On path-following methods for structural failure problems.

*(English)*Zbl 1398.74407Summary: We revisit the consistently linearized path-following method that can be applied in the nonlinear finite element analysis of solids and structures in order to compute a solution path. Within this framework, two constraint equations are considered: a quadratic one (that includes as special cases popular spherical and cylindrical forms of constraint equation), and another one that constrains only one degree-of-freedom (DOF), the critical DOF. In both cases, the constrained DOFs may vary from one solution increment to another. The former constraint equation is successful in analysing geometrically nonlinear and/or standard inelastic problems with snap-throughs, snap-backs and bifurcation points. However, it cannot handle problems with the material softening that are computed e.g. by the embedded-discontinuity finite elements. This kind of problems can be solved by using the latter constraint equation. The plusses and minuses of the both presented constraint equations are discussed and illustrated
on a set of numerical examples. Some of the examples also include direct computation of critical points and branch switching. The direct computation of the critical points is performed in the framework of the path-following method by using yet another constraint function, which is eigenvector-free and suited to detect critical points.

##### MSC:

74S05 | Finite element methods applied to problems in solid mechanics |

74G60 | Bifurcation and buckling |

74S30 | Other numerical methods in solid mechanics (MSC2010) |

74K25 | Shells |

74K99 | Thin bodies, structures |

##### Keywords:

nonlinear finite element analysis; path-following method; constraint equation; critical point computation; material softening; embedded-discontinuity finite elements
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\textit{A. Stanić} et al., Comput. Mech. 58, No. 2, 281--306 (2016; Zbl 1398.74407)

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