Showing papers in "International Journal of Solids and Structures in 2018"

On hierarchical honeycombs under out-of-plane crushing

Abstract: Hierarchy has been introduced to honeycomb structures in pursuing ultralight materials with outstanding mechanical properties. Nevertheless, the hierarchical honeycombs under the out-of-plane loads have not been well studied experimentally and analytically for energy absorption to date. This study aimed to apply a special structural hierarchy to the honeycomb by replacing the sides of hexagons with smaller hexagons. The quasi-static test of the hierarchical honeycomb specimen was first conducted experimentally to investigate the crushing behaviours; and then the corresponding finite element (FE) analyses were performed. Finally, the analytical solutions to the mean crushing force and plateau stress were derived based on the simplified super folding element (SSFE) method. It was shown that the experimental data and numerical results agreed well in terms of crushing force versus displacement relation and energy absorption characteristics; and the analytical results were validated by the experimental test. Importantly, the hierarchy could improve the energy absorption; and the increase in the order and number of replacement hexagons could excavate the advantage even further. Specifically, the second order honeycomb characterized by five smaller replacement hexagons at each order can yield a plateau stress 2.63 and 4.16 times higher than the regular honeycomb and the aluminium foam, respectively. While it might lead to global bending, structural hierarchy provides new architectural configurations for developing novel ultralight materials with exceptional energy absorption capacity under out-of-plane loads.

Crack twisting and toughening strategies in Bouligand architectures

Abstract: The Bouligand structure in some arthropods is a hierarchical composite comprised of a helicoidal arrangement of strong fibers in a weak matrix. In this study, we focus on the Bouligand structure present in the dactyl club of the smashing mantis shrimp due to its exceptional capability to withstand repetitive high-energy impact without catastrophic failure. We carry out a combined computational and experimental approach to investigate the high damage resistance of the Bouligand structure through a biomimetic composite material. This is studied by performing specific fracture experiments on the helicoidal composites specimens, where it was found that crack twisting, driven by the fiber architecture, is the main fracture mechanisms. This crack twisting mechanism competes with other alternative mechanisms such as crack branching and delamination, delaying catastrophic failure. The main mechanism of crack twisting is studied through specifically designed specimens in which the crack propagation path is controlled. Further quantification of the toughening mechanisms and crack growth rate is analyzed with analytical and finite element models. The biomimetic helicoidal composites are shown to have improved fracture resistance as the crack twists mainly driven by the increase in crack surface area and fracture mode mixity. Our analysis allowed us to study the effect of crack front shape, stress distribution and energy dissipation mechanisms.

Wave propagation in elastic metamaterial beams and plates with interconnected resonators

Abstract: In this work, new beam and plate metamaterials with interconnected local resonators are proposed. This design promotes the splitting and coupling between transverse and rotational vibration modes of the resonator chain. It produces a particular band structure with two band gaps: a wide band gap opens at the in-phase transverse natural frequency of the resonator chain and a second band gap, with narrower width, appears at higher frequencies. The Timoshenko beam and Mindlin–Reissner plate models are used to compute the band structure as well as the dynamic forced response. A parametric analysis of the band gaps is performed by varying the interconnection properties. The metamaterial plate presents a directional wave propagation pattern due to partial band gaps. In addition, a metamaterial beam manufactured by additive manufacturing is investigated. The experimental results are in agreement with the numerical predictions. Therefore, the proposed concept showed to be promising for metamaterial design aiming at creating singular band gaps with broadband absorption and directional/focalization features.

A cellular metastructure incorporating coupled negative thermal expansion and negative Poisson's ratio

Abstract: Current reported cellular metastructures can either achieve only tailorable thermal expansion or obtain only tunable Poisson's ratio. By contrast, here, we develop a kind of lightweight cellular metastructure which incorporates coupled tailorable thermal expansion and tunable Poisson's ratio. That is a wide range of positive, zero and especially negative values of both thermal expansion and Poisson's ratio can be simultaneously obtained. The ranges and constraints of the geometrical parameters are revealed, and the relative densities are only about 2%, indicating excellent lightweight character. Besides, analytical expressions for coefficient of thermal expansion (CTE) and Poisson's ratio (PR) are theoretically established and numerically simulated. Parameter analysis confirms that the range of tailorable CTE can be enhanced through rationally selecting large values of CTE ratio, first geometrical angle and height ratio. By adjusting the second and third geometrical angles, Poisson's ratio also can be tuned to be large negative, near zero and positive values. Particularly, the metastructure can give paired negative CTE and negative PR. Different combinations of paired characteristics including positive CTE + negative PR, positive CTE + positive PR and negative CTE + positive PR are also flexibly available. Moreover, CTE and PR are found to be highly coupled. To simultaneously obtain specific CTE and PR, design parameters should be selected with consideration of the coupling effect. The results here are expected to contribute feasibility to structures with both temperature and mechanical sensitivities.

