Search results
1 – 10 of over 4000A general first-invariant constitutive model has been derived in literature for incompressible, isotropic hyperelastic materials, known as Marlow model, which reproduces test data…
Abstract
Purpose
A general first-invariant constitutive model has been derived in literature for incompressible, isotropic hyperelastic materials, known as Marlow model, which reproduces test data exactly without the need of curve-fitting procedures. This paper aims to describe how to extend Marlow’s constitutive model to the more general case of compressible hyperelastic materials.
Design/methodology/approach
The isotropic constitutive model is based on a strain energy function, whose isochoric part is solely dependent on the first modified strain invariant. Based on Marlow’s idea, a principle of energetically equivalent deformation states is derived for the compressible case, which is used to determine the underlying strain energy function directly from measured test data. No particular functional of the strain energy function is assumed. It is shown how to calibrate the volumetric and isochoric strain energy functions uniquely with uniaxial or biaxial test data only. The constitutive model is implemented into a finite element program to demonstrate its applicability.
Findings
The model is well suited for use in finite element analysis. Only one set of test data is required for calibration without any need for curve-fitting procedures. These test data are reproduced exactly, and the model prediction is reasonable for other deformation modes.
Originality/value
Marlow’s basic concept is extended to the compressible case and applied to both the volumetric and isochoric part of the compressible strain energy function. Moreover, a novel approach is described on how both compressive and tensile test data can be used simultaneously to calibrate the model.
Details
Keywords
Divyanshu Kumar Lal and Arghya Das
Semi-implicit type cutting plane method (CPM) and fully implicit type closest point projection method (CPPM) are the two most widely used frameworks for numerical stress…
Abstract
Purpose
Semi-implicit type cutting plane method (CPM) and fully implicit type closest point projection method (CPPM) are the two most widely used frameworks for numerical stress integration. CPM is simple, easy to implement and accurate up to first order. CPPM is unconditionally stable and accurate up to second order though the formulation is complex. Therefore, this study aims to develop a less complex and accurate stress integration method for complex constitutive models.
Design/methodology/approach
Two integration techniques are formulated using the midpoint and Romberg method by modifying CPM. The algorithms are implemented for three different classes of soil constitutive model. The efficiency of the algorithms is judged via stress point analysis and solving a boundary value problem.
Findings
Stress point analysis indicates that the proposed algorithms are stable even with a large step size. In addition, numerical analysis for solving boundary value problem demonstrates a significant reduction in central processing unit (CPU) time with the use of the semi-implicit-type midpoint algorithm.
Originality/value
Traditionally, midpoint and Romberg algorithms are formulated from explicit integration techniques, whereas the present study uses a semi-implicit approach to enhance stability. In addition, the proposed stress integration algorithms provide an efficient means to solve boundary value problems pertaining to geotechnical engineering.
Details
Keywords
Junzhou Yang, Jianjun Wu, Qianwen Zhang, Yinxiang Ren, Han Ruolan and Kaiwei Wang
With the discussion on the linear relationship of determined material parameters, this study aims to propose a new method to analyze the deformation mechanism.
Abstract
Purpose
With the discussion on the linear relationship of determined material parameters, this study aims to propose a new method to analyze the deformation mechanism.
Design/methodology/approach
A modified constitutive model based on the hyperbolic sine Arrhenius equation has been established, which is applied to describe the flow behavior of Ti-6Al-4V alloy during the superplastic forming (SPF).
Findings
The modified constitutive model in this work has a good ability to describe the flow behavior for Ti-6Al-4V in SPF. Besides, a deformation map of titanium material is obtained based on the parameters. As the supplement, finite element models of high-temperature tensile tests are carried out as the application of the constitutive model.
Originality/value
The relationship between constitutive model parameters and forming mechanism is established, which is a new angle in rheological behavior research and constitutive model analysis.
Details
Keywords
Marinella Giunta and Aurora Angela Pisano
This paper proposes a new visco‐elastoplastic constitutive model for asphalt concretes able to reproduce the non linear time‐dependent behaviour of such materials.The constitutive…
Abstract
This paper proposes a new visco‐elastoplastic constitutive model for asphalt concretes able to reproduce the non linear time‐dependent behaviour of such materials.The constitutive model has been developed with the aim of making it fit specific experimental features previously observed. Moreover the proposed formulation will be demonstrated to be fully consistent with general thermodynamic requirements. Apart from a rigorous analytical formulation; a corresponding rheological sketch of the model is also given. From this representation, it can be shown that the model is essentially a combination of a generalized Maxwell model and a hardening visco‐plastic element.
Details
Keywords
Seishiro Matsubara, Kenjiro Terada, Ryusei Maeda, Takaya Kobayashi, Masanobu Murata, Takuya Sumiyama, Kenji Furuichi and Chisato Nonomura
This study aims to propose a novel viscoelastic–viscoplastic combined constitutive model for glassy amorphous polymers within the framework of thermodynamics at finite strain that…
Abstract
Purpose
This study aims to propose a novel viscoelastic–viscoplastic combined constitutive model for glassy amorphous polymers within the framework of thermodynamics at finite strain that is capable of capturing their rate-dependent inelastic mechanical behavior in wide ranges of deformation rate and amount.
Design/methodology/approach
The rheology model whose viscoelastic and viscoplastic elements are connected in series is set in accordance with the multi-mechanism theory. Then, the constitutive functions are formulated on the basis of the multiplicative decomposition of the deformation gradient implicated by the rheology model within the framework of thermodynamics. Dynamic mechanical analysis (DMA) and loading/unloading/no-load tests for polycarbonate (PC) are conducted to identify the material parameters and demonstrate the capability of the proposed model.
