Chein-Shan Liu ^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.17, No.2, pp. 73-94, 2007, DOI:10.3970/cmes.2007.017.073

Abstract The primary objectives of the present exposition focus on five different types of representations of the plastic equations obtained from an elastic-perfectly plastic model by employing different corotational stress rates. They are (a) an affine nonlinear system with a finite-dimensional Lie algebra, (b) a canonical linear system in the Minkowski space, (c) a non-canonical linear system in the Minkowski space, (d) the Lie-Poisson bracket formulation, and (e) a two-generator and two-bracket formulation. For the affine nonlinear system we prove that the Lie algebra of the vector fields is so(5,1), which has dimensions fifteen, and by the Lie theory the superposition… More >

K. Hashiguchi¹

CMES-Computer Modeling in Engineering & Sciences, Vol.17, No.1, pp. 55-62, 2007, DOI:10.3970/cmes.2007.017.055

Abstract Constitutive equation describing the mechanical properties of material has to be formulated in an identical form independent of coordinate systems by which it is described even if there exist any mutual configuration and/or mutual rotation between the material and coordinate systems. This mechanical requirement is attained by describing rate variables as corotational rate tensors with objectivity in constitutive equations in rate form. Besides, in order to use the material-time derivative of yield condition as a consistency condition it has to be replaced to the corotational derivative. In this note a general corotational rate for tensors in arbitrary order having the… More >

A. Le van¹, P. Le Grognec¹

CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.1, pp. 63-72, 2001, DOI:10.3970/cmes.2001.002.063

Abstract Necking is a bifurcation phenomenon observed in round bars under tensile loading and has been investigated in numbers of papers. In the present work, it is modeled within the framework of finite rate-independent plasticity. The theory is based on thermodynamic foundations developed for standard materials and results in a total Lagrangian formulation for finite plasticity, where the total strain is decomposed additively according to [Green and Nagdhi 1965)] and the hardening is characterized by a nonlinear isotropic hardening law of the saturation type.
The discretization and consistent linearization of the elastic-plastic equation set using the standard finite element procedure… More >

C.P . Providakis¹

CMES-Computer Modeling in Engineering & Sciences, Vol.1, No.3, pp. 123-130, 2000, DOI:10.3970/cmes.2000.001.425

Abstract Boundary and Finite Element methodologies for the determination of the inelastic response of thick plates resting on Winkler-type elastic foundations are compared and critically discussed. For comparison reasons the domain/boundary element and the finite element methodology use isoparametric elements of the same accuracy level. After a discretizaton of the integral equations of motion in both methodologies an efficient step-by-step time integration algorithm is used to solve the resulting matrix equations. Comparison studies are shown for impacted elastoplastic thick plates with smooth boundaries and supported on different Winkler-type foundations. The numerical results reveal that boundary element method appears to be a… More >

Chein-Shan Liu¹, Satya N. Atluri²

CMC-Computers, Materials & Continua, Vol.41, No.1, pp. 1-36, 2014, DOI:10.3970/cmc.2014.041.001

Abstract In this paper, we adopt the viewpoint of a nonlinear complementarity problem (NCP) to derive an index-one differential algebraic equations (DAEs) system for the problem of elastic-plastic wave propagation in an elastic-plastic solid undergoing small deformations. This is achieved by recasting the pointwise complementary trio in the elastic-plastic constitutive equations into an algebraic equation through the Fischer-Burmeister NCP-function. Then, for an isotropicallyhardening/ softening material under prescribed impulse loadings on a thin-walled tube with combined axial-torsional stresses, we can develop a novel algorithm based on the Lie-group differential algebraic equations (LGDAE) method to iteratively solve the resultant DAEs at each time… More >

Hamid Sharifi¹ and Augustin Gakwaya¹

CMC-Computers, Materials & Continua, Vol.3, No.2, pp. 77-96, 2006, DOI:10.3970/cmc.2006.003.077

Abstract In this paper, an object-oriented modeling of solid material constitutive behavior using the UML notation is presented. Material properties are first classified into large and small deformation kinematical models. In the small deformation package, we keep classes such as Elastic, ElastoPlastic, ViscoElastic and ViscoPlastic. In the large deformation package, we store classes such as ElastoPlastic, HyperElastic, HyperPlastic, HyperViscoElastic, HyperViscoPlastic and so on. The hierarchical structure, the association relationships as well as key attributes and methods of these classes are presented. We used a C++ implementation of the above model for developing HyperElastic, HyperElastoPlastic and Contact applications in the Diffpack environment. More >