Shear-induced anisotropy of granular materials with rolling resistance and particle shape effects

Abstract: The rolling resistance model has been employed in the discrete element modelling in geomechanics, as an alternative computationally efficient approach to capture the resistance of particle rotation due to irregularity in shape. This paper presents a series of 3D DEM simulations of triaxial compression tests on specimens with rolling resistance and non-spherical particles using an in-house code. The non-spherical particle shapes are two kinds of special super-ellipsoids (i.e., superballs and ellipsoids) corresponding to two kinds of typical distortion in shape. A comprehensive comparison between the rolling resistance and particle shape effects on shear-induced fabric variation and anisotropy within granular materials is carried out. The simulations show that the manners in which quantifiers of fabric and anisotropy approach their respective critical state values vary with shear strain levels. Using the rolling resistance model can reproduce the main features of shear-induced fabric variation and anisotropy for most of these fabric measures. However, the effect of particle shape with just slight distortion from sphere can be captured well by the rolling resistance model. Moreover, high shear strengths can be achieved with sufficiently strong rolling resistance, but this is not recommended due to the unrealistic induced fabric. These findings highlight that the rolling resistance model should be carefully used in investigations, especially for micro-macro bridging.

Buckling of quasi-perfect cylindrical shell under axial compression: A combined experimental and numerical investigation

Abstract: Imperfections from manufacturing process can cause a scattered reduction of the load-carrying capacity or buckling load of axially compressed cylindrical shell structures. To isolate the influence of geometric imperfections from other imperfections such as welding, a sub-scaled, integrally manufactured cylindrical shell with small-amplitude geometric imperfection was manufactured, analyzed and tested in this study. A test facility and measurement system (including imperfection measurement and buckling test) were constructed. Finite element (FA) numerical procedure for predicting the buckling load was developed. Results indicate that the buckling load predicted by the FE analysis is very close to that from the test. Knockdown factor (KDF) is discussed with reference to the NASA design document. Furthermore, the influence of pure geometric imperfections including imperfection component and amplitude on the buckling behavior is discussed based on Fourier series method. Some guidance for the dimensional tolerance in manufacturing process relating to the load-carrying capacity of thin-walled structures is provided.

Enhanced Piola–Hencky discrete models for pantographic sheets with pivots without deformation energy: numerics and experiments

Abstract: The problem of the synthesis of second gradient (meta)materials, via architectured microstructures made of micro-lattices, has been solved (Alibert et al., 2003; Seppecher et al., 2011) by choosing ideal pivots as preferred constraints. The obtained homogenized macro-equations (Boutin et al., 2017; Eremeyev et al., 2017) show some pathologies that reflect the exotic behavior of the considered metamaterials, even if they are of interest by themselves (Eremeyev et al., 2017). The theoretical issues that they raise not only represent an intellectual challenge but also means for disclosing potentially interesting new phenomena. To make such disclosure evident, the related technological demand arose, namely, to find an innovative design and production process to construct (Golaszewski et al., 2018), by using additive manufacturing, some pantographic sheets (made in this instance of polyamide but hopefully later also using metals or alloys) whose pivots do twist practically without deformation and with negligible dissipation. Remarkably the specimen could be printed as a monolith and required no post-assembly but only an easily standardized run-in procedure. In this paper, in order to introduce a mathematical description for pantographic sheets with perfect pivots and to avoid to face the aforementioned pathologies, a discrete, finite dimensional, Lagrangian model is formulated. Moreover, in order to include the case in which the beams interconnecting the pivots are long enough to store non negligible bending energy between the closest pairs of pivots, an enhanced Piola–Hencky discrete model is introduced. Two types of nodes are distinguished, the first one interconnects two pantographic fibers, the second one simply interconnects two different segments of the same fiber. The Vietnam long neck peculiar deformed shape experimentally observed in standard extension bias test is obtained with very short computing time, so that the innovative code that has been elaborated can be used as subroutine in more complex computation schemes. A preliminary digital image correlation analysis (Sutton et al., 2009; Hild and Roux, 2012b) is performed and shows that a remarkable agreement between theoretical predictions and experimental evidence can be obtained. This circumstance is easily explained by observing that the numerical code is based on a discrete model directly inspired by the mechanical properties of pantographic sheets and that, therefore, the passages to a continuum model via homogenization (dell’Isola et al., 2016) and then to the subsequent re-discretization, via the introduction of more or less suitable finite elements, are avoided. In our opinion a theory driven formulation of a directly discrete numerical model presents many advantages and it seems suitable for tackling future structural optimization problems.

