Search

A local damage model is proposed for the numerical assessment of the static performance of Adobe masonry components. The model was applied to simulate the experimental behaviour of sundried soil bricks and mud mortar tested in uniaxial compression and bending. Numerical simulations of the model are made mesh objective by means of a rate dependent regularization algorithm in statics. This is achieved using a generalization of the damage delay concept based on a decomposition of the Dirichlet boundary condition. It allows non-dimensionality of model parameters mathematically needed to prevent loss of ellipticity of the equilibrium equations of the model. The entire regularization algorithm is integrated within an implicit Newton-Raphson solver. © 2018 Elsevier Ltd

Although many aspects of the fracturing process of concrete are now well understood and successfully simulated with various models, it is still very difficult to properly simulate the different failure mechanisms observed in a concrete structure induced by ballistic impact. In this paper, an enhanced version of the effective-rate-dependent nonlocal damage model [Eng. Fracture Mechanics, 176 (2017)] is proposed to simulate the response of concrete in such events. Hydrostatic damage has been added to the formulation in order to take the damage of the material matrix observed while porosity reduces during compaction into account. Besides controlling the evolution of the nonlinear volumetric response of the material, this new damage variable contributes to the deterioration of the material stiffness upon confinement. It is demonstrated that the description of the nonlinear volumetric response of concrete by an equation of state (EOS) as a plasticity phenomenon, as it is commonly done in hydrodynamic constitutive modeling, is unrealistic for concrete. Such formulations fail to represent the effect of the loss of cohesion observed during compaction on the deviatoric response of the material. By taking this phenomenon into consideration, the proposed model systematically predicts the relevant failure modes (cratering, tunneling, radial cracking and spalling) observed during ballistic impact on a concrete plate as a function of the projectile velocity and plate thickness. © 2017 Elsevier Ltd

This contribution presents a numerical study towards the propagation and branching of cracks in quasi-brittle materials, using a new effective rate-dependent damage model, enhanced by a stress-based nonlocal (SBNL) regularization scheme. This phenomenological model is mesh objective and reproduces the major phenomena associated with crack propagation and branching in quasi-brittle materials. It is discussed and demonstrated that the branching phenomenon is not controlled by a specific, material dependent, crack speed. Instead, it is governed by the evolution of the principal stresses at the crack tip, which are controlled by the evolution of damage. It is demonstrated that, with increasing crack speeds, the principal stresses at the crack tip tend to evolve from a mode-I to a mixed-mode state. Beyond a certain (critical) crack speed, the stress distribution around the crack tip reaches a critical state at which a single crack is no longer stable. When this condition is met, crack branching occurs whenever the stress field at the crack tip is destabilized by either a physical discontinuity or an interfering stress wave reflected at the specimen boundaries.

From a macroscopic point of view, the dynamic tensile response of concrete is mainly due to the viscous behavior of the bulk material and inertia effects at multi-scale levels. It has been suggested that almost all of these mechanisms have to be considered as intrinsic material properties and explicitly included in the constitutive relations of the continuum model. It is discussed and demonstrated that the use of semi-empirical dynamic strength increase factor (DIF) functions to numerically describe rate effects do not characterize true constitutive relations of the material. A strain-rate dependent formulation is used to describe the strength and fracture energy increase of concrete under dynamic tensile loading conditions. However, instead of the commonly used e (instantaneous strain-rate) to update the constitutive law, an effective rate (R) is considered. With this new concept a time scale is introduced in the constitutive law which restrains the ‘evolution of rate’, to represent the inherent dynamic properties of concrete. This has a weak regularization effect and acts as a localization limiter. Mesh objectivity is recovered with the addition of a material length scale to the constitutive relations, here accomplished by an explicit stress-based nonlocal regularization scheme. Two sets of modified split Hopkinson bar tests are simulated for validation, using respectively notched and un-notched specimens. The results are objective and in good agreement with the experiments.

The development of realistic numerical tools to efficiently model the response of concrete structures subjected to close-in detonations and high velocity impact has been one of the major quests in defense research. Under these loading conditions, quasi-brittle materials undergo a multitude of failure (damage) mechanisms. Dynamic tensile failure (e.g. spalling), characterized by a significant strength increase associated with loading rate, has revealed to be particularly challenging to represent. In this contribution, a rate-dependent stress-based nonlocal damage model has been introduced for the simulation of dynamic tensile failure of quasi-brittle materials. The recently proposed stress-based nonlocal criterion has been updated in order to be consistently combined with a rate-dependent version of the well-known Mazars damage model. The model was implemented in LS-DYNA using a fully explicit computational scheme. Two sets of numerical examples have been presented. First, one-dimensional numerical analyses were conducted to evaluate the model capabilities, applicability and limitations. Second, the model has been validated against experimental results. It has been shown that the proposed model, in addition to correcting spurious mesh sensitivity, also provides a more realistic representation of damage initiation and growth, in particular around discontinuities (notches and free boundaries) and damaged areas.