Findings
The performance was validated in comparison with the series of the test results with different rates and amounts of deformation before unloading together. It has been confirmed that the proposed model can accommodate various material behaviors empirically observed, such as rate-dependent elasticity, elastic hysteresis, strain softening, orientation hardening and strain recovery.
Originality/value
This paper presents a novel rheological constitutive model in which the viscoelastic element connected in series with the viscoplastic one exclusively represents the elastic behavior, and each material response is formulated according to the multiplicatively decomposed deformation gradients. In particular, the yield strength followed by the isotropic hardening reflects the relaxation characteristics in the viscoelastic constitutive functions so that the glass transition temperature could be variant within the wide range of deformation rate. Consequently, the model enables us to properly represent the loading process up to large deformation regime followed by unloading and no-load processes.
Details
Keywords
Abstract
Purpose
The strength of printed parts by application of fused deposition modeling (FDM) has been broadly studied through experimental methods. However, constitutive behaviors of the printed parts in theory are still unclear. Therefore, this paper aims to focus on building an elasto-plastic model of the printed parts to reveal the constitutive behavior.
Design/methodology/approach
An elasto-plastic constitutive model that considers anisotropic characteristics is proposed. Tensile tests are performed for parameter identification by using different samples with varying printing angles. Finally, the constitutive model is completed and applied to the numerical analysis of a tensile procedure.
Findings
The experimental study indicated that the anisotropic characteristics are significant for elastic modulus and strength of printed parts. The polar anisotropic model is suitable for describing the anisotropic behavior of parts during the elastic deformation. The Hill model is suitable to describe the yield property. The elastic modulus and yield point of parts printed in any specific orientation can be calculated using the proposed constitutive model.
Originality/value
A theoretical model has been developed to describe the constitutive behavior of FDM printed part. This model can precisely describe the elastic behavior and yield point of parts printed with various orientations. This model can be applied to the finite element simulation of printed structures.
Details
Keywords
Liquefaction phenomenon and its catastrophic nature can be analysed as a particular material behaviour of granular media under certain loading paths. Proposes a definition of…
Abstract
Liquefaction phenomenon and its catastrophic nature can be analysed as a particular material behaviour of granular media under certain loading paths. Proposes a definition of liquefaction and its modelling by constitutive relations. Discusses this modelling in relation to the questions of stability and uniqueness. Considers the signs of three scalar quantities: the work of second order, the determinant of the symmetric part of the tangent constitutive tensor and the determinant of the tensor itself. Concludes that the liquefaction path is situated inside a potentially unstable domain and that in some cases this path reaches some states of loss of uniqueness, which are essentially bifurcation points.
Details
Keywords
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.
Details
Keywords
SUDIP S. BHATTACHARJEE and PIERRE LÉGER
The localized strain softening behaviour of concrete has been modelled by two approaches: (i) the stiffness degrading model based on the total stress‐strain constitutive…
Abstract
The localized strain softening behaviour of concrete has been modelled by two approaches: (i) the stiffness degrading model based on the total stress‐strain constitutive relationship, and (ii) the tangent softening model based on the incremental stress‐strain relationship. The models are implemented using a new softening initiation criterion proposed for application in multi‐dimensional finite element analysis. Parametric analyses on plain concrete beams, tested experimentally by other researchers, have been carried out to investigate the required numerical efforts, the mesh objectivity, and the energy dissipation characteristics of the structures. The stiffness degrading model is very stable even when applied with relatively coarse finite element meshes. However, the computational demand of this model is relatively high. The combination of a total stress‐strain constitutive relationship to compute the element responses, and an incremental relationship to formulate the stiffness matrix, appears to be computationally efficient and stable, provided that adequately refined finite element mesh is used to model the structure.
Details
Keywords
Shrushti Maheshwari, Zafar Alam and Sarthak S. Singh
The purpose of this study is to experimentally investigate the large deformation compression characteristics of fused deposition modelling (FDM)-printed poly lactic acid (PLA)…
Abstract
Purpose
The purpose of this study is to experimentally investigate the large deformation compression characteristics of fused deposition modelling (FDM)-printed poly lactic acid (PLA), considering the combined effect of infill density and strain rate, and to develop a constitutive viscoplastic model that can incorporate the infill density to predict the experimental result.
Design/methodology/approach
The experimental approach focuses on strain rate-dependent (2.1 × 10−4, 2.1 × 10−3, and 2.1 × 10−2 s−1) compression testing for varied infill densities. Scanning electron microscopy (SEM) imaging of compressed materials is used to investigate deformation processes. A hyperelastic-viscoplastic constitutive model is constructed that can predict mechanical deformations at different strain rates and infill densities.
Findings
The yield stress of PLA increased with increase in strain rate and infill density. However, higher degree of strain-softening response was witnessed for the strain rate corresponding to 2.1 × 10−2 s−1. While filament splitting and twisting were identified as the damage mechanisms at higher strain rates, matrix crazing was observed as the primary deformation mechanism for higher infill density (95%). The developed constitutive model captured yield stress and post-yield softening behaviour of FDM build PLA samples with a high R2 value of 0.99.
Originality/value
This paper addresses the need to analyse and predict the mechanical response of FDM print polymers (PLA) undergoing extensive strain-compressive loading through a hyperelastic-viscoplastic constitutive model. This study links combined effects of the printing parameter (infill density) with the experimental parameter (strain rate).
Details