Circular inhomogeneity with Steigmann–Ogden interface: Local fields, neutrality, and Maxwell's type approximation formula

Abstract: The boundary conditions for the [Steigmann, D.J., Ogden, R.W., 1997. Plain deformations of elastic solids with intrinsic boundary elasticity. Proc. R. Soc. London A 453, 853–877; Steigmann, D.J., Ogden, R.W., 1999. Elastic surface-substrate interactions. Proc. R. Soc. London A 455, 437–474.] model are re-derived for a two dimensional surface using general expression for surface energy that include surface tension. The model treats the interface as a shell of vanishing thickness possessing surface tension as well as membrane and bending stiffness. The two-dimensional plane strain problem of an infinite isotropic elastic domain subjected to the uniform far-field load and containing an isotropic elastic circular inhomogeneity whose interface is described by the Steigmann-Ogden model is solved analytically. Closed-form expressions for all elastic fields in the domain are obtained. Dimensionless parameters that govern the problem are identified. The Maxwell type approximation formula is obtained for the effective plane strain properties of the macroscopically isotropic materials containing multiple inhomogeneities with the Steigmann-Ogden interfaces. The “neutrality” conditions are analyzed. It is demonstrated that while the Steigmann-Ogden model theoretically reduces to the [Gurtin, M.E., Murdoch, A.I., 1975. A continuum theory of elastic material surfaces. Arch. Ration. Mech. Anal. 57, 291–323.; Gurtin, M.E., Murdoch, A.I., 1978. Surface stress in solids. Int. J. Solid. Struct. 14, 431–440.] model when the bending interphase effects are neglected, the two models (for the case of zero surface tension) describe two very different interphase regimes of seven regimes proposed by [Benveniste, Y., Miloh, T., 2001. Imperfect soft and stiff interfaces in two-dimensional elasticity. Mech. Mater. 33, 87–111.].

Imperfections and energy barriers in shell buckling

Abstract: The elastic buckling of shell structures such as spherical shells subject to external pressure and cylindrical shells loaded in axial compression is highly sensitive to imperfections and often catastrophic. Recent studies of spherical shells have provided accurate quantitative results for the relation between the buckling pressure and the amplitude and shape of geometric imperfections and, additionally, quantitative results for the energy barrier that must be overcome to buckle the shell by extraneous loadings or disturbances when it is loaded to pressures below the buckling pressure. Results for the simultaneous interaction of imperfections and energy barriers for spherical shells under external pressure will be presented. Numerical studies for probing forces illustrate their use in determining the buckling energy barrier, and new experimental results on energy barriers obtained by others by probing spherical shells will be discussed and compared with predictions. It will be argued that while imperfections determine the buckling load of a shell, the energy barrier at loads below the buckling load supplies important additional information about the relative safety or precariousness of the shell to additional disturbances. Results for the energy barrier for perfect and imperfect spherical shells under external pressure provide important insights into the shell's robustness, or lack thereof, at pressures below the buckling pressure. In particular, the energy barrier trends provide critical insights into the low knockdown factor usually employed in establishing the design load of unstiffened spherical and cylindrical shells. These design loads are shown to correlate with conventional predictions provided that imperfection amplitudes scale as the shell radius.

Truss-based nonlinear mechanical analysis for origami structures exhibiting bifurcation and limit point instabilities

Abstract: Origami, the art of paper folding, is a technologically transformative art with applications at many length scales from material microstructure design to space deployable structures. The transformation of a two-dimensional fold pattern to a three-dimensional structure makes origami a practical basis for deployability, light-weight materials, and self-actuation. In order to predict the complex motions of origami structures including path traversal of instabilities, accurate and efficient modeling techniques are required. While many approaches consider rigid facets and/or linear approximations to rotations, a truss and hinge finite element method is presented here within a global coordinate system framework to accurately capture the geometric nonlinearities while allowing for small to moderate facet deformation. Accurately capturing these modes of deformation is critical toward understanding the elastic energetic states required for design and analysis of multistable origami structures and mechanical metamaterials. Particular formulation developments that we address to solve origami mechanics problems include formulation of a continuous and differentiable fold angle, strategy for selecting fold path off the flat state, and integration of common numerical approaches important for origami (large rotation formulation, enforcement of periodic boundary conditions for tessellations, arc-length continuation method for solving highly nonlinear loading paths, and a perturbation strategy for handling bifurcations). After formulating this truss finite element method, we verify our modified finite element method on well-studied structures. The waterbomb fold pattern is studied, and the interplay of the stretching and folding energies are considered toward design of a bistable structure that exhibits a fold based snap-through instability. This study is followed by analysis of a cylindrical network of waterbombs (axial periodicity) that exhibits a stretch driven instability. Lastly, a tessellated square twist pattern, exhibiting multiple bifurcations off the flat state is presented that employs all aspects of our numerical method.

