing from the theoretical as well as practical points of view. The bibliography lists references to papers, conference proceedings and theses/dissertations that were published between 1990 and 2002. At the end of this paper, 509 references are listed dealing with subjects such as, fundamental relations and modelling in indentation testing, identification of mechanical properties for specific materials, fracture mechanics problems in indentation, scaling relationship for indentation, indenter geometry and indentation testing.

Details

Engineering Computations, vol. 21 no. 1
Type: Research Article
ISSN: 0264-4401

Keywords

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…

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.

Details

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

Keywords

Article
Publication date: 19 August 2019

Amir Norouzzadeh, Mohammad Faraji Oskouie, Reza Ansari and Hessam Rouhi

This paper aims to combine Eringen’s micromorphic and nonlocal theories and thus develop a comprehensive size-dependent beam model capable of capturing the effects of…

Abstract

Purpose

This paper aims to combine Eringen’s micromorphic and nonlocal theories and thus develop a comprehensive size-dependent beam model capable of capturing the effects of micro-rotational/stretch/shear degrees of freedom of material particles and nonlocality simultaneously.

Design/methodology/approach

To consider nonlocal influences, both integral (original) and differential versions of Eringen’s nonlocal theory are used. Accordingly, integral nonlocal-micromorphic and differential nonlocal-micromorphic beam models are formulated using matrix-vector relations, which are suitable for implementing in numerical approaches. A finite element (FE) formulation is also provided to solve the obtained equilibrium equations in the variational form. Timoshenko micro-/nano-beams with different boundary conditions are selected as the problem under study whose static bending is addressed.

Findings

It was shown that the paradox related to the clamped-free beam is resolved by the present integral nonlocal-micromorphic model. It was also indicated that the nonlocal effect captured by the integral model is more pronounced than that by its differential counterpart. Moreover, it was revealed that by the present approach, the softening and hardening effects, respectively, originated from the nonlocal and micromorphic theories can be considered simultaneously.

Originality/value

Developing a hybrid size-dependent Timoshenko beam model including micromorphic and nonlocal effects. Considering the nonlocal effect based on both Eringen’s integral and differential models proposing an FE approach to solve the bending problem, and resolving the paradox related to nanocantilever.

Details

Engineering Computations, vol. 37 no. 2
Type: Research Article
ISSN: 0264-4401

Keywords

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…

1791

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.

Details

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

Keywords

Article
Publication date: 1 April 1991

RENÉ DE BORST

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

1429

Abstract

Classical continuum models, i.e. continuum models that do not incorporate an internal length scale, suffer from pathological mesh‐dependence when strain‐softening models are employed in failure analyses. In this contribution the governing field equations are regularized by adding rotational degrees‐of‐freedom to the conventional translational degrees‐of‐freedom. This so‐called elasto‐plastic Cosserat continuum model, for which an efficient and accurate integration algorithm and a consistent tangent operator are also derived in this contribution, warrants convergence of the load—deflection curve to a unique solution upon mesh refinement and a finite width of the localization zone. This is demonstrated for an infinitely long shear layer and a biaxial test of a strain‐softening elasto‐plastic von Mises material.

Details

Engineering Computations, vol. 8 no. 4
Type: Research Article
ISSN: 0264-4401

Keywords

Open Access
Article
Publication date: 14 August 2017

Raffaele Barretta, Luciano Feo, Raimondo Luciano, Francesco Marotti de Sciarra and Rosa Penna

This study aims to model scale effects in nano-beams under torsion.

Abstract

Purpose

This study aims to model scale effects in nano-beams under torsion.

Design/methodology/approach

The elastostatic problem of a nano-beam is formulated by a novel stress-driven nonlocal approach.

Findings

Unlike the standard strain-driven nonlocal methodology, the proposed stress-driven nonlocal model is mathematically and mechanically consistent. The contributed results are useful for the design of modern devices at nanoscale.

Originality/value

The innovative stress-driven integral nonlocal model, recently proposed in literature for inflected nano-beams, is formulated in the present submission to study size-dependent torsional behavior of nano-beams.

Details

PSU Research Review, vol. 1 no. 2
Type: Research Article
ISSN: 2399-1747

Keywords

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