Proceedings of the 8th International Symposium on Solid Mechanics

Smart materials are inspired in natural characteristics being characterized by a multiphysics coupling that confer an adaptive behavior. This remarkable characteristic is motivating the creation of systems and structures with the ability to change properties due to environmental changes which makes possible sensing and actuating in different perspectives. This review paper presents a general overview of smart materials, discussing fundamentals and applications. Shape memory alloys and piezoelectric materials are of special interest. Earthquake-resistant structures; origami-inspired systems and structures; morphing structures; energy harvesting devices are some applications discussed.

In light of stringent environmental regulations, engineers and designers are under increasing pressure to reduce the structural weight of conventional aircraft to mitigate greenhouse gas emissions. The advent of electric-powered and hydrogen-powered aircraft concepts demands the incorporation of heavy battery blocks, large fuel tanks, or cells, which, in turn, makes high-performance lightweight structures indispensable for enhancing the operational range of future aerial and terrestrial vehicles. Metal-fiber-reinforced polymer hybrid structures (MP-HS) stand as potential solutions to meet these demands. These hybrid structures exhibit distinct solid interfaces characterized by sharp gradients in material properties. The inherent disparities between metals and polymer/composites pose substantial engineering challenges, demanding innovative and materials-friendly manufacturing approaches. Presently, the state-of-the-art production of MP-HS, such as the hybridization of metals with composites through semi-automated lamination techniques, is time-consuming and often unable to accommodate complex geometries, particularly those featuring internal 3D features. The integration of metal and fiber-reinforced polymer additive manufacturing (AM) with energy-efficient friction-based joining technologies holds the promise of overcoming these limitations. This chapter explores recent developments in the AM and joining of metal-fiber-reinforced thermoplastic hybrid structures with an emphasis on aircraft materials.

The combination of structural optimization with the orientation of the reinforcement paths in plates makes it possible to obtain excellent mechanical properties. Added to this, the exploration of the anisotropy of these materials is an effective tool for designing components produced in composites. This optimization can be performed by using a curve that represents the path of the fibers. In these cases, one of the factors that influences the efficiency of the optimization algorithm is the initial placement of the fibers. In this context, with the aim of investigating the influence of the initial directions on the result of the objective function, the optimization of B-splines was carried out in the work, which represented carbon fibers inserted in epoxy resin matrix plates. Thus, seeking to reduce flexibility, three distinct structures with different boundary conditions were optimized using linear programming. In each of them, rectilinear reinforcements were initially implemented and optimized from four different initial directions. The plate thickness, cross-sectional area of reinforcements, and number of reinforcements are identical. From the final results, the difference in flexibility and morphology of the reinforcements in each initial placement was noticeable. The final structures point to two factors for obtaining lower flexibility. The positioning of the ends of the reinforcements close to the supports and the point of application of the force obtain better results. Furthermore, when the distribution of filaments has a distribution that reduces the free areas of reinforcements in the matrices, it tends to reduce flexibility as well.

This study proposes to address the optimization challenge of minimizing compliance subjected to a volume and a natural frequency constraint for solid mechanics problems, employing the Topology Optimization of Binary Structures (TOBS) method as the optimization solver. The finite element method solves the linear elasticity equations and the eigenvalue problems considering a free vibration analysis. The modified SIMP model is proposed as the material interpolation model for obtaining compliance and natural frequency sensitivities. Modal Assurance Criterion (MAC)-based mode-tracking is implemented to observe the first three natural frequencies in each case, focusing on identifying modes crossing. Two bidimensional problems were studied to verify the algorithm’s efficacy - a biclamped beam and a tower subjected to a horizontal load. Different values of natural frequency constraints are examined to assess the final topology and modes crossing. Numerical results demonstrate that the TOBS method is well-suited for addressing the current problem, offering optimized layouts for structures exposed to vibrations while maintaining natural frequencies within specified levels established in the optimization problem.