Tuning frequency band gaps of tensegrity mass-spring chains with local and global prestress

Abstract: This work studies the acoustic band structure of tensegrity mass-spring chains, and the possibility to tune the dispersion relation of such systems by suitably varying local and global prestress variables. Building on established results of the Bloch–Floquet theory, the paper first investigates the linearized response of chains composed of tensegrity units and lumped masses, which undergo small oscillations around an initial equilibrium state. The stiffness of the units in such a state varies with an internal self-stress induced by prestretching the cables forming the tensegrity units, and the global prestress induced by the application of compression forces to the terminal bases. The given results show that frequency band gaps of monoatomic and biatomic chains can be effectively altered by the fine tuning of local and global prestress parameters, while keeping material properties unchanged. Numerical results on the wave dynamics of chains under moderately large displacements confirm the presence of frequency band gaps of the examined systems in the elastically hardening regime. Novel engineering uses of the examined systems are discussed.

Plastic anisotropy and ductile fracture of bake-hardened AA6013 aluminum sheet

Abstract: The anisotropic plastic flow and ductile fracture of AA6013 aluminum sheet is investigated under quasistatic conditions. The plasticity of the material is probed through uniaxial tension, plane-strain tension and disk-compression experiments, from which the Yld2004-18p non-quadratic 3D anisotropic yield criterion and the combined Swift-Voce hardening model are calibrated. The ductile fracture is characterized with two notched-tension (different notch radii), one center-hole tension and one shear experiment. These experiments cover a wide range of stress triaxialities, while requiring only a universal testing machine to be conducted. Digital Image Correlation is used throughout the experiments to assess the surface strain fields. The predictions of three plasticity models, i.e., von-Mises and Yld2004-18p with constant and with evolving exponents and the corresponding Swift-Voce curves, are compared to the measured force–displacement curves and surface strain histories. These models are then used to probe the stresses, strains, stress triaxiality and Lode angle parameter throughout the loading to fracture. It was found that this hybrid experimental-numerical approach for the fracture strain determination is very sensitive to the constitutive model adopted. As an independent assessment, a microstructure-based estimation of the fracture strains is described. This verified that the von–Mises yield criterion for this AA6013 aluminum sheet provides erroneous estimates of the fracture strains. The most suitable constitutive model is the Yld2004-18p with evolving exponent. Based on these results, the fracture loci are represented by the Oyane, Johnson–Cook and Hosford–Coulomb models.

Three scales asymptotic homogenization and its application to layered hierarchical hard tissues

Abstract: In the present work a novel multiple scales asymptotic homogenization approach is proposed to study the effective properties of hierarchical composites with periodic structure at different length scales. The method is exemplified by solving a linear elastic problem for a composite material with layered hierarchical structure. We recover classical results of two-scale and reiterated homogenization as particular cases of our formulation. The analytical effective coefficients for two phase layered composites with two structural levels of hierarchy are also derived. The method is finally applied to investigate the effective mechanical properties of a single osteon, revealing its practical applicability in the context of biomechanical and engineering applications.

Development of an RVE and its stiffness predictions based on mathematical homogenization theory for short fibre composites

Abstract: In this study an attempt is made to generate the microstructure of short fibre composites through representative volume element (RVE) approach and then analyzed using mathematical theory of homogenization with periodic boundary conditions to estimate the homogenized or effective material properties. An algorithm, based on random sequential adsorption technique (RSA), has been developed to generate the RVE for such materials. The goal of the present study is to demonstrate the methodology to generate RVEs which are effective in predicting the stiffness of the short fibre composites with repetitiveness. For this purpose, RVEs for four different scenarios of fibre orientations have been developed using this technique. These four different scenarios are: Fibres are aligned in a direction; fibres are oriented randomly in one plane; fibres are randomly oriented in one plane and partially random oriented in other plane and finally, fibres are completely random oriented. For each case three to four different fibre volume fractions are studied with five different RVEs for each volume fraction. These four cases presented different material behaviour at macroscale due to random location and orientation of fibres. The effective properties obtained from numerical technique are compared with popular non RVE methods like Halpin–Tsai and Mori–Tanaka methods for the case where fibres are aligned in a direction and were found to be in good agreement. The variation in the predicted properties for a given volume fraction of any of the four cases studied is less than 1%, which indicates the efficacy of the algorithm developed for RVE generations in repetitiveness of predicted effective properties. The four cases studied showed gradual change in macroscopic behaviour from transversely isotropic, with respect to a plane, to a nearly isotropic nature.

