Damijan Markovic

Strong coupling methods in multi-phase and multi-scale modeling of inelastic behavior of heterogeneous structures

In this work we address several issues pertaining to efficiency of the computational approach geared towards modeling of inelastic behavior of a heterogeneous structure, which is represented by a multi-scale model. We elaborate in particular upon the case where the scales remain coupled throughout the computations, implying a constant communication between the finite element models employed at each scale, and only briefly comment upon our treatment of inelastic analysis of a more classical case where the scales can be separated. We also discuss different manners of representing a complex multi-phase microstructure within the framework of the finite element model constructed at that scale, selecting a model problem of two-phase material where each phase has potentially different inelastic behavior. Several numerical examples are given to further illustrate the presented theoretical considerations.

MULTI-SCALE MODELLING OF HETEROGENEOUS STRUCTURES WITH INELASTIC CONSTITUTIVE BEHAVIOR

Purpose – To provide a computational strategy for highly accurate analyses of non‐linear inelastic behaviour for heterogeneous structures in civil and mechanical engineering applications Design/methodology/approach – Adapts recent developments on mathematical formulations of multi‐scale problems to the recently developed component technology based on C++ generic templates programming. Findings – Provides the understanding how theoretical hypotheses, concerning essentially the multi‐scale interface conditions, affect the computational precision of the strategy. Practical implications – The 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/value – Provides 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.

Constitutive model of coupled damage-plasticity and its finite element implementation

In this work we present a general theoretical framework for developing a constitutive model capable of coupling two basic types of inelastic behaviour, plasticity and damage. We elaborate upon the main novelty with respect to the previous models of this type, which pertains to a systematic use of criteria for defining the elastic domain, both for plasticity and damage, which can be adapted to a very wide variety of engineering materials, from metals with voids on one side to concrete compaction on the other side. The numerical implementation is first presented for a simple one-dimensional case, and subsequently extended to 2D and 3D criteria which are adequate for either metals or concrete.

Multi‐scale modelling of heterogeneous structures with inelastic constitutive behavior: Part II – software coupling implementation aspects

Purpose – 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. Design/methodology/approach – 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). Findings – 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. Originality/value – This paper elaborates upon a new multi‐scale solution strategy suitable for highly non‐linear inelastic problems.

Shape optimization of two-phase inelastic material with microstructure

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.

Partitioning based reduced order modelling approach for transient analyses of large structures

Purpose – The purpose of this paper is to describe reduced order modelling based on dynamic flexibility approximation and applied to transient analyses.Design/methodology/approach – 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.Findings – 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.Originality/value – 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 e...

Code-coupling strategy for efficient development of computer software in multiscale and multiphysics nonlinear evolution problems in computational mechanics

Abstract In this work we seek to provide an efficient approach to development of software computational platform for the currently very active research domain of multiphysics and multiscale analysis in fully nonlinear setting. The typical problem to be solved is nonlinear evolution problem, with different scales in space and time. We show here that a successful solution to such a problem requires gathering the sound theoretical formulation, the most appropriate discrete approximation and the efficient numerical implementation. We show in particular that the most efficient numerical implementation is obtained by reusing the existing codes, in order to accelerate the code development and validation. The key element that makes such an approach possible is the Component Template Library (CTL), presented in this work. We show that the CTL allows to seamlessly merge the existing software products into a single code at compilation time, regardless of their ‘heterogeneities’ in terms of programming language or redundancy in use of local variables. A couple of illustrative problems of fluid–structure interaction and multiscale nonlinear analysis are presented in order to confirm the advantage of the proposed approach.

Performance Based Earthquake-Resistant Design: Migrating Towards Nonlinear Models and Probabilistic Framework

In this work we present our recent works that follow two modern tendencies in modelling and design of engineering structures for extreme loading such as earthquakes: (i) fine scale models for providing the simplest, fine-scale interpretation of inelastic damage mechanisms at the origin of energy dissipation and damping phenomena, as opposed to coarse scale of stress resultants; (ii) the role of probability in this kind of modelling approach. We consider application of these ideas first to structures, especially irreplaceable structures, such as nuclear power plants, and move onto the complex systems such as water networks.

Micro-macro modeling of inelastic behavior of heterogeneous structures

Publisher Summary This chapter integrates within the analysis a physically more sound explanation of inelastic behavior of structures, which can be provided at the scale where dissipative mechanisms remain simple and uncoupled that is in general referred to as “microscale.” The ever increasing computational resources provide an important incentive to strive for a more refined modeling of inelastic behavior of engineering structures. In that sense, the role of the traditional phenomenological models, which have been predominantly used in engineering design, is nowadays being very actively reexamined.