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PurposeTo provide a computational strategy for highly accurate analyses of non‐linear inelastic behaviour for heterogeneous structures in civil and mechanical engineering applicationsDesign/methodology/approachAdapts recent developments on mathematical formulations of multi‐scale problems to the recently developed component technology based on C++ generic templates programming.FindingsProvides the understanding how theoretical hypotheses, concerning essentially the multi‐scale interface conditions, affect the computational precision of the strategy.Practical implicationsThe present approach allows a very precise modelling of multi‐scale aspects in structural mechanics problems and can play an essential tool in searching for an optimal structural design.Originality/valueProvides all the ingredients for constructing an efficient multi‐scale computational framework, from the theoretical formulation to the implementation for parallel computing. It is addressed to researchers and engineers analysing composite structures under extreme loading.

SUMMARYA flexibility-based component mode synthesis (CMS) is proposed for reduced-order modelling of dynamic behaviour of large structures. The approach employs partitioning via the localized Lagrange multiplier method. The use of the localized Lagrange multipliers leads to, unlike the classical Lagrange multipliers, a linearly independent set of interface forces without any redundancies at multiply connected interface nodes. The flexibility-based CMS method has shown significant advantages over the classical Craig-Bampton method. A key feature of the method is its substructural mode selection criterion that is independent of loading conditions. Unlike the majority of available CMS approaches, where one retains the full dimension of partition boundary degrees of freedom (DOFs), the flexibility-based method allows to reduce significantly the interface DOFs. The reduction of interface DOFs represents the major contribution of the present communication. The efficiency of the proposed approach is demonstrated on an analysis of a simple plate partitioned and of a more complex 3D structure, both partitioned into several substructures.

Dans ce travail on présente un cadre théorique général du développement des modèles de couplage de deux types de comportement anélastique, la plasticité et l'endommagement. On introduit la nouveauté principale par rapport aux modèles précédents de ce type en utilisant un critère pour définir le domaine élastique valable aussi bien pour la plasticité que pour l'endommagement, qui peut être adopté pour une grande variété des matériaux, d'une part pour les metaux poreux et d'autre part pour le béton en compaction. L'implantation numérique est d'abord présentée pour un cas unidimensionnel simple et ensuite généralisée pour les critères 2D et 3D, pertinents à des métaux ou des bétons.

PurposeThe 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.Design/methodology/approachIn 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).FindingsThe 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.Originality/valueThis paper elaborates upon a new multi‐scale solution strategy suitable for highly non‐linear inelastic problems.

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Purpose-Proposes a methodology for dealing with the problem of designing a material microstructure the best suitable for a given goal. Design/methodology/approach-The chosen model problem for the design is a two-phase material, with one phase related to plasticity and another to damage. The design problem is set in terms of shape optimization of the interface between two phases. The solution procedure proposed herein is compatible with the multi-scale interpretation of the inelastic mechanisms characterizing the chosen two-phase material and it is thus capable of providing the optimal form of the material microstructure. The original approach based upon a simultaneous/sequential solution procedure for the coupled mechanics-optimization problem is proposed. Findings-Several numerical examples show a very satisfying performance of the proposed methodology. The latter can easily be adapted to other choices of design variables. Originality/value-Confirms that one can thus achieve the optimal design of the nonlinear behavior of a given two-phase material with respect to the goal specified by a cost function, by computing the optimal form of the shape interface between the phases.