Mechanical properties and failure mechanisms of sandwich panels with ultra-lightweight three-dimensional hierarchical lattice cores

Abstract: Mechanical properties and failure mechanisms of sandwich panels with “corrugated-pyramidal” hierarchical lattice cores were investigated through analytical modeling and detailed numerical simulations. This included studying the behavior of hierarchical lattice core material under compression and shearing, as well as investigating the mechanical performance of sandwich panels subjected to in-plane compression and three-point bending. Failure maps were constructed for the hierarchical lattice cores, as well as sandwich panels with hierarchical lattice cores by deriving analytical closed-form expressions for strength for all possible failure modes under each loading. 3D printed samples were manufactured and tested under out-of-plane compression in order to provide limited experimental validation of the study. Our study provides insights into the role of structural hierarchy in tuning the mechanical behavior of sandwich structures, and new opportunities for designing ultra-lightweight lattice cores with optimal performance.

A 3-D model for simulation of weak interface slippage for fracture height containment in shale reservoirs

Abstract: Shale formations often consist of multiple distinct layers with varying rock properties, in-situ stress states, and interface properties between layers. Weak horizontal interfaces often affect fracture height growth and induced complex fracture geometry. In this paper, a fully three-dimensional displacement discontinuity method is developed to investigate slippage of weak horizontal interfaces and understand the effects of the slippage on fracture height growth. Horizontal fracture segments are regarded as weak horizontal interfaces and vertical fractures would either be arrested or step over interfaces. Results indicate that a width jump of the vertical fracture occurs at the crossing position of the horizontal interface, as a result of shear displacement discontinuities along the horizontal fracture segment. The width jump hinders the vertical fracture growth in the height direction, which is regarded as a new mechanism of fracture height containment. Shear displacement discontinuities and width jump increase with the increment of the distance between the center of the vertical fracture and horizontal fracture segment. The larger the width jump, the more difficult the vertical fracture continues to propagate in the height direction, which implies that the vertical fracture tends to be arrested by the interface when the wellbore is far away from the interface.

Nonlinear dynamic analysis and active control of visco-hyperelastic dielectric elastomer membrane

Abstract: Dynamic analysis and active control are important bases for dielectric elastomer (DE) applications. Most of the DE materials exhibit significant viscoelasticity. Although the visco-hyperelastic constitutive relations of DEs have been studied before, the dynamic analysis of the DEs with the consideration of viscoelasticity has rarely been explored. In this study, we lay out the dynamic equations for the visco-hyperelastic DE structures. The Gent hyperelastic model is applied to take into account the strain-stiffening effect of the elastomer. Based on the model, we derive an analytical solution for the dynamic DE under homogeneous in-plane deformation. We show that the model can capture the nonlinear oscillation of the DE and allows us to investigate how the viscoelasticity and strain-stiffening effect influence the resonant frequencies and oscillation amplitudes of the system. Given the nonlinear and viscoelastic nature of the material, its dynamic response could be complicated and deviate from the desired harmonic oscillation pattern. To achieve precise control over the outputs, we employ a PID controller to build a closed-loop feedback control and demonstrate its feasibility to correct most of the undesired outputs such as nonlinear oscillation, beating phenomenon, phase lag and so on.

Optimization of postbuckling behaviour of variable thickness composite panels with variable angle tows: Towards “Buckle-Free” design concept

