a variational model for determining fracture modes in frcm systems

Abstract: The bond strength at the yarn to matrix interface is one of the key factor affecting the FRCM mechanical behavior. The interaction between multi-filament yarn and cementitious matrix, governed by complex mechanisms, determines the behavior and failure mode of this composite system. An experimental campaign comprising of 20 pull out tests on multifilament carbon yarns embedded in a cementitious matrix was carried out. Different bond lengths have been analyzed, equal to 20 and 50 mm. Failure modes observed were different depending on the bond length: slippage of the yarn for a bond length of 20 mm and failure of the external filaments when the bond length was increased to 50 mm. The maximum load recorded at fibers breakage was lower than the tensile strength of the yarn, confirming the fact that only the external filaments of the yarn are engaged in the load transfer mechanism and the effective area is only a portion of the total area. This work aims to propose a variational model to reproduce the behavior and possible failure modes of multifilament carbon yarns embedded in a cementitious matrix. Smeared crack terms are incorporated into the energy functional of the model to account for possible fracture in the yarn and in the matrix, and for debonding at the yarn-matrix interface. The evolution problem is formulated as an incremental energy minimization problem, and discretized by finite elements. Numerical simulations are able to accurately describe the composite behaviours and to reproduce experimental results

The variational theory of fracture: diffuse cohesive energy and elastic-plastic rupture

This communication anticipates some results of a work in progress [1], addressed to explore the efficiency of the diffuse cohesive energy model for describing the phenomena of fracture and yielding. A first local model is partially successful, but fails to reproduce the strain softening regime. A more robust non-local model, obtained by adding an energy term depending on the deformation gradient, describes many typical features of the inelastic response observed in experiments, including strain localization and necking. Fracture occurs as the result of extreme strain localization. The model predicts different fracture modes, brittle and ductile, depending on the analytical form of the cohesive energy function

A DIFFUSE COHESIVE ENERGY APPROACH TO FRACTURE AND PLASTICITY: THE ONE-DIMENSIONAL CASE

Abstract. In the fracture model presented in this paper, the basic assumption is that the energy is the sum of two terms, elastic and cohesive, depending on the elastic and inelastic part of the deformation, respectively. Two variants are examined, a local model, and a non-local model obtained by adding a gradient term to the cohesive energy. While the local model only applies to materials which obey Drucker's postulate and only predicts catastrophic failure, the non-local model describes the softening regime, and predicts two collapse mechanisms, one for brittle and one for ductile fracture. In its non-local version, the model has two main advantages over the models existing in the literature. The first is that the basic elements of the theory (yield function, hardening rule, evolution laws) are not assumed, but are determined as necessary conditions for the existence of solutions in incremental energy minimization. This reduces to a minimum the number of the independent assumptions required to construct the model. The second advantage is that, with appropriate choices of the analytical shape of the cohesive energy, it becomes possible to reproduce, with surprising accuracy, a big variety of observed experimental responses. In all cases, the model provides a description of the entire evolution, from the initial elastic regime to final rupture

Numerical comparison of high-order absorbing boundary conditions and perfectly matched layers for a dispersive one-dimensional medium

High-order absorbing boundary conditions (ABC) and perfectly matched layers (PML) are two powerful methods to numerically solve wave problems in unbounded domains. The aim of the proposed study is to analyze and compare the performance of these methods in the one-dimensional problem governed by the dispersive wave equation. The PMLs proposed in literature for time-harmonic dynamics are applied to time-dependent wave problems, and linear, quadratic and cubic polynomial stretching functions are considered. The resulting PMLs exhibit a double absorbing action: (i) they reduce the amplitude of the incident waves and (ii) they delay the wave propagation. Then the ABC proposed by Givoli and Neta and those proposed by Hagstrom, Mar-Or and Givoli are considered. The former are a reformulation of the Higdon high-order non-reflecting boundary conditions, the latter improve the Higdon conditions and extend them to take into account evanescent waves. The accuracy of the PMLs and ABCs, implemented in a finite element code, is first investigated with respect to the frequency of the incident wave, being it progressive or evanescent. Then the response to a wave train characterized by a broad frequency spectrum, resulting from an impulsive force, is studied. A detailed analysis is performed to detect the influence of the parameters of both the ABCs and the PMLs on the absorption of waves. The performances of PMLs and ABCs are compared, and merits and drawbacks of the two methods are pointed out

