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

A multi-phase cohesive segments method for the simulation of self-healing materials

The backbone of a numerical technique for the simulation of self-healing mechanisms is the cohesive segements method. This method, which is based on the partition of unity method, allows for the simulation of multiple interacting cracks in a heterogeneous medium, irrespective of the structure of the finite element mesh. In this paper, a concise overview of the cohesive segments method is given. The performance of the method is illustrated with an example

A convergence study of monolithic simulations of flow and deformation in fractured poroelastic media

A consistent linearisation has been carried out for a monolithic solution procedure of a poroelastic medium with fluid‐transporting fractures, including a comprehensive assessment of the convergence behaviour. The fracture has been modelled using a sub‐grid scale model with a continuous pressure across the fracture. The contributions to the tangential stiffness matrix of the fracture have been investigated to assess their impact on convergence. Simulations have been carried out for different interpolation orders and for Non‐Uniform Rational B‐Splines as interpolants vs Lagrangian polynomials. To increase the generality of the results, Newtonian as well as non‐Newtonian (power‐law) fluids have been considered. Unsurprisingly, a consistent linearisation invariably yields a quadratic convergence, but comes at the expense of a loss of symmetry and recalculation of the contribution of the interface to the stiffness matrix at each iteration. When using a linear line search however, the inclusion of only those terms of the interface stiffness which result in a symmetric and constant tangential stiffness matrix is sufficient to obtain a stable and convergent iterative process

A new arc-length control method based on the rates of the internal and the dissipated energy

Purpose - The purpose of this paper is to introduce a new arc-length control method for physically non-linear problems based on the rates of the internal and the dissipated energy. Design/methodology/approach - In this paper, the authors derive from the second law of thermodynamics the arc-length method based on the rate of the dissipated energy and from the time derivative of the energy density the arc-length method based on the rate of the internal energy. Findings - The method requires only two parameters and can automatically trace equilibrium paths which display multiple snap-through and/or snap-back phenomena. Originality/value - A fully energy-based control procedure is developed, which facilitates switching between dissipative and non-dissipative arc-length control equations in a natural way. The method is applied to a plate with an eccentric hole using the phase field model for brittle fracture and to a perforated beam using interface elements with decohesion