Abstract: Variable Angle Tow (VAT) laminates that generally exhibit variable stiffness properties not only provide extended design freedom, but also offer beneficial stress distributions. In this paper, the prospect of VAT composite panels with significantly reduced loss of in-plane compressive stiffness in the postbuckled state in comparison with conventional structures, is studied. Specifically, we identify that both thickness and local fiber angle variation are required to effectively define “buckle-free” panels under compression loading. In this work, the postbuckling behaviour of variable thickness VAT composite panels is analyzed using an efficient and robust semi-analytical approach. Most previous works on the postbuckling of VAT panels assume constant thickness. The additional benefits of tailoring thickness variation in the design of VAT composite panels are seldom studied. However, in the process of manufacturing VAT laminates, either by using the conventional Advanced fiber Placement (AFP) machine (tow overlap) or the newly developed Continuous Tow Shearing (CTS) process (tow shrink) thickness build-up is inevitable. The postbuckling optimization for the design of VAT layups is conducted by a two-level framework using lamination parameters as intermediate design variables. The objective is to determine optimal lamination parameters and thickness distributions for maximizing the axial compressive stiffness of VAT laminates that are loaded in the postbuckling regime. The thickness variation due to both manufacturing of VAT laminates and for where it is independent of manufacturing process are considered. In accordance with the first-level optimal postbuckling solutions in terms of lamination parameters, we investigate a practical “buckle-free” VAT panel using a blended layup configuration. This blended VAT panel consists of a piecewise combination of segmental CTS layers and constant-thickness VAT layers. The prospect of taking advantage of a benign combination of stiffness and thickness to improve the overall compressive strength of VAT panels is studied. Finally, the optimal results are analysed to provide insight into the manufacturing of VAT laminates using either the AFP or the CTS process for improved postbuckling stiffness under compression loading.

3D numerical study on fracture process of concrete with different ITZ properties using X-ray computerized tomography

Abstract: A three-dimensional (3D) realistic numerical modelling method is proposed to simulate the fracture process of concrete based on its meso-structure. In the 3D realistic numerical modelling method, CT technology is first applied to capture the microstructure of the concrete as a series of cross-sectional CT images. An improved digital image processing (DIP) technique is then developed to identify and characterize the aggregates and the interfacial transition zones (ITZ) in the CT images. After that, a 3D realistic three-phase structure model of the concrete is reconstructed on the basis of the processed CT images using the vectorized transformation and volume rendering method, which is integrated into a well-established 3D Realistic Failure Process Analysis (RFPA 3D ) code. In this way, the 3D realistic numerical modelling method is developed. It is validated by building a 3D realistic numerical model of the concrete and comparing the results between numerically and experimentally obtained. Finally, using the 3D realistic numerical modelling method, the effects of the ITZ strength on the fracture process of the concrete under uniaxial compression and tension are studied and further clarified. The proposed 3D realistic numerical modelling method provides a new tool to study the fracture mechanism of concrete at the mesoscopic/microscopic levels under complex loading conditions.

Local fields and overall transverse properties of unidirectional composite materials with multiple nanofibers and Steigmann–Ogden interfaces

Abstract: This paper presents the semi-analytical solution for the transverse local fields and overall transverse properties of composite materials with aligned multiple cylindrical nanofibers. The interface between each fiber and the matrix is treated as a material surface described by the Steigmann–Ogden model, which accounts for the effects of surface tension as well as for membrane and bending stiffness of the surface. Assuming a plane strain setting, the problem is formulated in the transverse plane as an infinite elastic matrix with multiple circular inhomogeneities subjected to a uniform far-field load. The expressions for all elastic fields in the composite system are obtained analytically in the form of infinite series expressions. The Maxwell methodology is used to obtain the overall transverse elastic properties. The goal of this work is twofold: (a) to study the influence of the interactions between the inhomogeneities on the local fields and overall transverse properties of the composite system, and (b) to reveal the connection of the Steigmann–Ogden model (with zero surface tension) to a specific uniform interphase layer model. The results presented in this paper demonstrate that for fiber composite materials with medium to high volume fractions, the influence of the interactions can be significant.

New yield criteria for isotropic and textured metallic materials

Abstract: In this paper a new isotropic criterion that describes well yielding of randomly oriented face-centered polycrystalline metallic materials is proposed. The extension of this criterion such as to describe orthotropy is developed using generalized invariants of the stress deviator. This new orthotropic criterion is general and applicable to three-dimensional stress states. The procedure for the identification of the material parameters is outlined. Illustration of the predictive capabilities of the new orthotropic is demonstrated through comparison between the model predictions and data on aluminum sheet samples.

Simulating drop-weight impact and compression after impact tests on composite laminates using conventional shell finite elements

Abstract: Simulating polymer-based composite structures under low-velocity impact and sequencing compression after impact loading, is a complex problem that requires using well-suited constitutive models and defining advanced finite element capabilities. Therefore, developing simplified and efficient, but sufficiently accurate finite element models to solve such problems, is of interest. Here, a finite element modelling strategy is presented for simulating low-velocity impact and compression after impact tests on composite laminates using Abaqus/Explicit software. The strategy is based on using conventional shell elements and cohesive surfaces. The proper out-of-plane structural response is solved by considering surface elements located on the bottom and top faces of the layers. The key parameters requested for defining the models are concisely described and the values selected are well justified. The accuracy of the modelling strategy is proved by simulating monolithic and rectangular laboratory coupons. The results of the simulations reveal good agreement with most of the experimental data reported.

