Analysis of delamination growth with discontinuous finite elements

In this contribution a new finite element is presented for the simulation of delamination growth in thin layered composite materials. The element is based on the solid-like shell element, a volume element that can be used in very thin applications due to a higher order displacement field in thickness direction. The delamination crack is incorporated in this element as a jump of the displacement field by means of the partition of unity method. The kinematics of the element as well as the finite element formulation are described. The performance of the element is demonstrated by means of two examples

Analysis of delamination growth with discontinuous solid-like shell elements

Delamination is one of the most important failure mechanisms in laminates. Normally, it is modelled using interface elements. These elements are placed between two layers that are modelled with continuum elements. The interface elements are equipped with a softening or damage model in order to simulate debonding. This method has some drawbacks, both in a numerical and in a mechanical sense. A recent alternative is to simulate the crack by adding a discontinuous displacement mode to the continuum elements according to the partition of unity method. The elements do not contain the discontinuity prior to cracking, but when the ultimate stress in the bulk material is exceeded, delamination is initiated and additional degrees-of-freedom are activated. Beside this, a slightly different implementation is examined also. A discontinuity is predefined and has an initial dummy stiffness. Delamination is initiated when the tractions in the discontinuity exceed a threshold value. The results of both versions of this partition of unity model are compared mutually and with conventional interface elements by means of two examples

Computational modelling of cracks in viscoplastic media

A newly developed numerical model is used to simulate propagating cracks in a strain softening viscoplastic medium. The model allows the simulation of displacement discontinuities independently of a finite element mesh. This is possible using the partition of unity concept, in which fracture is treated as a coupled problem, with separate variational equations corresponding to the continuous and discontinuous parts of the displacement field. The equations are coupled through the dependence of the stress field on the strain state. Numerical examples show that allowing displacement discontinuities in a viscoplastic Von Mises material can lead to a failure mode that differs from a continuum-only model

A generalisation of J2-flow theory for polar continua

A pressure-dependent J2-flow theory is proposed for use within the framework of the Cosserat continuum. To this end the definition of the second invariant of the deviatoric stresses is generalised to include couple-stresses, and the strain-hardening hypothesis of plasticity is extended to take account of micro-curvatures. The temporal integration of the resulting set of differential equations is achieved using an implicit Euler backward scheme. This return-mapping algorithm results in an exact satisfaction of the yield condition at the end of the loading step. Moreover, the integration scheme is amenable to exact linearisation, so that a quadratic rate of convergence is obtained when Newton's method is used. An important characteristic of the model is the incorporation of an internal length scale. In finite element simulations of localisation, this property warrants convergence of the load-deflection curve to a physically realistic solution upon mesh refinement and to a finite width of the localisation zone. This is demonstrated for an infinitely long shear layer and for a biaxial specimen composed of a strain-softening Drucker-Prager material

Structural softening, mesh dependence, and regularisation in non‐associated plastic flow

A severe dependence of numerical simulations on the mesh density is usually attributed to the presence of strain softening in the constitutive relation. However, other material instabilities, like non‐associated plastic flow, can also cause mesh sensitivity. Indeed, loss of ellipticity in quasi‐static analyses is the fundamental cause of the observed mesh dependence. It has been known since long that non‐associated plastic flow can cause loss of ellipticity, but the consequence for mesh sensitivity, and subsequently, for the difficulty of the equilibrium‐finding iterative procedure to converge have remained largely unnoticed. We first demonstrate at the hand of a biaxial test structural softening and a marked mesh dependence for an ideally plastic material equipped with a non‐associated flow rule. The phenomena are then analysed in depth using an infinitely long shear layer. Finally, it is shown that the mesh effect disappears when the standard continuum model is replaced by a Cosserat continuum, a well‐known regularisation method for strain‐softening constitutive relations

Delay performance in random-access grid networks

We examine the impact of torpid mixing and meta-stability issues on the delay performance in wireless random-access networks. Focusing on regular meshes as prototypical scenarios, we show that the mean delays in an $L\times L$ toric grid with normalized load $\rho$ are of the order $(\frac{1}{1-\rho})^L$. This superlinear delay scaling is to be contrasted with the usual linear growth of the order $\frac{1}{1-\rho}$ in conventional queueing networks. The intuitive explanation for the poor delay characteristics is that (i) high load requires a high activity factor, (ii) a high activity factor implies extremely slow transitions between dominant activity states, and (iii) slow transitions cause starvation and hence excessively long queues and delays. Our proof method combines both renewal and conductance arguments. A critical ingredient in quantifying the long transition times is the derivation of the communication height of the uniformized Markov chain associated with the activity process. We also discuss connections with Glauber dynamics, conductance and mixing times. Our proof framework can be applied to other topologies as well, and is also relevant for the hard-core model in statistical physics and the sampling from independent sets using single-site update Markov chains