René de Borst

Discrete and smeared crack models for concrete fracture are discussed in a historical perspective. It is argued that these two computational approaches, originally conceived as very different, can be brought together by exploiting the partition‐of‐unity property of finite element shape functions. The cohesive segments method, which exploits this partition‐of‐unity property, exhibits advantages of both the discrete and smeared crack approaches, and is capable of describing the transition from distributed micro‐cracking to a dominant crack. The versatility of the cohesive methodology is shown by incorporating water diffusion and ion transport into the formulation. Copyright © 2004 John Wiley & Sons, Ltd.

A concise overview is given of various numerical methods that can be used to analyse localization and failure in engineering materials. The importance of the cohesive‐zone approach is emphasized and various ways to incorporate the cohesive‐zone methodology in discretization methods are discussed. Numerical representations of cohesive‐zone models suffer from a certain mesh bias. For discrete representations this is caused by the initial mesh design, while for smeared representations it is rooted in the ill‐posedness of the rate boundary value problem that arises upon the introduction of decohesion. A proper representation of the discrete character of cohesive‐zone formulations which avoids any mesh bias can be obtained elegantly when exploiting the partition‐of‐unity property of finite element shape functions. The effectiveness of the approach is demonstrated for some examples at different scales. Moreover, examples are shown how this concept can be used to obtain a proper transition from a plastifying or damaging continuum to a shear band with gross sliding or to a fully open crack (true discontinuum). When adhering to a continuum description of failure, higher‐order continuum models must be used. Meshless methods are ideally suited to assess the importance of the higher‐order gradient terms, as will be shown. Finally, regularized strain‐softening models are used in finite element reliability analyses to quantify the probability of the emergence of various possible failure modes. Copyright © 2004 John Wiley & Sons, Ltd.

An elasto‐plastic material model is proposed that can be used to simulate the cyclic deterioration of railway tracks. The model describes the envelope of the irreversible, plastic material response generated during a cyclic loading process, thereby distinguishing the mechanisms of frictional sliding and volumetric compaction. The reversible response is represented by a pressure‐dependent, hypo‐elastic material law. After the numerical integration of the model is specified, the model is calibrated on laboratory experiments and employed in a finite‐element case study of the long‐term settlement behaviour of a railway track. The main features of the model are illustrated by comparing the computed response with the response obtained by in situ track measurements. Copyright © 2003 John Wiley & Sons, Ltd.

The present contribution is concerned with the design of a family of consistent fluid–structure interaction algorithms based on a unique temporal and spatial discretization of the governing equations. The characterization of the moving fluid–structure interface is realized by means of the arbitrary Lagrangian Eulerian technique. The spatial discretization is performed with the finite‐element method, whereby either a first‐order upwind scheme or the classical second‐order upwind Petrov–Galerkin technique are used to discretize the linearized fluid equations while the standard Bubnov–Galerkin method is applied to the structural equations. In order to streamline coupling, the structure is discretized in a velocity‐based fashion. The temporal discretization of both the fluid and the structural equations is embedded in the generalized‐α framework by making use of classical Newmark approximations in time. To quantify the sources of error of the proposed algorithms, systematic studies in terms of the one‐dimensional piston model problem are presented. Copyright © 2003 John Wiley & Sons, Ltd.

It is shown how modern concepts to integrate the elasto‐plastic rate equations of standard plasticity via an implicit algorithm can be generalized to plasticity without an explicitly defined yield surface and to overstress‐type models of viscoplasticity, where the stress point can be located outside the loading surface. For completeness, a tangent operator is derived that is consistent with the update algorithm. Copyright © 2002 John Wiley & Sons, Ltd.

A new model is presented for the simulation of delamination in laminated composite materials. A key feature is that the material structure and the finite element mesh are uncoupled. The displacement discontinuities that arise during the delamination process are described mathematically using discontinuous functions. This leads naturally to a set of coupled equations for the continuous and the discontinuous parts of the response. Discontinuities can pass through solid finite elements arbitrarily, with the displacement jump continuous across element boundaries. The performance of the model is demonstrated for several problems of delamination and geometric instability. Copyright © 2002 John Wiley & Sons, Ltd.

A numerical model is developed which allows the inclusion of displacement discontinuities in a strain‐softening medium, independent of the finite element mesh structure. Inelastic deformations develop in the continuum and, when a critical threshold of inelastic deformation is reached, a displacement discontinuity is inserted. Discontinuities are introduced using the partition of unity concept which allows discontinuous functions to be added to the standard finite element basis. It is shown that the introduction of displacement discontinuities at the later stages of the failure process can lead to a failure mode that is fundamentally different than that using a continuum model only. This combined continuum‐discontinuous model is better able to describe the entire failure process than a continuum or a discrete model alone and treats mode‐I and mode‐II failure in a unified fashion. Copyright © 2001 John Wiley & Sons, Ltd.

An overview is given of some recent developments in computational modelling of localization and failure phenomena in solids. Cohesive‐zone models are considered as well as enrichment of continua using gradients in space and in time. The latter models are applied to static instabilities as well as to propagative instabilities. The determination of the additional parameters that emerge in gradient continua is treated and attention is paid to the spatial resolution that is necessary to properly capture bands of localized deformation. Finally, the impact is considered which imperfection patterns may have on the failure mode. Copyright © 2001 John Wiley & Sons, Ltd.

In local approaches to fracture, crack initiation and growth are regarded as the ultimate consequences of a gradual, local loss of material integrity. Standard degradation models, however, are unable to deal with localisation instabilities and the singular strains at the crack tip. As a consequence, finite element analyses become highly sensitive to the spatial discretisation. Adding nonlocal terms to the models enhances their ability to describe fracture processes. An essential role is played by the treatment of the boundary of the equilibrium problem, particularly the internal boundary which represents the crack contour. If the appropriate boundary conditions are applied and the crack region is removed from the discrete equilibrium problem, finite element analyses become mesh-objective.