A variational approach to gradient plasticity

In this talk, a variational model for gradient plasticity is proposed, which is based on an energy functional sum of a stored elastic bulk energy, a non-convex dissipative plastic energy, and a quadratic non-local term, depending on the gradient of the plastic strain. The basic modelling ingredients are presented in a simple one-dimensional setting, where the key physical aspects of the phenomena can easily be extracted. The evolution laws are deduced by using the mathematical tool of incremental energy minimization, and they are commented, highlighting the main differences and similarities with variational damage models. The typical assumptions of classical plasticity, such as yield condition, hardening rule, consistency condition, and elastic unloading, are obtained as necessary conditions for a minimum. Then, analytical solutions are determined, and attention is focused on the correlations between the convex-concave properties of the plastic energy and the distribution of the deformation field. The issue of solution stability is also addressed. Finally, some numerical results are discussed. First, tensile tests on steel bars and concrete samples are reproduced, and, then, a more complex two-dimensional crystal plasticity is proposed, and the process of microstructures evolution in metals is described by assuming a double-well plastic potential.Non UBCUnreviewedAuthor affiliation: Polytechnic University of MarcheFacult

Phase-field modelling of ductile failure in fiber-reinforced composites

In this talk, a variational model is proposed for the description of ductile failure in composite materials consisting of short strengthening fibers embedded in brittle matrices. The composite is schematized as a mixture of two phases coupled by elastic bonds: a brittle phase and a plastic phase account for matrix and fibers contributions, respectively. Balance and evolution equations are variationally deduced, and the role played by three different internal lengths is discussed. Finally, results of numerical simulations are shown.Non UBCUnreviewedAuthor affiliation: Polytechnic University of MarcheResearche

Dinamica di piastre incoerenti

Il tema principale di questa tesi è la deduzione e lo studio di alcune soluzioni di un sistema di equazioni alle derivate parziali che regola la dinamica delle piastre elettroelastiche lineari incoerenti. Nell'incoerenza risiede l'elemento principale di novità del modello che viene costruito; conviene chiarire subito il significato del termine, limitandosi per semplicità al caso puramente meccanico. Una piastra tipica è un cilindro retto di modesto spessore, di asse z, costituito da un materiale che, se non è isotropo, ha di regola almeno un asse c che assegna l'orientamento locale della risposta in sforzo alla deformazione: ad esempio, il materiale può essere trasversalmente isotropo rispetto alla direzione c, oppure monoclino rispetto ad una giacitura perpendicolare a c. Una piastra è incoerente quando z £ c 6= 0, cioè, quando la geometria d'assieme e la geometria locale della risposta materiale non sono coerenti nel senso specificato. L'esame degli effetti dell'incoerenza in una teoria di piastre è stato intrapreso solo molto di recente ([5, 66]). Questo carattere è assente in tutte le teorie di piastre classiche (Germain-Lagrange [78], Kirchhoff-Love [26, 42], Reissner-Mindlin [47, 45, 68, 69] e loro varianti), così come in teorie più moderne e generali [38, 59], et pour cause: tutte le teorie standard di piastre mirano ad ottenere un problema bidimensionale che abbia la massima semplicità compatibile con l'ottenere le predizioni desiderate senza risolvere il problema tridimensionale corrispondente; invece l'incoerenza rende ogni teoria nella quale sia presente più complessa della corrispondente teoria coerente, tanto che introdurre incoerenza sembra addirittura contraddire la nostra intuizione profonda del comportamento di una piastra sottile. Perchè, allora, studiare piastre incoerenti? Le ragioni sono varie, oltre naturalmente alla mera curiosità. Intanto, una piastra reale puµo ben avere un indesiderato difetto di coerenza, che va rivelato e,possibilmente, quantificato. Poi, dato che una pur modesta incoerenza distrugge uno dei principali pregi di molte teorie coerenti, la separabilità dei comportamenti membranale e fessionale, un attuatore a forma di piastra potrebbe avere maggior capacità di azione se incoerente, un sensore avere una risposta insieme a spettro piµu ampio e a risoluzione più fine. Mentre dispositivi di questo genere non sono ancora stati realizzati, non è difficile immaginare alcuni elementari test di coerenza, quali quelli basati sulla propagazione di onde di cui trattiamo nel Capitolo 5