A computational framework for G/XFEM material nonlinear analysis

Monteiro, Anelize Borges; Wolenski, Anderson Renato Vobornik; Barros, Felício Bruzzi; Pitangueira, Roque Luiz da Silva; Penna, Samuel Silva

doi:10.1016/j.advengsoft.2017.08.002

Cited by 11 publications

(10 citation statements)

References 32 publications

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“…(24). In Gupta [40], the solution (25) = 10 8 ⋅ E ⋅ J convergence and growth rate of the condition number are investigated for an h-refinement performed for both global and local meshes. Here, the mesh is kept constant and only the number of nodes enriched with the local solution in the global scale is considered.…”

Section: Numerical Examplesmentioning

confidence: 99%

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SGFEM: a numerical investigation of the two-scale simulation of 3D elastic fracture

Santos¹,

Barros²

2020

J Braz. Soc. Mech. Sci. Eng.

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The Generalized/eXtended Finite Element Method (G/XFEM) is applied as a very useful tool in the resolution of complex structural models using an effective approach to represent the existence of cracks and other micro-defects. This is an unconventional formulation of the Finite Element Method (FEM), in that there is an expansion of the approximate solution field from the use of enrichment functions associated with the nodes. Enrichment functions can be singular functions derived from analytic deductions, polynomial functions or even functions resulting from other solution processes, such as the global-local strategy. The Stable Generalized Finite Method (SGFEM) is a variation of the G/XFEM with a simple modification in its enrichment functions, reducing the condition number of the stiffness matrix as well as the approximate error in the so-called blending elements. Considering this under the global-local strategy, the solution quality and the conditioning of the stiffness matrix in 3D linear fracture problems are investigated here. The crack surface is described by the Heaviside discontinuous functions and singular/crack front functions on a local scale. The solution of the local problem is used to enrich the approximation in the global domain, which may cause bad conditioning of the resulting system of equations and poor approximation errors in the solution. In order to overcome this problem, its projection into the linear polynomial space, according to the SGFEM strategy, is subtracted from the enrichment. Numerical examples, with different load and crack configurations, of linear elastic fracture mechanics are employed. Differently from other works, the meshes of the two scales are kept constant. Only the number of nodes associated with the local enrichment functions is changing. The impact on the accuracy and conditioning of the analysis is assessed, and the importance of using the SGFEM strategy is highlighted.

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Section: Numerical Examplesmentioning

confidence: 99%

“…Combinations of polynomials, discontinuous and singular functions were initially used as enrichment in two-dimensional [6] and three-dimensional linear elastic problems [4]. Later, nonlinear problems were also considered in [7,8].…”

Section: Introductionmentioning

confidence: 99%

SGFEM: a numerical investigation of the two-scale simulation of 3D elastic fracture

Santos¹,

Barros²

2020

J Braz. Soc. Mech. Sci. Eng.

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“…This system has been expanded by Alves et al [14] with the enclosing the standard version of GFEM formulation with minimum impact in the code structure. Based on this expansion an object oriented design of GFEM to physically nonlinear analysis has been extended by Monteiro et al [15], being used in all simulations of this paper. Further details about the INSANE system can be found in INSANE Project [16].…”

Section: Figurementioning

confidence: 99%

“…The experimental results obtained by the author were used by Monteiro at al. [15] and extended here to compare with the numerical results of the simulations performed with GFEM and FEM approaches.…”

Section: Three-point Bendingmentioning

confidence: 99%

Nonlinear analysis of concrete structures using GFEM enrichment strategy with a microplane constitutive model

Wolenski¹,

Monteiro

Penna

et al. 2018

Rev. IBRACON Estrut. Mater.

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One of the most widespread methods to the nonlinear analysis of structures is the Finite Element Method (FEM). However, there are phenomena whose behavior is not satisfactorily simulated by the standard FEM and this fact has quickened the development of new strategies such as the Generalized Finite Element Method (GFEM), understood as a variation of the FEM. In parallel, nonlinear analysis of concrete structures requires the use of constitutive models that represents the nucleation and propagation of cracks. In this paper it is used an anisotropic constitutive model, based on the microplane theory, which is able to represent the behavior of concrete structures, together with the GFEM approach. These resources are incorporated on the INSANE system (INteractive Structural ANalysis Environment), used in the numerical simulations presented here to demonstrate the feasibility of using the GFEM enrichment strategy, in the nonlinear analysis of concrete structures, with validation made from comparisons with experimental results available in the literature.

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“…One of these models is the smeared crack method, which relate the tangent of the softening curve to the finite element size Oliver [11], Rots [12], and Bazant [13]. An alternative powerful method is the Partition of Unity Finite Element Method (PUFEM) Melenk and Babuska [14], which developed in the last decade in the form of the mesh free methods Rabczuk [15], or the Extended Finite Element Method (XFEM) Unger [16] and Monteiro [17]. Huang [18] used three point loading test for mortar specimen with different thickness.…”

Section: Introductionmentioning

confidence: 99%

Finite Element Analysis of Concrete Beam under Flexural Stresses Using Meso-Scale Model

Al-Zuhairi

Taj

2018

CivileJournal

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Two dimensional meso-scale concrete modeling was used in finite element analysis of plain concrete beam subjected to bending. The plane stress 4-noded quadrilateral elements were utilized to model coarse aggregate, cement mortar. The effect of aggregate fraction distribution, and pores percent of the total area -resulting from air voids entrapped in concrete during placement on the behavior of plain concrete beam in flexural was detected. Aggregate size fractions were randomly distributed across the profile area of the beam. Extended Finite Element Method (XFEM) was employed to treat the discontinuities problems result from double phases of concrete and cracking that faced during the finite element analysis of concrete beam. Cracking was initiated at a small notch located at the middle of the bottom face of the concrete beam. The response of plain concrete beam subjected to pure bending via two point load application was detected using (XFEM) analysis of meso-scale concrete model. Assuming full bond between aggregate particles, and mortar at interfacial zone, the flexural strength of plain concrete beam is increased when aggregate particles size is increased, so that bending and shear stress were affected by void percentage and aggregate particles distribution. The maximum deflection at midspan was increased when the aggregate particles size decreases.

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A computational framework for G/XFEM material nonlinear analysis

Cited by 11 publications

References 32 publications

SGFEM: a numerical investigation of the two-scale simulation of 3D elastic fracture

SGFEM: a numerical investigation of the two-scale simulation of 3D elastic fracture

Nonlinear analysis of concrete structures using GFEM enrichment strategy with a microplane constitutive model

Finite Element Analysis of Concrete Beam under Flexural Stresses Using Meso-Scale Model

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