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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.

An efficient implementation of a constitutive model for reinforced concrete plates is discussed in this work. The constitutive model is set directly in terms of stress resultants and their energy conjugate strain measures, relating their total values. The latter simplification is justified by our primary goal being an evaluation of the limit load of a reinforced concrete plate. A concept of the ‘rotating crack model’ is utilized in proposing the constitutive model to relate the principal values of bending moments and the corresponding values of curvatures. Efficient implementation is provided by a very robust, but inexpensive plate element. The element is based on an assumed shear strain field and a set of incompatible bending modes, which provides that the non‐linear computations, pertinent to constitutive model, can be carried out locally, i.e. independently at each numerical integration point. Set of numerical examples is presented to demonstrate a very satisfying performance of the proposed model.

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.

This paper presents several methods for enhancing computational efficiency in both static and dynamic analysis of structural systems with localized non‐linear behaviour. A significant reduction of computational effort with respect to brute‐force non‐linear analysis is achieved in all cases at the insignificant (or no) loss of accuracy. The presented methodologies are easily incorporated into a standard computer program for linear analysis.

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 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.

To present a new constitutive model for capturing inelastic behavior of brittle materials.

The multi‐surface plasticity theory is employed to describe the damage‐induced mechanisms. An original feature in that respect concerns the multi‐surface criterion which limits the principle values of elastic strains, which is equivalent to Saint‐Venant plasticity model. The latter allows to represent the damage both in tension and in compression.

Provides a quite realistic description of cracking phenomena in brittle materials, with a very few parameters, leading to a very useful tool for analyzing practical engineering problems.

The model is recast in terms of stress resultants and employed within a flat shell elements in order to provide a very efficient tool for analysis of cellular structures. Moreover, a detailed description of the numerical implementation is given.

The constitutive relationship of a four‐node flat shell finite element with six degrees of freedom per node and a modified five‐point quadrature, previously presented by the authors, is extended to include symmetric and unsymmetric orthotropy. Through manipulation of the kinematic assumptions, provision is made for out‐of‐plane warp. A wide range of membrane and thin to moderately thick plate and shell examples are used to demonstrate the accuracy and robustness of the resulting element.