4 results for Areias, P.M.A.

  • A new approach for modelling slip lines in geological materials with cohesive models

    Rabczuk, T.; Areias, P.M.A. (2006)

    Journal Articles
    University of Canterbury Library

    A methodology to model slip lines as strong displacement discontinuities within a continuum mechanics context is presented. The loss of hyperbolicity of the IBVP is used as the criterion for switching from a classical continuum description of the constitutive behaviour to a traction-separation model acting at the discontinuity surface. A version of the element-free Galerkin (EFG) method is employed where the slip line is represented as a set of slipped particles. The representation of the slip line as set of cohesive segments promises to remove difficulties in the propagation of the slip line. Two-dimensional examples are studied using the Drucker–Prager material model.

    View record details
  • A simplified meshfree method for shear bands with cohesive surfaces

    Rabczuk, T.; Areias, P.M.A.; Belytschko, T. (2007)

    Journal Articles
    University of Canterbury Library

    A simple methodology to model shear bands as strong displacement discontinuities in a mesh-free particle method is presented. The shear band is represented as a set of sheared particles. A sheared particle is developed through enrichment by tangential displacement discontinuities. The representation of the shear band as set of cohesive segments provides a simple and versatile model of shear bands. The loss of material stability is used as the criterion for switching from a classical continuum description of the constitutive behaviour to a traction-separation law acting on the discontinuity surface. The method is implemented for two and three dimensions. Examples of shear band progression in rate-dependent and rate-independent materials are presented, including the Kalthoff problem, where the transition from brittle fracture to shear banding is studied.

    View record details
  • Quasi-static crack propagation in plane and plate structures using set-valued traction-separation laws

    Areias, P.M.A.; Rabczuk, T. (2008)

    Journal Articles
    University of Canterbury Library

    We introduce a numerical technique to model set-valued traction-separation laws in plate bending and also plane crack propagation problems. By use of recent developments in thin (Kirchhoff-Love) shell models and the extended finite element method, a complete and accurate algorithm for the cohesive law is presented and is used to determine the crack path. The cohesive law includes softening and unloading to origin, adhesion and contact. Pure debonding and contact are obtained as particular (degenerate) cases. A smooth root finding algorithm (based on the trust region method) is adopted. A step-driven algorithm is described with a smoothed law which can be made arbitrarily close to the exact non smooth law. In the examples shown the results were found to be step-size insensitive and accurate. In addition, the method provides the crack advance law, extracted from the cohesive law and the absence of stress singularity at the tip.

    View record details
  • A meshfree thin shell method for nonlinear dynamic fracture

    Rabczuk, T.; Areias, P.M.A.; Belytschko, T. (2007)

    Journal Articles
    University of Canterbury Library

    A meshfree method for thin shells with finite strains and arbitrary evolving cracks is described. The C1 displacement continuity requirement is met by the approximation, so no special treatments for fulfilling the Kirchhoff condition are necessary. Membrane locking is eliminated by the use of a cubic or quartic polynomial basis. The shell is tested for several elastic and elasto-plastic examples and shows good results. The shell is subsequently extended to modelling cracks. Since no discretization of the director field is needed, the incorporation of discontinuities is easy to implement and straight forward

    View record details