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

Computational Analysis of Crack Deflection at a Bi-Material Interface by means of Initially Rigid and Elastic Mixed-mode Traction-Separation Laws.

Numerical analyses of interfaces in layered samples are commonly performed with cohesive zone models, for which several types of traction-separation laws have been proposed. Most laws are initially elastic, which may result in an undesired compliance of the material when modeling bulk fracture. To overcome this problem, this study presents an exponential initially rigid tractionseparation law.\u3cbr/\u3eThe initially rigid model is compared to an initially elastic model for various loading conditions. It is shown that the proposed model is capable of describing both single mode and mixed-mode behavior, and correctly determines the work-of-separation. A dissipation-based arc-length solver, compatible with both models, is implemented to account for snap-backs in the load-displacement\u3cbr/\u3ecurve.\u3cbr/\u3eThe competition between bulk fracture and delamination in a bi-material sample is analyzed, in which the substrate is modeled with subsequently initially rigid and initially elastic models. The results are in agreement with an LEFM solution for substrate fracture, but the assumption of pure shear opening of the interface results in an overprediction of the required load for delamination. Both models predict similar substrate-to-interface strength and toughness ratios at which transition between the failure modes occurs and an increased load is observed for equal fracture length scales of the substrate and interface

Computational modelling of delamination

Delamination in composite structures is best modelled at a mesoscopic level. In this approach, the plies are modelled as continua, which can either be assumed to behave linearly elastically or to degrade according to a damage law. Delamination in the interfaces between them is modelled using a discrete relation between interface tractions and relative displacements. Key in this type of modelling is the presence of a work of separation or fracture energy, which governs the growth of the delamination. This cohesive-surface approach has traditionally been implemented numerically using special interface elements which connect the continuum elements that are used to model the plies. Exploiting the partition-of-unity property of finite element shape functions to model the interface separation process offers some advantages, since interfaces can be inserted at the onset of delamination and not a priori, as in the conventional approach. As a consequence, elastic compliance of the interface prior to onset of delamination, spurious traction oscillations ahead of the delamination front and spurious wave reflections because of the presence of a high stiffness value are avoided. Moreover, unlike the conventional approach, unstructured meshes can be employed

Efficient modelling of delamination growth using adaptive isogeometric continuum shell elements

The computational efficiency of CAE tools for analysing failure progression in large layered composites is key. In particular, efficient approximation and solution methods for delamination modelling are crucial to meet today’s requirements on virtual development lead times. For that purpose, we present here an adaptive continuum shell element based on the isogeometric analysis framework, suitable for the modelling of arbitrary delamination growth. To achieve an efficient procedure, we utilise that, in isogeometric analysis, the continuity of the approximation field easily can be adapted via so-called knot insertion. As a result, the current continuum shell provides a basis for an accurate but also computationally efficient prediction of delamination growth in laminated composites. Results show that the adaptive modelling framework works well and that, in comparison to a fully resolved model, the adaptive approach gives significant time savings even for simple analyses where major parts of the domain exhibit delamination growth

Delamination buckling of fibre-metal laminates

A fibre–metal laminate is a composite of metal and fibre-reinforced prepreg layers. An example of such a material is Glare. It consists of alternating layers of aluminium and glass-fibre-reinforced prepreg. The material can be sensitive to delamination buckling, which occurs when a partially delaminated panel is subjected to a compressive force. The interaction of local buckling and extension of the delaminated zone typically results in a decrease of the residual strength and, eventually, in a collapse of the structure. This phenomenon can be observed in experimental tests, but numerical analyses are needed to obtain a better understanding of the mechanisms and the critical parameters. In this paper, some experimental observations are discussed regarding delamination buckling in Glare and, on the basis of these observations, a numerical model is constructed at a meso-mechanical level. In this approach, solid-like shell elements are used to model the individual layers. They are connected by interface elements, which are capable of modelling delamination between the layers

A cohesive segments approach for dynamic crack growth

In the cohesive segments method, a crack is represented by a set of overlapping cohesive segments which are inserted into finite elements as discontinuities in the displacement field using the partition-of-unity property of shape functions. The evolution of decohesion of the segments is governed by a relation between the displacement jump and traction across the segment. The formulation permits both crack nucleation and discontinuous crack growth to be modelled. Here, the cohesive segments formulation for dynamic crack growth is presented and application of the methodology is illustrated in two numerical examples

An evaluation of the accuracy of discontinuous finite elements in explicit dynamic calculations

The use of partition of unity based discontinuous finite element formulations for the simulation of crack propagation with implicit simulations is now well established. However, in explicit simulations the accuracy is still a point of concern. Some outstanding issues will be addressed in this paper

Multi-dimensional wavelet reduction for the homogenisation of microstructures

\u3cp\u3eOne of the recent fields of interest in computational homogenisation is the development of model order reduction frameworks to address the significant computational costs enabling fast and accurate evaluation of the microstructural volume element. Model order reduction techniques are applied to computationally challenging analyses of detailed micro- and or macro-structural problems to reduce both computational time and memory usage. In order to alleviate the costly integration, a wavelet-reduced order model for one-dimensional microstructural problems was presented in van Tuijl et al. (2019). This novel approach addresses both the large number of degrees of freedom and integration costs and provides control on errors in the microstructural fields. In this work, this wavelet reduced order model is extended to a multi-dimensional framework and benchmarked for more realistic multi-scale problems. The Wavelet-Reduced Order Model consists of two reduction steps. First, a Reduced Order Model is constructed to reduce the dimensionality of the microstructural model. Second, a wavelet representation is applied to reduce the integration costs of the microstructural model, whilst maintaining control over the local integration error. The multi-dimensional Wavelet-Reduced Order Model is demonstrated for a set of two-dimensional path-dependent microstructural models, evaluating their accuracy and reduction with respect to the full order models on the microstructural and homogenised fields.\u3c/p\u3