Shina D. Oloniiju^† , Sicelo P. Goqo, Precious Sibanda

Frontiers in Heat and Mass Transfer, Vol.13, pp. 1-8, 2019, DOI:10.5098/hmt.13.19

Abstract In some recent studies, it has been suggested that non–Newtonian fluid flow can be modeled by a spatially non–local velocity, whose dynamics are described by a fractional derivative. In this study, we use the space fractional constitutive relation to model heat and mass transfer in a nanofluid. We present a numerically accurate algorithm for approximating solutions of the system of fractional ordinary differential equations describing the nanofluid flow. We present numerically stable differentiation matrices for both integer and fractional order derivatives defined by the one–sided Caputo derivative. The differentiation matrices are based on the series expansion of the unknown functions… More >

N. Vijaya^a,*, S. M. Arifuzzaman^b, N. Raghavendra Sai^c, Ch. Manikya Rao^d

Frontiers in Heat and Mass Transfer, Vol.15, pp. 1-9, 2020, DOI:10.5098/hmt.15.26

Abstract The upfront intension of this study is to explore the advances in electrically conducting Casson fluid induced due to a porous elongated surface taking Arrhenius activation energy, viscous dissipation and joule heating into account. Uniform magnetic and electric fields are imposed on the given flow. Variables of similarity are induced to transmute partial differential equations into dimensionless equations and resolved numerically by elegant method bvp4c. To scrutinize the behavior of critical parameters on flow configurations graphs and table are portrayed. From graphical moments, it is analyzed that velocity of the liquid diminish for advanced values of non-Newtonian rheology parameter, magnetic… More >

D.K. Anding¹

Structural Durability & Health Monitoring, Vol.1, No.2, pp. 95-106, 2005, DOI:10.3970/sdhm.2005.001.095

Abstract The paper deals with the implementation of constitutive equations for isotropic viscoplastic material behaviour into modern Finite Element codes like ABAQUS. ABAQUS provides an user interface called UMAT (USER MATERIAL) for the definition of quite general material behaviour. The user can take advantage of the complete Finite Element code from ABAQUS and has to focus only on the solution of the constitutive equations. Key problems are accuracy and stability of this local solution procedure, which comes from the numerical stiffness of the governing equations (mostly first order ordinary differential equations). The numerical stiffness does not allow to use explicit integration… More >

K.Y. Volokh¹

Molecular & Cellular Biomechanics, Vol.2, No.2, pp. 77-86, 2005, DOI:10.3970/mcb.2005.002.077

Abstract Recently Volokh and Lev (2005) argued that residual stresses could appear in growing arteries because of the arterial anisotropy. This conclusion emerged from a continuum mechanics theory of growth of soft biological tissues proposed by the authors. This theory included Lagrangian constitutive equations, which were formulated directly with respect to the reference configuration. Alternatively, it is possible to formulate Eulerian constitutive equations with respect to the current configuration and to 'pull them back' to the reference configuration. Such possibility is examined in the present work. The Eulerian formulation of the constitutive equations is used for a study of arterial growth.… More >

Boštjan Brank¹, Adnan Ibrahimbegovic² and Uroš Bohinc³

CMES-Computer Modeling in Engineering & Sciences, Vol.33, No.1, pp. 85-108, 2008, DOI:10.3970/cmes.2008.033.085

Abstract In this work we study the accuracy of modern higher-order shell finite element formulations in computation of 3d stress state in elastic shells. In that sense we compare three higher-order shell models: (i) with seven displacement-like kinematic parameters, and (ii, iii) with six displacement-like kinematic parameters plus one strain-like kinematic parameter introduced by two different versions of enhanced assumed strain (EAS) concept. The finite element approximations of all shell models are based on 4-node quadrilateral elements. Geometrically nonlinear and consistently linearized forms of considered formulations are given. Several numerical examples are presented, where computed stresses are compared with analytical solutions.… More >