Anisotropic fracture forming limit diagram considering non-directionality of the equi-biaxial fracture strain

Abstract: This paper is concerned with modeling of anisotropic fracture forming limit diagram considering non-directionality of the equi-biaxial fracture strain. A new anisotropic ductile fracture criterion is developed based on the Lou–Huh ductile fracture criterion (Lou et al., 2012). In an attempt to predict the forming severity of advanced high-strength steel (AHSS) sheets, the proposed fracture criterion is converted into a Fracture Forming Limit Diagram (FFLD) and anisotropic fracture locus considering the sheet metal orientation. Tensile tests of the DP980 steel sheet with the thickness of 1.2 mm are conducted using various specimen geometries including pure shear, dog-bone, and flat grooved specimens. With Digital Image Correlation (DIC) method, equivalent plastic strain distribution on the specimen surface is computed until surface crack initiates. The fracture predictability of the proposed fracture criterion is evaluated with the experimental results which cover a wide range of stress states in various loading directions. By comparing fracture strains obtained from the experiments with the ones predicted from the proposed fracture criterion, it is clearly confirmed that the fracture criterion proposed is capable of predicting the equivalent plastic strain at the onset of fracture with great accuracy over a wide range of stress states while keeping non-directionality of the equi-biaxial fracture strain.

A novel positive/negative projection in energy norm for the damage modeling of quasi-brittle solids

Abstract: The asymmetric tensile/compressive material behavior and microcracks closure-reopening (MCR) effects exhibited by quasi-brittle solids are of significant importance to the nonlinear responses of engineering structures under cyclic loading, e.g., earthquake excitations. Based on our previous work (Cervera et al., 1995; Faria et al., 1998; Wu et al., 2006) this work addresses a novel thermodynamically consistent unilateral damage model for concrete. In particular, the positive/negative projection (PNP) of the effective stress tensor and the additive bi-scalar damage constitutive relation are maintained owing to the conceptual simplicity and computational efficiency. It is found that the classical PNP widely adopted in the literature is not optimal for this damage model, since the resulting stiffness is not always of major symmetry. Consequently, a well-defined free energy potential does not exist in general cases and the model cannot be cast into the framework of thermodynamics with internal variables. Furthermore, the damage induced anisotropy cannot be captured, exhibiting excessive lateral deformations under uniaxial tension. To overcome the above issues, a novel PNP, variationally interpreted as the closest point projection of the effective stress in energy norm, is proposed with closed-form solution. With the novel PNP, the secant stiffness tensor of the proposed unilateral damage model always possesses major symmetry and exhibits orthotropic behavior under uniaxial tension and mixed tension/compression. The corresponding thermodynamics framework is then given, resulting in an energy release rate based rounded-Rankine type damage criterion appropriate for tensile failure in quasi-brittle solids. Several numerical examples of single-point verifications and benchmark tests are presented. It is demonstrated that the proposed model is capable of characterizing localized failure of concrete under proportional and non-proportional static loading, as well as the MCR effects under seismic cyclic loading.

Low-velocity impact predictions of composite laminates using a continuum shell based modeling approach part A: Impact study

Abstract: This paper introduces a shell based finite element (FE) model for predicting the impact response and dominant failure mechanisms of fiber reinforced polymer matrix composites subject to low-velocity impact. The model utilizes Enhanced Schapery Theory (EST) for capturing the matrix non-linearity due to micro cracking as well as macroscopic intra-lamina failure, that is, matrix cracking and fiber rupture in the 1–2 failure plane of a lamina. Discrete cohesive elements (DCZM) are utilized for capturing the inter-lamina failure initiation and propagation. The intra- and inter-lamina damage and failure models are implemented as user subroutines in the commercial finite element solver, ABAQUS Explicit. The model is compared against low-velocity impact experimental data. High fidelity non-destructive inspection (NDI) methods are used to quantify the impact damage for a detailed comparison to the model predictions. The modeling technique shows excellent agreement with experimental results, both for impact response and damage evolution.

Modelling of the mechanical behavior of polyurethane foams by means of micromechanical characterization and computational homogenization

Abstract: A modelling strategy based on micromechanical characterization and computational homogenization has been developed to determine the mechanical behavior of rigid, closed-cell PU foams taking into account the microstructural features. The macroscopic mechanical properties of the foam were obtained by means of the finite element simulation of a representative volume element of the PU foam. The foam microstructure in the model was obtained from the Laguerre tessellation of the space from a random close-packed sphere distribution, which followed the cell size distribution of the foam. The faces and edges of the polyhedra representing the cell walls and struts and were discretized using shell and beam elements, respectively, and their geometric features (shape, thickness, etc.) were carefully measured by means of X-ray computed tomography. Finally, the elastic modulus and yield strength of the solid polyurethane in the foam were measured using instrumented nanoindentation. The numerical simulations of the mechanical behavior of the foam in compression were in agreement with the experimental results of the elastic modulus and of the stress at the onset of instability, which was triggered by the localization of damage in a section of the microstructure by the elasto-plastic buckling of the struts.

