The cohesive band model: A cohesive surface formulation with stress triaxiality

In the cohesive surface model cohesive tractions are transmitted across a two-dimensional surface, which is embedded in a three-dimensional continuum. The relevant kinematic quantities are the local crack opening displacement and the crack sliding displacement, but there is no kinematic quantity that represents the stretching of the fracture plane. As a consequence, in-plane stresses are absent, and fracture phenomena as splitting cracks in concrete and masonry, or crazing in polymers, which are governed by stress triaxiality, cannot be represented properly. In this paper we extend the cohesive surface model to include in-plane kinematic quantities. Since the full strain tensor is now available, a three-dimensional stress state can be computed in a straightforward manner. The cohesive band model is regarded as a subgrid scale fracture model, which has a small, yet finite thickness at the subgrid scale, but can be considered as having a zero thickness in the discretisation method that is used at the macroscopic scale. The standard cohesive surface formulation is obtained when the cohesive band width goes to zero. In principle, any discretisation method that can capture a discontinuity can be used, but partition-of-unity based finite element methods and isogeometric finite element analysis seem to have an advantage since they can naturally incorporate the continuum mechanics. When using interface finite elements, traction oscillations that can occur prior to the opening of a cohesive crack, persist for the cohesive band model. Example calculations show that Poisson contraction influences the results, since there is a coupling between the crack opening and the in-plane normal strain in the cohesive band. This coupling holds promise for capturing a variety of fracture phenomena, such as delamination buckling and splitting cracks, that are difficult, if not impossible, to describe within a conventional cohesive surface model. © 2013 Springer Science+Business Media Dordrecht

Generalized Interpolation Material Point Approach to High Melting Explosive with Cavities Under Shock

Criterion for contacting is critically important for the Generalized Interpolation Material Point(GIMP) method. We present an improved criterion by adding a switching function. With the method dynamical response of high melting explosive(HMX) with cavities under shock is investigated. The physical model used in the present work is an elastic-to-plastic and thermal-dynamical model with Mie-Gr\"uneissen equation of state. We mainly concern the influence of various parameters, including the impacting velocity $v$, cavity size $R$, etc, to the dynamical and thermodynamical behaviors of the material. For the colliding of two bodies with a cavity in each, a secondary impacting is observed. Correspondingly, the separation distance $D$ of the two bodies has a maximum value $D_{\max}$ in between the initial and second impacts. When the initial impacting velocity $v$ is not large enough, the cavity collapses in a nearly symmetric fashion, the maximum separation distance $D_{\max}$ increases with $v$. When the initial shock wave is strong enough to collapse the cavity asymmetrically along the shock direction, the variation of $D_{\max}$ with $v$ does not show monotonic behavior. Our numerical results show clear indication that the existence of cavities in explosive helps the creation of ``hot spots''.Comment: Figs.2,4,7,11 in JPG format; Accepted for publication in J. Phys. D: Applied Physic