A. M. Rajendran¹, D. J. Grove²

CMES-Computer Modeling in Engineering & Sciences, Vol.3, No.3, pp. 367-380, 2002, DOI:10.3970/cmes.2002.003.367

Abstract This paper presents detailed computational analyses investigating the ability of constitutive relationships to describe the response of a 99.5% pure alumina (AD995) subjected to a wide range of stress/strain loading states. Using a shock-wave-propagation-based finite element code, one and two-dimensional simulations were performed for the following shock and impact configurations: plate-on-plate impact; rod-on-rod impact; single-density plate-on-rod impact; graded-density plate-on-rod impact; and rod penetration into a thick plate. The detailed analyses presented in this paper include a model constant sensitivity study through comparisons of computed wave profiles with experimental measurements. More >

B.T. Tang^1,2, X.Y. Lu¹, H. Xie²

CMES-Computer Modeling in Engineering & Sciences, Vol.73, No.2, pp. 171-182, 2011, DOI:10.3970/cmes.2011.073.171

Abstract The Traditional Inverse Analysis Method (TIAM) of sheet metal stamping has the shortcoming of neglecting the effects of deformation history on stress prediction. An Updated Inverse Analysis Method (UIAM) is proposed based on the final workpiece in Euler coordinate system. The UIAM uses the constitutive equation based on pseudo flow theory of plasticity to consider the loading history. In order to avoid numerous iterations to ensure the numerical stability in Newton-Raphson scheme to obtain plastic multiplier ∆λ, the equation in unknown stress vectors is transformed into a scalar equation using the notion of the equivalent stress. Thus a scalar equation… More >

M. Tanaka^1,2, H. Noguchi¹, M. Fujikawa^3,4, M. Sato³, S. Oi³, T. Kobayashi³, K. Furuichi⁵, S. Ishimaru⁵, C. Nonomura⁵

CMES-Computer Modeling in Engineering & Sciences, Vol.62, No.3, pp. 265-290, 2010, DOI:10.3970/cmes.2010.062.265

Abstract This paper describes the development of a proper constitutive model of woven fabrics and its implementation in nonlinear finite shell elements in order to simulate the large deformation behavior of cloth. This work currently focuses on a macroscopic continuum constitutive model that is capable of capturing the realistic mechanical behavior of cloth that is characterized by two families of yarns, i.e., warp and weft. In this study, two strategies are considered. One is a rebar layer model and the other is a polyconvex anisotropic hyperelastic material model. The latter avoids non-physical behavior and can consider the effect of the interaction… More >

Lorenzo Codecasa¹, Francesco Trevisan²

CMES-Computer Modeling in Engineering & Sciences, Vol.59, No.2, pp. 155-180, 2010, DOI:10.3970/cmes.2010.059.155

Abstract Electromagnetic problems spatially discretized by the so called Discrete Geometric Approach are considered, where Discrete Counterparts of Constitutive Relations are discretized within an Energetic Approach. Pairs of oriented dual grids are considered in which the primal grid is composed of (oblique) parallelepipeds, (oblique) triangular prisms and tetrahedra and the dual grid is obtained according to the barycentric subdivision. The focus of the work is the evaluation of the constants bounding the approximation error of the electromagnetic field; the novelty is that such constants will be expressed in terms of the geometrical details of oriented dual grids. A numerical analysis will… More >

L. Codecasa¹, R. Specogna², F. Trevisan³

CMES-Computer Modeling in Engineering & Sciences, Vol.31, No.3, pp. 129-144, 2008, DOI:10.3970/cmes.2008.031.129

Abstract In the paper we introduce a methodology to construct discrete constitutive matrices relating magnetic fluxes with magneto motive forces (reluctance matrix) and electro motive forces with currents (conductance matrix) needed for discretizing eddy current problems over hexahedral primal grids by means of the Finite Integration Technique (FIT) and the Cell Method (CM). We prove that, unlike the mass matrices of Finite Elements, the proposed matrices ensure both the stability and the consistency of the discrete equations introduced in FIT and CM. More >