The increasing concentration of carbon dioxide (CO\(_2\)) in the atmosphere has spurred the need for effective Carbon Capture, Storage, and Utilization (CCSU) technologies. Supercritical CO\(_2\) (sCO\(_2\)) has emerged as a promising working fluid in CCSU applications due to its compactness and efficiency in transportation and power generation cycles. However, the highly nonlinear behavior of sCO\(_2\) near the critical point requires further research to enhance numerical design models. In this context, this study focuses on the fluid-structural interaction (FSI) in the analysis of centrifugal compressors used in CCSU applications. The use of sCO\(_2\) as a working fluid enables the construction of more compact and efficient components, but it also poses challenges related to aerodynamic loads resulting from FSI. Structural failure modes, modal analysis, and resonance conditions are critical to ensure safe and reliable operation of sCO\(_2\)-based compressors. Three case studies are presented in this work, including a literature-based compressor and two cases with application in CCSU. Static and modal structural analyses are conducted, and new geometries for the compressors are proposed based on the findings. The results reveal that while aerodynamic loads had minimal influence on the static behavior of the literature-based and the first-stage compressors, they were a significant source of load and required detailed treatment in the case of the fourth-stage compressor.

This work analyzes the effective strength of porous solids with orthotropic matrix material, obeying Hill’s criterion and containing periodically distributed parallel cylindrical voids. The study considers both analytical and numerical evaluations. Analyzes are restricted to transversely isotropic materials under axisymmetric loading. In the theoretical side, a closed-form yield criterion is developed by means of a static analysis, which is expected to provide a lower bound to the overall strength. The analytical homogenized model consists of a simple parabolic function depending on the void volume fraction, the matrix material anisotropic strength properties, the mean lateral and Hill’s equivalent stresses. Theoretical results are compared with finite element calculations considering a cubic unit cell with a centered cylindrical void. Distinct material porosity and anisotropy levels as well as a wide range of stress triaxialities are considered. It is therefore possible to assess the combined effects of the material porosity and anisotropy on its effective macroscopic strength. Comparisons with the Benzerga-Besson upper bound are also carried out. Overall, the present model provides more conservative predictions in comparison with the Benzerga-Besson approach. Both analytical models coincide in the cases of longitudinal or purely hydrostatic loading. Comparison with the numerical results shows that the present model provides reasonably good predictions when compared to the finite element simulations, higher differences (up to \(20\%\)) being observed for lower porosities and higher stress triaxialities. The main outcome of this work is a closed-form yield function proving fairly accurate predictions to engineering applications, in which anisotropic porous solids with cylindrical voids are dealt with.

Exponentially graded viscoelastic solids constitute an important class of advanced composite materials. Such materials exhibit physical, chemical or both properties enriched in order to satisfy specifics applications. This work presents an investigation of the linear elastic and viscoelastic behaviour of three-dimensional isotropic Functionally Graded Materials (FGMs) using the Boundary Element Method (BEM). The present work considers here a special FGM which presents an exponential gradient of the elastic modulus along one, two, or three directions. The material gradation is modelled using a fundamental solution available in the literature which is readily incorporated into the traditional boundary integral kernels. To include the viscoelastic behaviour of the material into the BEM formulation an approach based on the differential constitutive relations for linear viscoelasticity employing rheological solids models has been used. Practical problems involving displacement and fracture mechanics parameters have been presented herein assuming creep behaviour of the Kelvin-Voigt and Boltzmann materials. Useful informations regarding displacement, traction and stress intensity factors are discussed.

The mechanical strength of porous material is investigated using virtual tests by a computational homogenization method based on three-dimensional representative volume elements (RVE). The RVE consists of an elastic-perfectly plastic metal matrix, that obeys the von Mises criterion, having randomly distributed non-overlapping spherical voids. By using mixed boundary conditions and varying certain loading parameters, it is possible to obtain different macroscopic stress triaxialities. The macroscopic stress tensor is considered as the mean of its microscopic counterpart, taken for a stabilized RVE response in an asymptotic state. An in-house Abaqus post-processing tool developed in Python was used to examine the asymptotic behavior of porous microstructures. The analyzes are performed with different void volumes, multiple and single pores, and different boundary conditions. The Gurson and Gurson-Tvergaard-Needleman (GTN) models were compared with the results of the computational homogenization. The best GTN model that satisfies the homogenized numerical results is achieved among yield criterion parameters from various references. An examination of the shear macroscopic stresses nullity is also performed, demonstrating that it can produce significant values in specific scenarios.