A glass-polymer system of a polyurethane elastomeric matrix with a single 3 mm-diameter glass particle was investigated using a split Hopkinson pressure bar (SHPB) setup for revealing the dynamic compressive mechanical response. This study produced the characteristics of the dynamic stress-strain relation and the relations for the rate dependencies of yield stress, maximum stress and strain energy. A high-speed camera was applied to record crack initiation, propagation and fragmentation fracture. Scanning electron microscopy (SEM) was employed to explore the dynamic damage mechanisms. The static and dynamic compressive mechanical properties of a glass-polymer system were compared with these of monolithic polyurethane elastomeric polymer material. The results of this study provide the dynamic response at unit cell level and are used for development and evaluation of transparent, impact-resistant protection concepts of glass-polymer systems.

In this study, the impact of a steel spherical projectile on an alumina ceramic is considered. New experimental and numerical results are presented and analysed. Numerical results are obtained using the Finite Element Method and the upgraded viscosity regularized Johnson-Holmquist-2 constitutive model to describe the ceramic material behaviour. First, a short investigation is done using 2d Finite Element simulations to establish a proper numerical framework. Second, the numerical framework is extended to 3d and experimental results are used to validate the framework and the ceramic material model. This shows that all relevant ceramic failure mechanisms are captured correctly and the framework and model can be used to simulate sphere impact on ceramic material. Third, the simulations are used to analyse the failure processes in the ceramic material in more detail. Here the focus lies in obtaining information which can currently not be retrieved from experiments. Timing and interaction of propagating conical and radial cracks are investigated and corroborate with the typical failure mechanisms observed in sphere impact on ceramic material.

Alumina ceramic is often used in armour systems. This material is known to have a brittle response under tensile loading, while a ductile response is found when sufficiently high pressures are reached. During projectile impact a ceramic material experiences both tensile loading and high pressures, hence fails in both a brittle and ductile way. Properly capturing the ceramic failure in a single material model remains challenging. A viscosity regularized Johnson-Holmquist-2 model has been used to simulate dynamic loading on alumina ceramic. The simulations show that the brittle and ductile nature of the material can not be captured simultaneously in the current material model. A new failure strain formulation is proposed where the behaviour under tensile and compressive loading can be controlled independently. This allows to properly capture both the brittle and ductile response of the material in a single constitutive framework, with a single set of model parameters. © 2019 Elsevier Ltd

A local damage model has been recently developed for the numerical simulation of the static behaviour of adobe bricks. Mesh insensitivity of the local model was obtained by generalizing the damage delay concept based on a Dirichlet boundary condition decomposition integrated in an implicit solver. The regularization properties of the model were proven before only in statics. In this study, mesh independence is demonstrated in dynamics analysing the problem of a cantilever bar uniaxially loaded at high deformation rates. Furthermore, the physical background of the delay formulation is interpreted regarding the main failure processes in compression exhibited by quasi brittle materials used in masonry. Two limitations of the model in correctly simulating the dynamic behaviour of masonry bricks have been observed. Corrections to the original damage delay formulation are proposed in this study. These enhance the capability of the model to address also distributed failure of traditional geo-materials and the inherent rate dependence also at high strain rate regimes. The improvements are demonstrated in this paper by means of numerical simulations of both theoretical tests and practical applications. These consist of experimental tests in compression recently performed by the authors at different strain rates, from statics to high velocity impact tests.

In this work, findings of a numerical study performed to investigate the impact behavior of porous concrete, modeled as a four phase cementitious composite consisting of aggregates, cement paste, interfacial transition zones (ITZ) and air, are presented. The numerical analyses contributed to the process of designing a special type of concrete for safety purposes i.e. as a protective building material to be used in safety walls outside important buildings or munition magazines for storing explosives. In case of an explosion, large concrete fragments that are formed, cause a very important threat. Therefore, in the scope of a research project, designing a special type of concrete having sufficient strength, but fracturing into small fragments under impact loading was aimed. In the numerical analyses, model porous concretes, in which the amounts and properties of pores and aggregates could be varied individually, were used to see the sole effect of each parameter. According to the results, it was found that at constant total porosity, the impact strength increased with decreasing pore size while multiple fragmentation was observed. On the other hand, the impact strengths of porous concretes with different size aggregates (with constant total aggregate content and porosity) were approximately the same when no ITZ was defined. However, when ITZ was present, the impact strength was found to decrease as the aggregates were finer. This trend was also valid for the respective full concretes. Representative experimental results of porous concretes were also presented in order to support the numerical results.