Experimental fracture characterisation of an anisotropic magnesium alloy sheet in proportional and non-proportional loading conditions

Abstract: A comprehensive experimental investigation was performed to characterize the fracture behaviour of a rare-earth magnesium alloy sheet, ZEK100-O, under both proportional and non-proportional loading conditions. This material possesses severe plastic anisotropy and tension-compression asymmetry that evolve with plastic deformation and is an excellent candidate to experimentally evaluate phenomenological fracture modelling strategies. Different types of specimen geometries were fabricated in different orientations with respect to the rolling direction of the sheet to reveal the anisotropic fracture response of the alloy. Moreover, three different types of plane-strain tension tests, namely, v-bend, butterfly, and Nakazima dome tests were conducted and compared in terms of their applicability for fracture characterization of sheet materials. To visualize directional dependency of the fracture response of the magnesium alloy, experimental fracture loci for different orientations were constructed. Furthermore, non-proportional tests were performed in which abrupt changes in stress state were imposed to study the role of the loading history on fracture behaviour of the alloy. The non-proportional tests entailed pre-straining the material in uniaxial and equi-biaxial tension up to a prescribed plastic work level, followed by extreme strain path changes to plane-strain tension and shear states. Non-proportional deformations with such severe strain path variations have not been reported in the literature for materials with complex anisotropic behaviour such as ZEK100-O. The results of which have enabled the direct experimental evaluation of phenomenological damage models without performing an inverse calibration from finite element simulations. Based on the results of the non-proportional tests, it was shown that simple damage indicators were unable to describe the influence of severe changes in the strain path on fracture.

Nonreciprocal phenomenon in nonlinear elastic wave metamaterials with continuous properties

Abstract: The nonreciprocal phenomenon appears in nonlinear acoustic metamaterial which are composed of a linear phononic crystal and a nonlinear layer. Based on the nonlinear characteristics, the acoustic waves can pass in one direction and are prohibited in reverse. Naturally, people will wonder whether the nonreciprocal phenomenon can be found in nonlinear elastic wave metamaterial. Because of the coupling of the multi-displacements, this problem becomes more complicated but interesting for waves in solid. Motivated by this enlightenment, we will discuss the band gap and transmission properties of elastic waves in both linear and nonlinear periodic systems. The fundamental and double frequency waves can be generated by the interaction between SH waves and the nonlinearity of materials. According to continuity conditions of incident SH wave, the transfer matrices are derived. The stop band and transmission coefficient are obtained by Bloch's law. This research is expected to be helpful to develop new elastic wave metamaterial devices.

Stress-point method for stabilizing zero-energy modes in non-ordinary state-based peridynamics

Abstract: Non-ordinary state–based peridynamics is a promising continuum mechanics theory that combines non-local dynamics with conventional material models. Within this theory, the correspondence principle can be invoked to compute deformation gradients from the computed displacement fields. However, correspondence based models are prone to a zero-energy mode. This paper proposes the use of stress points to resolve this issue in the peridynamic family with nearest-neighbor discretizations. Each particle horizon is assigned with stress points at which derivatives of field variables are computed. The method is first demonstrated in a simple 1D problem and is compared with the analytical solution and other control methods. 2D and 3D examples are compared with the finite-element method. Zero-energy modes are shown to be completely damped in all cases. The computation efficiency of the explicit stress-point based peridynamic model is analyzed in the end.

Design of ultra-thin shell structures in the stochastic post-buckling range using Bayesian machine learning and optimization

Abstract: A data-driven computational framework combining Bayesian regression for imperfection-sensitive quantities of interest, uncertainty quantification and multi-objective optimization is developed for the design of complex structures. The framework is used to design ultra-thin carbon fiber deployable shells subjected to two bending conditions. Significant increases in the ultimate buckling loads are shown to be possible, with potential gains on the order of 100% as compared to a previously proposed design. The key to this result is the existence of a large load reserve capability after the initial bifurcation point and well into the post-buckling range that can be effectively explored by the data-driven approach. The computational strategy here presented is general and can be applied to different problems in structural and materials design, with the potential of finding relevant designs within high-dimensional spaces.