The possibilities of influencing the behavior of propagating waves using the appropriate choice of materials is a field of interest in engineering. Traditional materials have very limited control of sound waves. Thus, new artificial composite materials with good vibration absorbing properties are needed to solve this problem. This paper investigates the band structure and waves modes of a two-dimensional (2-D) Sierpinski fractal phononic crystals (PnC). These PnC consist of various lattice inclusions of one and two materials with large impedance mismatch in a rubber matrix. The inclusions present square and circular cross sections and are concentrically aligned. The chosen materials allow elastic waves to be forbidden from propagation within certain frequency bands, the so-called band gaps or stop bands. Structures with fractal distributions and higher stages favor the appearance of several absolute gaps and with larger bandwidth. The band structure and wave mode shapes are calculated by the Finite Element (FE) and Plane Wave Expansion (PWE) methods, considering the Bloch-Floquet periodic conditions.

This study presents a computational analysis of the dynamic behavior of a simply supported beam subjected to a moving mass and corresponding load that travels along its entire length. It aims to understand the behavior of the structure and to determine transversal response of the structure. Consideration of the dynamic behavior of a structure allows to evaluate the results with greater reliability, since it brings the model closer to reality, as the actual masses and corresponding loads vary with time and, therefore, produce dynamic effects. Here, a discretized simply supported beam model was developed, based on the Finite Element Method, using numerical integration by Newmark’s Method for the solution of ordinary differential equations and obtaining the deflections of the structure in the time domain, to evaluate its behavior due to moving masses and loads. The analysis is made in different velocities, applying optimization technique to obtain the maximum transversal deflections of the structure. The main objective is to apply the results obtained with the method to obtain deflections due to moving loads in structures such as bridges and viaducts, among other applications, and to obtain the critical velocities, where the greatest deflections of the structure are promoted.

Micro-perforated chamber mufflers are effective sound absorbers that reduce sound levels by offering high acoustic resistance and low mass reactance due to their micro-perforations. When arranged periodically, these mufflers exhibit enhanced efficiency in sound absorption. The transmission loss of sound waves in both mufflers and periodic acoustic devices are closely related. Specific frequency bands can generate the Bragg and local resonance effects, producing stop bands where waves cannot propagate. Dispersion curves can be calculated to identify these bands using the Floquet-Bloch theorem. This study utilized the Transfer Matrix method to analyze a periodic micro-perforated chamber muffler with three unit cells. Porosity variations are analyzed, and sound pressure level and transmission loss are calculated and presented. Additionally, a parametric optimization is conducted using differential evolution method, leading to a significant improvement in the efficiency of the originally proposed micro-perforated chamber muffler. The results indicate that transmission loss is not directly proportional to the number of micro-holes, emphasizing the importance of studying porosity in muffler design. The diameter ratio directly influences transmission loss, with the best value observed at a 0.8 mm micro-hole diameter.

In stochastic structural mechanics it is possible to associate uncertainties with material properties, geometry, and external loading, whereas response estimates are found in the displacement, stress, strain, frequency, and phase difference fields, among others. This paper presents the stochastic formulation of elliptic differential equations associated with the beam bending problem and explores the propagation of uncertainty from the perspective of the Neumann-Monte Carlo (NMC) asymptotic complexity methodology and the Spectral Stochastic Finite Element Method (SSFEM). The variational solution is studied for the classical Euler-Bernoulli theory (EBT) and for theories involving Timoshenko shear deformation (TBT) and Levinson-Bickford (LBT). The numerical results present the expected value, variance and covariance function for the displacement field of those three beam theories. Observations on the relationship between beam length and height are included in the comments for cases in which the initial variability is associated with the random coefficients of the stiffness matrix.

Deformation of polymers, due to their molecular structures, as well as their motion and relaxation mechanisms, are greatly influenced by temperature and mechanical load history. This work describes and simulates a structural phase-field model for polytetrafluorethylene (PTFE) polymer. The constitutive multimechanism model used considers an isothermal non-linear elastoviscoplastic model, which can represent both elastic molecular interactions and viscoplastic flow from polymer segments. The material parameters for these complex rheological models are determined through a genetic algorithm, which adjusts the curves obtained from simulated models to match the stress-strain experiments available in literature. The stress-strain curves, up to the point of rupture, are then compared with experimental results.

The extremely rapid development of new metamaterials opens the way to many interesting engineering applications. However, the complexity of their microstructure makes the direct analysis of full-scale real systems made of metamaterials almost prohibitive. The two-scale asymptotic homogenization represents a promising tool for the design and optimization of such systems. In this paper, we will discuss the role of homogenization in the development of practical applications of metamaterials. Two examples will be presented: the optimization of auxetic materials for impact protection and the design of a system for energy localization that includes locally resonant materials. A significant computational advantage is obtained by substituting the metamaterial with an equivalent homogenized continuum.