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The purpose of this paper is to investigate internal forces in bridges induced by moving vehicles and compare them to earthquake loading.

Dynamic analysis of bridges is performed for moving support actions, for spectral method with Eurocode 8 parameters and for moving vehicle influence. Results from all three methods have been compared on two examples and conclusions have been made. Moving vehicle analysis could be based on the moving force and on the moving mass approach where the later one requires rather accurate knowledge of structural accelerations. It has been shown that the classical Newmark formulation produces accelerations of low accuracy and a novel impulse acceleration method has been devised.

It is found that the actions induced by the moving load could be comparable or larger than those caused by the earthquake on bridges whose mass is not too large in comparison to the vehicle mass.

The developed method will be applied to a broader choice of examples and more reliable conclusions made.

There are bridges where it would be appropriate to perform moving vehicle dynamic analysis, in which case the vertical earthquake actions could be neglected in the analysis.

In order to assess actions from moving vehicles, Newmark method has been generalized in a novel way. Paper describes vector formulation of Newmark method that permits free mixing of integration parameters that could vary from node to node. The method is advantageous for moving load analysis where loading conditions of nodes change in time.

The purpose of this paper is to present a finite element model capable of describing both the diffuse damage mechanism which develops first during the loading of massive brittle structures and the failure process, essentially due to the propagation of a macro‐crack responsible for the softening behaviour of the structure. The theoretical developments for such a model are presented, considering an isotropic damage model for the continuum and a Coulomb‐type criterion for the localized part.

This is achieved by activating subsequently diffuse and localized damage mechanisms. Localized phenomena are taken into account by means of the introduction of a displacement discontinuity at the element level.

It was found that, with such an approach, the final crack direction is predicted quite well, in fact much better than the prediction made by the fracture mechanics type of models considering combination of only elastic response and softening.

The presented model has the potential to describe complex damage phenomena in a cyclic and/or non‐proportional loading program, such as crack closing and re‐opening, cohesive resistance deterioration due to tangential sliding, by using only a few parameters compared to the traditional models for cyclic loading.

The purpose of this paper is to discuss the inelastic behavior of heterogeneous structures within the framework of finite element modelling, by taking into the related probabilistic aspects of heterogeneities.

The paper shows how to construct the structured FE mesh representation for the failure modelling for such structures, by using a building‐block of a constant stress element which can contain two different phases and phase interface. All the modifications which are needed to enforce for such an element in order to account for inelastic behavior in each phase and the corresponding inelastic failure modes at the phase interface are presented.

It is demonstrated by numerical examples that the proposed structured FE mesh approach is much more efficient from the non‐structured mesh representation. This feature is of special interest for probabilistic analysis, where a large amount of computation is needed in order to provide the corresponding statistics. One such case of probabilistic analysis is considered in this work where the geometry of the phase interface is obtained as the result of the Gibbs random process.

The paper confirms that one can make the most appropriate interpretation of the heterogeneous structure properties by taking into account the fine details of the internal structure, along with the related probabilistic aspects with the proper source of randomness, such as the one addressed herein in terms of porosity.

The purpose of this paper is to study the partitioned solution procedure for thermomechanical coupling, where each sub‐problem is solved by a separate time integration scheme.

In particular, the solution which guarantees that the coupling condition will preserve the stability of computations for the coupled problem is studied. The consideration is further generalized for the case where each sub‐problem will possess its particular time scale which requires different time step to be selected for each sub‐problem.

Several numerical simulations are presented to illustrate very satisfying performance of the proposed solution procedure and confirm the theoretical speed‐up of computations which follow from the adequate choice of the time step for each sub‐problem.

The paper confirms that one can make the most appropriate selection of the time step and carry out the separate computations for each sub‐problem, and then enforce the coupling which will preserve the stability of computations with such an operator split procedure.

The purpose of this paper is to describe how a discrete element model is used to predict the penetration depth and the perforation caused by a non‐deformable missile against a thin reinforced concrete slab.

Initial calibration of the model was done with a series of flat‐nose missile tests. Additional simulations were performed with varying the percentage of reinforcement. The present numerical model is compared to experimental test data provided by the French Atomic Energy Agency (CEA) and the French Electrical Power Company (EDF).

