A model for the axisymmetric growth and coalescence of small internal voids in elastoplastic solids is proposed and assessed using void cell computations. Two contributions existing in the literature have been integrated into the enhanced model. The first is the model of Gologanu-Leblond-Devaux, extending the Gurson model to void shape effects. The second is the approach of Thomason for the onset of void coalescence. Each of these has been extended heuristically to account for strain hardening. In addition, a micromechanically-based simple constitutive model for the void coalescence stage is proposed to supplement the criterion for the onset of coalescence. The fully enhanced Gurson model depends on the flow properties of the material and the dimensional ratios of the void-cell representative volume element. Phenomenological parameters such as critical porosities are not employed in the enhanced model. It incorporates the effect of void shape, relative void spacing, strain hardening, and porosity. The effect of the relative void spacing on void coalescence, which has not yet been carefully addressed in the literature. has received special attention. Using cell model computations, accurate predictions through final fracture have been obtained for a wide range of porosity, void spacing, initial void shape, strain hardening, and stress triaxiality. These predictions have been used to assess the enhanced model. (C) 2000 Elsevier Science Ltd. All rights reserved.

An extended model for void growth and coalescence - application to anisotropic ductile fracture

Free vibration analysis of functionally graded conical, cylindrical shell and annular plate structures with a four-parameter power-law distribution

Recent developments in finite element analysis for laminated composite plates

A review of theories for the modeling and analysis of functionally graded plates and shells

A review of meshless methods for laminated and functionally graded plates and shells

3D semi-analytical solution of hygro-thermo-mechanical multilayered doubly-curved shells

A finite element model based on the Timoshenko theory is developed to compute the critical buckling loading of functionally graded beams. The Trefftz criteria is used for the stability analysis considering both fundamental and incremental states. A finite element formulation is derived from the principle of virtual work. The Lagrange interpolation functions are used to approximate the field variables. Numerical results are validated with several benchmark problems found in literature. Keywords— buckling analysis, functionally graded materials, stability, finite element method, Trefftz criterion

/pdf/buckling-analysis-of-functionally-graded-timoshenko-beams-4olp1sin28.pdf

Buckling Analysis of Functionally Graded Timoshenko Beams

In this paper, a finite element model for the nonlinear analysis of laminated shell structures and through-thickness functionally graded shells is presented. A tensor-based finite element formulation is presented to describe the deformation and constitutive laws of a shell in a natural and simple way by using curvilinear coordinates. In addition, a family of high-order elements with Lagrangian interpolations is used to avoid membrane and shear locking; no mixed interpolations are employed. A first-order shell theory with seven parameters is derived with exact nonlinear deformations and under the framework of the Lagrangian description. This approach takes into account thickness changes and, therefore, 3D constitutive equations are utilized. Numerical comparisons of the present results with those found in the literature for typical benchmark problems involving isotropic and laminated composite plates and shells as well as functionally graded plates and shells are found to be excellent and show the validity of the developed finite element model. Moreover, the simplicity of this approach makes it attractive for applications in contact mechanics and damage propagation in shells.

Nonlinear Analysis of Composite and FGM Shells using Tensor-Based Shell Finite Elements

In this paper, we study the nonlocal linear bending behavior of functionally graded beams subjected to distributed loads. A finite element formulation for an improved first-order shear deformation theory for beams with five independent variables is proposed. The formulation takes into consideration 3D constitutive equations. Eringen’s nonlocal differential model is used to rewrite the nonlocal stress resultants in terms of displacements. The finite element formulation is derived by means of the principle of virtual work. High-order nodalspectral interpolation functions were utilized to approximate the field variables, which minimizes the locking problem. Numerical results and comparisons of the present formulation with those found in the literature for typical benchmark problems involving nonlocal beams are found to be satisfactory and show the validity of the developed finite element model.

https://repositorioacademico.upc.edu.pe/bitstream/10757/651836/1/Garbin_2020_IOP_Conf._Ser.__Mater._Sci._Eng._739_012045.pdf

Bending Analysis of Nonlocal Functionally Graded Beams

The purpose of this research is to study the bending behavior of micropolar beams by using an improved first-order shear deformation theory. The proposed formulation employs five independent variables for the displacement field and a single parameter for microrotations. The model considers thickness stretching and 3D constitutive parameters. A finite element formulation is developed with spectral interpolation functions to avoid shear and Poisson locking. Convergence analysis of vertical deflections is presented to illustrate the performance of high-order elements. Numerical results obtained for cantilever and simply supported beams demonstrate the validity of the present approach. Keywords—Micropolar elasticity, Micropolar beams, Nonclassical continuum.

/pdf/bending-analysis-of-micropolar-beams-cpw0n67das.pdf

R.A. Arciniega

Papers

3D semi-analytical solution of hygro-thermo-mechanical multilayered doubly-curved shells

Buckling Analysis of Functionally Graded Timoshenko Beams

Nonlinear Analysis of Composite and FGM Shells using Tensor-Based Shell Finite Elements

Bending Analysis of Nonlocal Functionally Graded Beams

Bending Analysis of Micropolar Beams