Numerical simulation of crack growth in an isotropic solid with randomized internal cohesive bonds.

*(English)*Zbl 0974.74008Summary: A virtual internal bond (VIB) model with randomized cohesive interactions between material particles is proposed for the integration of continuum models with cohesive surfaces und atomistic models with interatomic bonding. This approach differs from an atomistic model in that a phenomenological “cohesive force law” is assumed to act between “material particles” which are not necessarily atoms; it also differs from a cohesive surface model in that, rather than imposing a cohesive law along a prescribed set of discrete surfaces, a randomized network of cohesive bonds is statistically incorporated into the constitutive law of the material via the Cauchy-Born rule, i.e. by equating the strain energy function on the continuum level to the potential energy stored in the cohesive bonds due to an imposed deformation. This work is motivated by the notion that materials exhibit multiscale cohesive behaviors ranging from interatomic bonding to macroscopic ductile failure.

It is shown that the linear elastic behavior of the VIB model is isotropic and obeys the Cauchy relation; the instantaneous elastic properties under equibiaxial stretching are transversely isotropic, with all the in-plane components of the material tangent moduli vanishing in the cohesive stress limit; the instantaneous properties under equitriaxial stretching are isotropic with a finite strain modulus. We demonstrate through two preliminary numerical examples that the VIB model can be applied in direct simulation of crack growth without a presumed fracture criterion.

It is shown that the linear elastic behavior of the VIB model is isotropic and obeys the Cauchy relation; the instantaneous elastic properties under equibiaxial stretching are transversely isotropic, with all the in-plane components of the material tangent moduli vanishing in the cohesive stress limit; the instantaneous properties under equitriaxial stretching are isotropic with a finite strain modulus. We demonstrate through two preliminary numerical examples that the VIB model can be applied in direct simulation of crack growth without a presumed fracture criterion.

##### MSC:

74A45 | Theories of fracture and damage |

74R10 | Brittle fracture |

74B20 | Nonlinear elasticity |

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

74A60 | Micromechanical theories |

##### Keywords:

virtual internal bond model; cohesive force law; crack bifurcation; crack propagation; finite strain; crack arrest; finite element method; Cauchy-Born rule; strain energy; potential energy; interatomic bonding; equibiaxial stretching; equitriaxial stretching; crack growth
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\textit{H. Gao} and \textit{P. Klein}, J. Mech. Phys. Solids 46, No. 2, 187--218 (1998; Zbl 0974.74008)

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