Crack growth modeling in micropolar elasticity

The generalized continuum theories, such as micropolar elasticity, are used to model heterogeneous materials in cases, when the material microstructure has significant effect on the deformation. The microstructural effects are accounted for by introducing the intrinsic material length scale directly into the constitutive equations. In the case of the micropolar elasticity, each infinitesimal material element also has additional (rotational) degrees of freedom and the deformed state is described by two asymmetric – stress and couple-stress – tensors.

Boundary element method has a number of advantages, in comparison with the domain-type methods, for problems with geometrical discontinuities, such as domains with cracks.  Due to the integral representation of the solutions, it yields accurate results in approximating the fields with high gradients, such as the stress field in the vicinity of a crack tip, and estimating such fundamental fracture parameters, as the stress intensity factors.

In this project we have implemented the dual boundary element method for the stress analysis in plane micropolar elasticity and evaluated stress intensity factors for various crack configurations. The obtained data now will be used to formulate the criteria of crack growth and simulate the crack propagation paths.

The boundary element method formulation also allows include into consideration voids and inclusions of different materials and analyze their effect on the crack paths.

Example: Angular distribution of stresses and couple-stresses around the crack tip for an edge-crack in a finite plate in Mode I.


For technical details please see:

E. Atroshchenko, S.P.A. Bordas, Fundamental Solutions and Dual Boundary Element Method for Crack Problems in Plane Cosserat Elasticity, 2014,