Micromechanics of spatially uniform heterogeneous media: A critical review and emerging approaches

Pindera, Marek‐Jerzy; Khatam, Hamed; Drago, A.; Bansal, Yogesh

doi:10.1016/j.compositesb.2009.03.007

Cited by 221 publications

(99 citation statements)

References 134 publications

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“…Gli approcci PMAs non sono invece utilizzabili per l'analisi dell'interazione della microstruttura con fenomeni macroscopici, come ad esempio la propagazione di un difetto. La letteratura specifica dei metodi PMAs è estesissima, dato il loro ampio utilizzo; si citano qui solo alcuni riferimenti di base, [15][16][17][18]. Nell'impiego di microcampi periodici risultano particolarmente critiche le fasi di: (i) definizione del microcampo stesso, rappresentativo della struttura; (ii) definizione delle condizioni al contorno (periodicità, simmetria, antisimmetria); (iii) definizione dei carichi meccanici o termici.…”

Section: Metodi Basati Su Microstrutture Discreteunclassified

La modellazione microstrutturale di materiali a struttura eterogenea: princìpi ed applicazioni

Collini

2010

Frattura Ed Integrità Strutturale

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sono facilmente risolvibili con gli approcci tradizionali. Oltre allo studio delle proprietà effettive dei solidi eterogenei, vi è la crescente necessità di incorporare un maggiore numero di informazioni sui meccanismi di deformazione e danneggiamento generati alla microscala, anche per i materiali abitualmente considerati omogenei. Micromeccanismi di cavitazione e concentrazioni locali di tensione e deformazione, sono indispensabili per spiegare fenomeni non-lineari come la rottura di fatica o il cedimento duttile, altrimenti non inquadrabili con approcci classici di tensioni e deformazioni medie. La micromeccanica si occupa della determinazione precisa, o di una stima accurata, di grandezze di campo microstrutturali locali. In questo lavoro sono illustrati i princìpi che sono alla base dell'approccio micromeccanico, come i concetti di multiscala, di distribuzione statistica delle fasi, di descrizione mediante volumi di riferimento e di omogeneizzazione e localizzazione, e, attraverso alcune applicazioni pratiche delle principali tecniche di modellazione, sono illustrati e discussi criticamente i risultati della ricerca effettuata su varie strutture di ghisa nodulare. ABSTRACT.There are many problems in Solid Mechanics, Physics of Solids and Materials Science that can not been solved using conventional approaches. Besides the effective properties of non-homogeneous bodies, there is an increasing need for incorporating more physical information about small-scale mechanisms of deformation and damage into phenomenological models of plasticity and rupture of materials which are usually considered homogeneous. Cavitation, local stress or strain concentrations at small scale are essential to explain nonlinear phenomena, such as fatigue or ductile rupture, which are not understandable from the simple point of view of average stresses or strains. Precise determination or accurate estimation of local fields is the domain of micromechanics. This work treats the basic concepts of the micromechanics in a simple way, with some practical suggestion on the most commonly used modelling techniques and some applications made by the author on various nodular cast iron microstructures. KEYWORDS.Modellazione micromeccanica; Materiali a struttura eterogenea; Compositi; Comportamento elasto-plastico. INTRODUZIONE ALLA MECCANICA DEI MATERIALI MICROSTRUTTURATIMateriali microstrutturati e concetto di scala di osservazione a Micro-e Meso-Meccanica del Continuo è una branca relativamente giovane della Meccanica dei Materiali, che studia il comportamento meccanico dei materiali a livello microstrutturale. Molti dei materiali di interesse industriale ed ingegneristico, e la maggior parte dei materiali "naturali", presentano una struttura eterogenea, formata cioè da più costituenti o "fasi", distinguibili ad una certa (ridotta) scala di osservazione. In altre parole, ciò che al L

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Section: Metodi Basati Su Microstrutture Discreteunclassified

La modellazione microstrutturale di materiali a struttura eterogenea: princìpi ed applicazioni

Collini

2010

Frattura Ed Integrità Strutturale

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“…By using triangular elements as mentioned above, the enrichment shape function M S , in (36), looks like that depicted in Figure 4-a. The numerical integration of expression (39) and (41) is performed by means of two quadrature points.…”

