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**Energy release control for numerical simulations of failure in quasi-brittle solids.**
*(English)*
Zbl 1047.74551

Summary: A path-following constraint is developed which is based on the energy release during failure. This makes it applicable to the simulation of quasi-brittle materials when no previous knowledge is available on the failure behaviour of a body and, consequently, indirect displacement control methods like CMOD cannot be applied. The constraint is derived from the first principle of thermodynamics for a finite-element discretization of a solid with a continuum damage model. The performance of the constraint is demonstrated by means of a bending test on a single-edge-notched beam.

### MSC:

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

### Keywords:

path-following technique; arc-length control; quasi-brittle solids; energy release; finite-element method; nonlinear analysis
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\textit{M. A. Gutiérrez}, Commun. Numer. Methods Eng. 20, No. 1, 19--29 (2004; Zbl 1047.74551)

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### References:

[1] | Riks, An incremental approach to the solution of snapping and buckling problems, International Journal of Solids and Structures 15 pp 529– (1979) · Zbl 0408.73040 |

[2] | Ramm, Nonlinear Finite Element Analyses in Structural Mechanics (1981) |

[3] | Crisfield, Non-Linear Finite Element Analysis of Solids and Structures (1991) · Zbl 0809.73005 |

[4] | de Borst, Computation of post-bifurcation and post-failure behaviour of strain-softening solids, Computers and Structures 25 pp 211– (1987) · Zbl 0603.73046 |

[5] | Geers, Enhanced solution control for physically and geometrically non-linear problems Part I-The subplane control approach, International Journal for Numerical Methods in Engineering 46 pp 177– (1999) · Zbl 0957.74034 |

[6] | Geers, Enhanced solution control for physically and geometrically non-linear problems Part II-Comparative performance analysis, International Journal for Numerical Methods in Engineering 46 pp 205– (1999) · Zbl 0957.74034 |

[7] | Lemaitre, Mechanics of Solids Materials (1990) |

[8] | Simo, Finite deformation post-buckling analysis involving inelasticity and contact constraints, International Journal of Numerical Methods in Engineering 23 pp 779– (1986) · Zbl 0584.73045 |

[9] | Crisfield, A fast incremental/iterative solution procedure that handles ’snap-through’, Computers and Structures 13 pp 55– (1981) · Zbl 0479.73031 |

[10] | Peerlings, Gradient-enhanced damage modelling of concrete fracture, Mechanics of Cohesive-Frictional Materials 3 pp 323– (1998) |

[11] | de Vree, Comparison of nonlocal approaches in continuum damage mechanics, Computers and Structures 55 pp 581– (1995) · Zbl 0919.73187 |

[12] | Schlangen E Experimental and numerical analysis of fracture processes in concrete 1993 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.