For thin concrete slabs, the evolution of the penetration depth in terms of percentage of reinforcement was compared with experimental results: quantitatively the results are very coherent.

The modeling scale is higher than the heterogeneity scale, so the model may be used to simulate real structures, which means that the discrete element method is mainly used here for its ability to account for discontinuities; an identification process based on quasi‐static tests is used, so the quasi‐static behavior of concrete is reproduced. This identification process is the key point, to allow a complete predictive computation for complex impact configurations, especially when the missile diameter and the thickness of the concrete slab are on the same order in size.

The purpose of this paper is to consider the computational tools for solving a strongly coupled multi‐scale problem in the context of inelastic structural mechanics.

In trying to maintain the highest level of generality, the finite element method is employed for representing the microstructure at this fine scale and computing the solution. The main focus of this work is the implementation procedure which crucially relies on a novel software product developed by the first author in terms of component template library (CTL).

The paper confirms that one can produce very powerful computational tools by software coupling technology described herein, which allows the class of complex problems one can successfully tackle nowadays to be extended significantly.

This paper elaborates upon a new multi‐scale solution strategy suitable for highly non‐linear inelastic problems.

The purpose of this paper is to provide the methodology for structural design of complex massive structures under impact by a large airplane.

Using case studies, the issues related to multi‐scale modelling of inelastic damage mechanisms for massive structures are discussed, as well as the issues pertaining to the time integration schemes in presence of different scales in time variation of different sub‐problems, brought by a particular nature of loading with a very short duration) and finally the issues related to model reduction seeking to provide an efficient and yet sufficiently reliable basis for parametric studies which are an indispensable part of a design procedure.

Several numerical simulations are presented in order to further illustrate the approaches proposed herein. Concluding remarks are stated regarding the current and future research in this domain.

Proposed design procedure for complex massive engineering structures under impact by a large airplane provides on one side a very reliable representation of inelastic damage mechanisms and external loading represented by the solution of the corresponding contact/impact problem, and on the other side a very efficient basis obtained by model reduction for performing the parametric design studies.

The purpose of this paper is to discuss the identification of the model parameters for constitutive model capable of representing the failure of massive structures, from two kinds of experiments: a uniaxial tensile test and a three‐point bending test.

A detailed development of the ingredients for constitutive model for failure of massive structures are presented in Part I of this paper. The salient feature of the model is in its ability to correctly represent two different failure mechanisms for massive structures, the diffuse damage in so‐called fracture process zone with microcracks and localized damage in a macrocrack. The identification of such model parameters is best performed from the tests under heterogeneous stress field. Two kinds of tests are used: the simple tension test and the three‐point bending test. The former allows us illustrate the non‐homogeneity of the strain field at failure even under homogeneous stress, whereas the latter provides a very good illustration for the proposed inverse optimization problem for which the specimen is subjected to a heterogeneous stress field.

Several numerical examples are presented in order to illustrate a very satisfying performance of the proposed methodology for identifying the corresponding material parameters of the constitutive model for failure of massive structures.

The paper confirms that one can make a very good use of the proposed identification procedure for estimating the corresponding parameters of damage model for localized failure of massive structure, and the advantages to using the experimental results obtained by testing under heterogeneous stress field.

The purpose of this paper is to describe reduced order modelling based on dynamic flexibility approximation and applied to transient analyses.

This work is based on a recently proposed flexibility‐based component modes synthesis (CMS) approach which was shown to be very efficient for solving large eigenvalue problems. The model reduction approach is based on partionning via the localized Lagrange multipliers method, which makes it very appropriate to handle coupled problems.

In particular, it is demonstrated in this paper how the utilised model reduction method can be applied only to one part of the structure and efficiently coupled to a full finite element model. The performance of the method is investigated on numerical examples of plate and 3D problems.

The proposed flexibility‐based CMS approach can be used as a very efficient tool for complex engineering structures under dynamic load where the mode superposition method applies. The efficiency of the computations is brought about by the model reduction.