Search results

1 – 2 of 2
Per page
102050
Citations:
Loading...
Access Restricted. View access options
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

Keywords

Access Restricted. View access options
Article
Publication date: 10 August 2018

Rahul Kumar and Jeeoot Singh

The purpose of this paper is to assess different five variables shear deformation plate theories for the buckling analysis of FGM plates.

134

Abstract

Purpose

The purpose of this paper is to assess different five variables shear deformation plate theories for the buckling analysis of FGM plates.

Design/methodology/approach

Governing differential equations (GDEs) of the theories are derived by employing the Hamilton Principle. A polynomial radial basis function (RBF)-based Meshless method is used to discretize the GDEs, and a MATLAB code is developed to solve these discretize equations.

Findings

Numerical results are obtained for buckling loads. The results are compared with other available results for validation purpose. The effect of the span-to-thickness ratio and grading index is observed. It is observed that some theories underpredict the deflection for thick plates, while at the same time they seem to be in good agreement with other theories for thin plates.

Originality/value

This paper assesses the different theories with the same method to determine their applicability.

Details

Multidiscipline Modeling in Materials and Structures, vol. 14 no. 5
Type: Research Article
ISSN: 1573-6105

Keywords

1 – 2 of 2
Per page
102050