Analysis of nonlinear phenomena in heterogeneous materials by means of homogenization and multiscale techniques

Abstract

Over the past decade, scientific and industrial communities have shared their expertise to improve mechanical and structural design favoring the exploration and development of new technologies, materials and ad-vanced modeling methods with the aim to design structures with the highest structural performances. The most promising materials used in many advanced engineering applications are fiber- or particle-rein-forced composite materials. Specifically, materials with periodically or randomly distributed inclusions embedded in a soft matrix offer excel-lent mechanical properties with respect to traditional materials (for in-stance, the capability to undergo large deformations). Recent applica-tions of these innovative materials are advanced reinforced materials in the tire industry, nanostructured materials, high-performance structural components, advanced additive manufactured materials in the form of bio-inspired, functional or metamaterials, artificial muscles, tunable vi-bration dampers, magnetic actuators, energy-harvesting devices when these materials exhibit magneto- or electro-mechanical properties. To-day the scientific community recognizes that, to develop new advanced materials capable of satisfying increasingly restrictive criteria, it is vital fully understanding the relationship between the macroscopic behavior of a material, and its microstructure. Composite materials are charac-terized by complex microstructures and they are commonly subjected also to complex loadings, therefore their macroscopic response can be evaluated by adopting advanced strategies of micro-macro bridging, such as numerical homogenization and multiscale techniques. The aim of this thesis is to provide theoretical and numerical methods able to model the mechanical response of heterogeneous materials (fiber- or particle-reinforced composite materials) in a large deformation context predicting the failure in terms of loss of stability considering also the interaction between microfractures and contact. In the past literature, several theories have been proposed on this topic, but they are preva-lently limited to the analysis of microscopic and macroscopic instabili-ties for not damaged microstructures, whereas the problem of interac-tion between different microscopic failure modes in composite materi-als subjected to large deformations in a multiscale context still has not been investigated in-depth and it represents the main aspect of novelty of the present thesis. The thesis starts with a literature review on the previously announced topic. Then, the basic hypotheses of the numerical homogenization strategy are given together with a review of the most recurring mul-tiscale strategies in the modeling of the behavior of advanced composite materials following a classification based on the type of coupling be-tween the microscopic and the macroscopic levels. In addition, a theo-retical non-linear analysis of the homogenized response of periodic composite solids subjected to macroscopically uniform strains is given by including the effects of instabilities occurring at microscopic levels and the interaction between microfractures and buckling instabilities. Subsequently, the numerical results obtained were reported and dis-cussed. Firstly, the interaction between microfractures and buckling instabili-ties in unidirectional fiber-reinforced composite materials was investi-gated by means of the nonlinear homogenization theory. In such mate-rials, the investigated interaction may lead to a strong decrease in the compressive strength of the composite material because buckling causes a large increase in energy release rate at the tips of preexisting cracks favoring crack propagation or interface debonding. Thus, mi-crocracked composite materials characterized by hyperelastic constitu-ents and subjected to macrostrain-driven loading paths were firstly in-vestigated giving a theoretical formulation of instability and bifurcation phenomena. A quasi-static finite-strain continuum rate approach in a variational setting has been developed including contact and frictionless sliding effects. It worth noting that, the above developments show that non-standard self-contact terms must be included in the analysis for an accurate prediction of microscopic failure; these terms are usually ne-glected when contact is modelled in the framework of cohesive inter-face constitutive laws. The influence of the above-mentioned non-standard contributions on the instability and bifurcation critical loads in defected fiber-reinforced composites can be estimated in light of the results which will be presented in this thesis. Thus, the role of non-standard crack self-contact rate contributions to the stability and non-bifurcation conditions was pointed out by means of comparisons with simplified formulations and it was clearly shown that these contribu-tions have a notable role in an accurate prediction of the real failure behavior of the composite solid. Secondly, two multiscale modeling strategies have been adopted to an-alyze the microstructural instability in locally periodic fiber-reinforced composite materials subjected to general loading conditions in a large deformation context. The first strategy is a semiconcurrent multiscale method consisting in the derivation of the macroscopic constitutive re-sponse of the composite structure together with a microscopic stability analysis through a two-way computational homogenization scheme. The second approach is a novel hybrid hierarchical/concurrent mul-tiscale approach able to combine the advantages inherent in the use of hierarchical and concurrent approaches and based on a two-level do-main decomposition; such a method allows to replace the computation-ally onerous procedure of extracting the homogenized constitutive law for each time step through solving a BVP in each Gauss point by means of a macro-stress/macro-strain database obtained in a pre-processed step. The viability and accuracy of the proposed multiscale approaches in the context of the microscopic stability analysis in defected compo-site materials have been appropriately evaluated through comparisons with reference direct numerical simulations, by which the ability of the second approach in capturing the exact critical load factor and the boundary layer effects has been highlighted. Finally, the novel hybrid multiscale strategy has been implemented also to predict the mechanical behavior of nacre-like composite material in a large deformation context with the purpose to design a human body protective bio-inspired material. Therefore, varying the main micro-structural geometrical parameters (platelets aspect ratio and stiff-phase volume fraction), a comprehensive parametric analysis was performed analyzing the penetration resistance and flexibility by means of an in-dentation test and a three-point bending test, respectively. A material performance metric, incorporating the performance requirements of penetration resistance and flexibility in one parameter and called pro-tecto-flexibility, was defined to investigate the role of microstructural parameters in an integrated measure. The results have been revealed that advantageous microstructured configurations can be used for the design and further optimization of the nacre-like composite material.