Section: Implementation Of An E-fem Technique For the Macroscalementioning

confidence: 99%

“…Introducing the interpolated displacements and strain fields, defined in (36) and (37), into the incremental equilibrium problem described in equation (6) of Box 1; and performing variations respect to u and β (both of these vectors collect all the element vectors u e and β e respectively), we can derive the following two incremental equilibrium equations:…”

Section: Implementation Of An E-fem Technique For the Macroscalementioning

confidence: 99%

A two‐scale failure model for heterogeneous materials: numerical implementation based on the finite element method

Toro

Sánchez

Huespe

et al. 2013

Numerical Meth Engineering

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In the first part of this contribution, a brief theoretical revision of the mechanical and variational foundations of a Failure-Oriented Multiscale Formulation (FOMF) devised for modeling failure in heterogeneous materials is described.The proposed model considers two well separated physical length scales, namely: (i) the "macro" scale where nucleation and evolution of a cohesive surface is considered as a medium to characterize the degradation phenomenon occurring at the lower length scale, and (ii) the "micro" scale where some mechanical processes that lead to the material failure are taking place, such as strain localization, damage, shear band formation, etc. These processes are modeled using the concept of Representative Volume Element (RVE). On the macro scale, the traction separation response, characterizing the mechanical behavior of the cohesive interface, is a result of the failure processes simulated in the micro scale. The traction separation response is obtained by a particular homogenization technique applied on specific RVE subdomains. Standard, as well as, Non-Standard boundary conditions are consistently derived in order to preserve "objectivity" of the homogenized response with respect to the micro-cell size.In the second part of the paper, and as an original contribution, the detailed numerical implementation of the two-scale model based on the Finite Element Method is presented. Special attention is devoted to the topics which are distinctive of the FOMF, such as: (i) the finite element technologies adopted in each scale along with their corresponding algorithmic expressions, (ii) the generalized treatment given to the kinematical boundary conditions in the RVE and (iii) how these kinematical restrictions affect the capturing of macroscopic material instability modes and the posterior evolution of failure at the RVE level.Finally, a set of numerical simulations is performed in order to show the potentialities of the proposed methodology, as well as, to compare and validate the numerical solution furnished by the two-scale model with respect to a mono-scale Direct Numerical Simulation (DNS) approach.

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“…Initially developed to help solve fluid mechanics problems, finite-volume theory has rapidly evolved during the past 20 years in the solid mechanics area after transitioning from the fluid mechanics field. The contributions of Pindera and his colleagues [60][61][62] have the spurred extensive use of finite-volume theory in predicting the stress-strain behaviors and fracture phenomena in a wide range of fiber-reinforced composite materials. The accuracies of homogenized and local responses have been shown to be comparable to those of the FE method but with even greater efficiency.…”

Section: Composite Materials and Structuresmentioning

confidence: 99%

Basic research on machinery fault diagnostics: Past, present, and future trends

et al. 2017

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Machinery fault diagnosis has progressed over the past decades with the evolution of machineries in terms of complexity and scale. High-value machineries require condition monitoring and fault diagnosis to guarantee their designed functions and performance throughout their lifetime. Research on machinery Fault diagnostics has grown rapidly in recent years. This paper attempts to summarize and review the recent R&D trends in the basic research field of machinery fault diagnosis in terms of four main aspects: Fault mechanism, sensor technique and signal acquisition, signal processing, and intelligent diagnostics. The review discusses the special contributions of Chinese scholars to machinery fault diagnostics. On the basis of the review of basic theory of machinery fault diagnosis and its practical applications in engineering, the paper concludes with a brief discussion on the future trends and challenges in machinery fault diagnosis.

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Micromechanics of spatially uniform heterogeneous media: A critical review and emerging approaches

Cited by 221 publications

References 134 publications

La modellazione microstrutturale di materiali a struttura eterogenea: princìpi ed applicazioni

La modellazione microstrutturale di materiali a struttura eterogenea: princìpi ed applicazioni

A two‐scale failure model for heterogeneous materials: numerical implementation based on the finite element method

Basic research on machinery fault diagnostics: Past, present, and future trends

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