Plasticity models are frequently used to describe ceramic materials. Well established and often used ceramic models are those by Johnson and Holmquist. These are softening plasticity models for which mesh dependency is a well known problem. A viscosity or rate dependency can be added to the material model to provide regularization and solve the mesh dependency problems. For the Johnson-Holmquist models a viscosity is proposed to work on the hydrostatic tensile strength. A consistency visco-plastic formulation is used. For the Johnson-Holmquist-2 model it is demonstrated that the proposed viscosity indeed removes the mesh dependency problems. This is shown for both quasi-static and dynamic loading. In addition it is shown that the proposed viscosity can predict an experimentally measured rate dependent spall strength of alumina ceramic, while the original model fails to do so.

The resilience of a city confronted with a terrorist bomb attack is the background of the paper. The resilience strongly depends on vital infrastructure and the physical protection of people. The protection buildings provide in case of an external explosion is one of the important elements in safety assessment. Besides the aspect of protection, buildings facilitate and enable many functions, e.g., offices, data storage, -handling and -transfer, energy supply, banks, shopping malls etc. When a building is damaged, the loss of functions is directly related to the location, amount of damage and the damage level. At TNO Defence, Security and Safety methods are developed to quantify the resilience of city infrastructure systems (Weerheijm et al. 2007b). In this framework, the dynamic response, damage levels and residual bearing capacity of multi-storey RC buildings is studied. The current paper addresses the aspects of dynamic response and progressive collapse, as well as the proposed method to relate the structural damage to a volume-damage parameter, which can be linked to the loss of functionality. After a general introduction to the research programme and progressive collapse, the study of the dynamic response and damage due to blast loading for a single RC element is described. Shock tube experiments on plates are used as a reference to study the possibilities of engineering methods and an explicit finite element code to quantify the response and residual bearing capacity. Next the dynamic response and progressive collapse of a multi storey RC building is studied numerically, using a number of models. Conclusions are drawn on the ability to predict initial blast damage and progressive collapse. Finally the link between the structural damage of a building and its loss of functionality is described, which is essential input for the envisaged method to quantify the resilience of city infrastructure.

The handling of explosives and ammunition introduces a safety risk for personnel and third parties. Accidents related to storage, transport and transshipment may result in severe injury and material damage. Dispersion of structural debris is one of the main hazards resulting from detonations inside structures. Reliable prediction models for debris dispersion are essential for risk assessment methods. In this article we give a statistical description of the dispersion of explosion produced debris. The basis is a general expression for the projectile areal number density in the horizontal and vertical plane. Combined with engineering models for the launch conditions, predictions can be made. An analytical solution to the equations of motion may be used to allow for fast calculations. A parameter study shows consistent results. The model has been validated with internal detonation tests of bare charges in reinforced concrete structures. The validation clearly shows the prediction capabilities of the model for three loading regimes described in the literature. We give a thorough description of the validity and limitations of the model, and an outlook of current and future research. Examples are the failing debris mass distribution prediction for reinforced concrete in the shock overloading regime, and ricochet and roll and break-up at impact phenomena.

In this study, an experimental configuration that reveals the dynamic response of porous concretes in a drop weight impact test was introduced. Through the measurement of particle velocity at the interface, between the impactor and the concrete target, the dynamic response was obtained in an easily applicable way. Laser Doppler velocimetry (LDV) was used in monitoring the time history of the particle velocity at the interface, which was subsequently analyzed to determine the dynamic strengths of the concrete specimens tested. The velocity measurements were analyzed using a special reverberation application of the impedance mismatch method. The test results showed that the experimental configuration was sufficient to measure the dynamic strengths of porous concretes and a normal concrete with moderate strength. The method was validated by using impactors having different dynamic impedances in testing the same material and was also verified to be precise enough to distinguish between different types of porous concrete mixtures.

A deterministic model has been developed that describes the throw of debris or fragments from a source with an arbitrary geometry and for arbitrary initial conditions. The initial conditions are defined by the distributions of mass, launch velocity and launch direction. The item density in an exposed area, i.e. the number of impacting debris or fragments per unit of area, has been expressed analytically in terms of these initial conditions. While existing models make use of the Monte Carlo technique, the present model uses the source function theorem, an underlying mathematical relation between the debris density and the initial distributions. This gives fundamental insight in the phenomenon of throw, and dramatically reduces the required number of trajectory calculations. The model has been formulated for four basic source geometries: a point source, a vertical cylinder, a horizontal cylinder, and a vertical plane. In combination with trajectory calculations the item density can be quantified. As an illustration of the model, analytical results are presented and compared for the vertical plane and the vertical cylinder geometry under simplified assumptions. If uncertainties exist in the initial conditions, the model can be used to investigate these initial conditions based on experimental data. This has been illustrated on the basis of a trial with 5 ton of ammunition stacked in an ISO container. In this case the model has been successfully applied to determine the debris launch angle and velocity distribution, by means of backward calculations. If, on the other hand, sufficient information on the initial conditions is available, the model can be used as an effect model in risk assessment methods, or for the requirements on protective measures. The model can be used to predict safety distances based on any desired criterion. © 2007 Elsevier Ltd. All rights reserved.