Arc-length procedures with BEM in physically nonlinear problems

Mallardo, Vincenzo; Alessandri, Claudio

doi:10.1016/j.enganabound.2003.11.002

Cited by 26 publications

(22 citation statements)

References 38 publications

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“…Referring to the compressive tests, see for example Fig. (18), it is worth observing that, to take the analysis beyond the critical points, it might be necessary to implement some numerical scheme to improve the convergence of the analysis in the post-critical branch [105,106], like for example generalpurpose arc-length procedures [107,108] or some additional dissipative terms in the cohesive laws [105]. Moreover, performing the numerical tests, it has been noticed that the memory required by the solver PARDISO, see Appendix C, during the symbolic and numerical factorization phases, constitutes a bottleneck of the numerical method.…”

Section: Discussion and Further Developmentsmentioning

confidence: 99%

A three-dimensional cohesive-frictional grain-boundary micromechanical model for intergranular degradation and failure in polycrystalline materials

Benedetti

Aliabadi

2013

Computer Methods in Applied Mechanics and Engineering

116

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In this study, a novel three-dimensional micro-mechanical crystal-level model for the analysis of intergranular degradation and failure in polycrystalline materials is presented. The polycrystalline microstructures are generated as Voronoi tessellations, that are able to retain the main statistical features of polycrystalline aggregates. The formulation is based on a grain-boundary integral representation of the elastic problem for the aggregate crystals, that are modeled as threedimensional anisotropic elastic domains with random orientation in the three-dimensional space. The boundary integral representation involves only intergranular variables, namely interface displacement discontinuities and interface tractions, that play an important role in the micromechanics of polycrystals. The integrity of the aggregate is restored by enforcing suitable interface conditions, at the interface between adjacent grains. The onset and evolution of damage at the grain boundaries is modeled using an extrinsic non-potential irreversible cohesive linear law, able to address mixed-mode failure conditions. The derivation of the traction-separation law and its relation with potential-based laws is discussed. Upon interface failure, a non-linear frictional contact analysis is used, to address separation, sliding or sticking between micro-crack surfaces. To avoid a sudden transition between cohesive and contact laws, when interface failure happens under compressive loading conditions, the concept of cohesive-frictional law is introduced, to model the smooth onset of friction during the mode II decohesion process. The incrementaliterative algorithm for tracking the degradation and micro-cracking evolution is presented and discussed. Several numerical tests on pseudo-and fully three-dimensional polycrystalline microstructures have been performed. The influence of several intergranular parameters, such as cohesive strength, fracture toughness and friction, on the microcracking patterns and on the aggregate response of the polycrystals has been analyzed. The tests have demonstrated the capability of the formulation to track the nucleation, evolution and coalescence of multiple damage and cracks, under either tensile or compressive loads.

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Section: Discussion and Further Developmentsmentioning

confidence: 99%

A three-dimensional cohesive-frictional grain-boundary micromechanical model for intergranular degradation and failure in polycrystalline materials

Benedetti

Aliabadi

2013

Computer Methods in Applied Mechanics and Engineering

116

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“…The approach used to compute the domain integrals is to adopt internal cells, see for example [2,9,14,16,17,21,[26][27][28][29][30]33,[35][36][37][38][39][40][41][43][44][45][46]50,[53][54][55][56][57][59][60][61]63,65,66]. These cells are like finite elements in appearance, but the main difference is that they do not introduce any additional unknowns to the problem.…”

Section: Introductionmentioning

confidence: 99%

Efficient elastoplastic analysis with the boundary element method

2007

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Conventional numerical implementation of the boundary element method (BEM) for elasto-plastic analysis requires a domain discretization into cells. This requires more effort for the discretization of the problem and additional computational effort. A new technique is proposed here for the analysis of 2D and 3D elasto-plastic problems with the boundary element method. In this approach the domain does not need to be discretised into cells prior to the analysis. Plasticity is assumed to start from the boundary and the cells are generated from the boundary data automatically during the analysis. Using the cell generation process, elasto-plastic analysis with the BEM becomes much more user friendly and efficient than the standard approach with a pre-definition of cells. The accuracy and efficiency of the solution obtained by the new approach is verified by several numerical examples.

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“…As mentioned by [20,35], one of the main differences between the present boundary element method and the finite element method with regard to the implementation of the arc length technique is that the unknown solution vector in BEM is a mixture of displacement and boundary force components, while in FEM, only displacements components are contained in { X}. In the literature, one may find discussions on some techniques as line search to accelerate the convergence.…”

mentioning

confidence: 96%

“…This form of the arc length technique for the boundary element method was first proposed by Zhang and Atluri [20], a different implementation of the arc length technique to BEM was proposed recently by Mallardo and Alesandri [35] with applications to physically non-linear problems, instead of geometrically non-linear. The arc length implementation in [35] was based on a truncated Taylor series expansion of the system equation together with the constrain equation, leading to a system matrix with a total of 5(N + L)+1 variables in the case of Formulations C and D or 5N +10L +1 variables in the case of Formulations A and B.…”

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confidence: 98%

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Post buckling analysis of shear deformable shallow shells by the boundary element method

Baiz

Aliabadi

2010

Numerical Meth Engineering

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SUMMARYThis paper presents four boundary element formulations for post buckling analysis of shear deformable shallow shells. The main differences between the formulations rely on the way non-linear terms are treated and on the number of degrees of freedom in the domain. Boundary integral equations are obtained by coupling boundary element formulation of shear deformable plate and two-dimensional plane stress elasticity. Four different sets of non-linear integral equations are presented. Some domain integrals are treated directly with domain discretization whereas others are dealt indirectly with the dual reciprocity method. Each set of non-linear boundary integral equations are solved using an incremental approach, where loads and prescribed boundary conditions are applied in small but finite increments. The resulting systems of equations are solved using a purely incremental technique and the Newton-Raphson technique with the Arc length method. Finally, the effect of imperfections (obtained from a linear buckling analysis) on the post-buckling behaviour of axially compressed shallow shells is investigated. Results of several benchmark examples are compared with the published work and good agreement is obtained.

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Arc-length procedures with BEM in physically nonlinear problems

Cited by 26 publications

References 38 publications

A three-dimensional cohesive-frictional grain-boundary micromechanical model for intergranular degradation and failure in polycrystalline materials

A three-dimensional cohesive-frictional grain-boundary micromechanical model for intergranular degradation and failure in polycrystalline materials

Efficient elastoplastic analysis with the boundary element method

Post buckling analysis of shear deformable shallow shells by the boundary element method

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