A propagating fluid driven fracture in a rock mass is expected to interact with geological interfaces on a wide variety of length scales. The vertical growth of hydraulic fractures in layered rocks ...is of pivotal importance for the successful stimulation in reservoir development. In this study, 2D discrete element modeling is used to investigate the influence of the stiffness and toughness ratio, as well as stress contrast between layers on the hydraulic fracture height growth. In particular, the ultimate goal is to better understand mechanisms of the fracture height containment by contrasts of different rock properties and to quantitatively determine which parameters provide a stronger influence. In addition, the analysis is performed in the context of hydraulic fracture regimes, whereby the dominant dissipation mechanism in the system can either be associated with fracture toughness or viscous fluid flow. As a starting point, we investigated the propagation of a plane strain hydraulic fracture from a low stiffness layer to a high stiffness layer and vice versa, while keeping the stress constant. The influence of stress on hydraulic fracture propagation in layered rocks is investigated afterwards. The numerical results demonstrate that the hydraulic fracture can either directly pass through the geological interface, be arrested at the interface, or stop before reaching the interface. The interface itself is assumed to be perfectly bonded, therefore no slippage is considered. Ability of the hydraulic fracture to approach the interface is first determined by the elastic modulus ratio of the two adjacent layers. Once reached the interface, the further growth is then affected by the toughness ratio between the layers. After that, if the fracture crosses the interface, then it is affected by the stress contrast. The propagation regime has an important influence on the fracture propagation in layered rocks. If the propagation regime is closer to the viscosity dominated, the hydraulic fracture is likely to cross the interface. In contrast, it is more difficult for a fracture to cross the barrier if the propagation regime is near the toughness dominated. A map of fracture crossing behavior versus propagation regime and contrast in properties has been constructed, that can be used to quantify strength of mechanical barriers and to deduce hydraulic fracture height growth behavior for various scenarios.
Shape-morphing finds widespread utility, from the deployment of small stents and large solar sails to actuation and propulsion in soft robotics. Origami structures provide a template for ...shape-morphing, but rules for designing and folding the structures are challenging to integrate into broad and versatile design tools. Here, we develop a sequential two-stage optimization framework to approximate a general surface by a deployable origami structure. The optimization is performed over the space of all possible rigidly and flat-foldable quadrilateral mesh origami. So, the origami structures produced by our framework come with desirable engineering properties: they can be easily manufactured on a flat reference sheet, deployed to their target state by a controlled folding motion, then to a compact folded state in applications involving storage and portability. The attainable surfaces demonstrated include those with modest but diverse curvatures and unprecedented ones with sharp ridges. The framework provides not only a tool to design various deployable and retractable surfaces in engineering and architecture, but also a route to optimizing other properties and functionality.
•An inverse design framework to approximate surfaces by deployable origami.•Easy manufacture and controlled deployment for origami.•Wide adaptation to demands for programming functionality using origami.
A ductile fracture criterion is newly proposed to model fracture behavior of sheet metals for nucleation, growth and shear coalescence of voids during plastic deformation. In the new ductile fracture ...criterion, void nucleation is described as a function of the equivalent plastic strain, void growth is a function of the stress triaxiality and void coalescence is controlled by the normalized maximal shear stress. The new ductile fracture criterion is applied to construct a fracture forming limit diagram (FFLD) of a dual phase steel sheets of DP780 (1.0t). The FFLD is approximated using both the reverse engineering method and circle grid analysis (CGA) since DP780 fails with slight thickness reduction from the analysis of the fracture surface. Predicted FFLDs are compared to experimental results to validate the performance of the new criterion in the intermediate stress triaxiality between 1/3 and 2/3. The new criterion is also applied to construct the fracture locus of Al 2024-T351 (Bao and Wierzbicki, 2004) to validate the performance of the new criterion in the low and negative stress triaxiality. The fracture locus constructed by the new criterion are close to the experimental data points for all these two materials in a wide stress range from the uniaxial compression to the balanced biaxial tension. The new ductile fracture criterion is recommended to be utilized in finite element analysis to predict the onset of ductile fracture of sheet metals.
We investigate the complex band structure and forced response of flexural waves propagating in an elastic metamaterial thick plate. Mindlin-Reissner thick plate theory is considered. We study the ...influence of periodic arrays of spring-mass resonators attached to the surface of a homogeneous thick plate on the formation of Bragg-type and locally resonant band gaps. The plane wave expansion and extended plane wave expansion approaches are used to compute the complex band structure and wave shapes of the metamaterial thick plate with attached spring-mass resonators. An experimental analysis is conducted with a 3D-printed metamaterial plate with resonators. Modal shapes, forced response and band structure are computed by finite element and wave finite element methods. Analytical, numerical and experimental results present good agreement.
This work represents the first step towards the application of machine learning techniques in the prediction of statistical design allowables of composite laminates. Building on data generated ...analytically, four machine algorithms (XGBoost, Random Forests, Gaussian Processes and Artificial Neural Networks) are used to predict the notched strength of composite laminates and their statistical distribution, associated to the uncertainty related to the material properties and geometrical features. This work focuses not only on the so-called Legacy Quad Laminates (0°/90°/±45°), typically used in the design of composite aerostructures, but also on the newer concept of double-double (or double-angle ply) laminates. Very good representations of the design space, translating in low generalization relative errors of around ±10%, and very accurate representations of the distributions of notched strengths around single design points and corresponding B-basis allowables are obtained. All machine learning algorithms, with the exception of the Random Forests, show very good performances, with Gaussian Processes outperforming the others for very small number of data points while Artificial Neural Networks have better performance for larger training sets. This work serves as basis for the prediction of first-ply failure, ultimate strength and failure mode of composite specimens based on non-linear finite element simulations, providing further reduction of the computational time required to virtually obtain the design allowables for composite laminates.
•A 2D elastic metamaterial is designed using compliant amplification mechanisms.•The unit cell mechanism is topologically optimized to obtain an ultrawide band gap.•Numerical and experimental ...frequency responses match very well.•Ultrawide gaps are experimentally shown for longitudinal and transverse excitations.•Largest normalized bandwidth (181%) is attained among 2D designs in the literature.
The aim of this study is to design a two-dimensional solid structure with embedded inertial amplification mechanisms that shows an ultrawide stop band (band gap) at low frequencies. First of all, a unique compliant inertial amplification mechanism is suggested. The compliant (flexure) hinge connections are designed and the topology of the beams in the unit cell mechanism are optimized to achieve the maximum possible stop band width. Then, a two-dimensional periodic structure is formed by using this topologically optimized inertial amplification mechanism. Thereafter, the formed periodic structure is manufactured. Experimental and finite element analyses show that an ultrawide stop band between 29 Hz and 590 Hz is obtained for both longitudinal and transverse excitations. This outcome reveals a phononic gap whose upper and lower limits have a ratio that exceeds 20 (i.e., arithmetic mean normalized bandwidth of 181% or geometric mean normalized bandwidth of 429%). This much bandwidth has not been achieved in the literature for two dimensions, so far.
The shear resistance of 3D printed periodic auxetic chiral mechanical metamaterial was quantified via a picture-frame apparatus. The experimental set-up allowed the accurate measurement of the ...effective shear modulus of the material. Also, a rigid-rod-rotational spring model shows that the effective shear modulus of the material is directly related to the chiral geometry and the rotational rigidity of the center joints and the corner joints in the chiral cell. To facilitate practical design, design guidelines were developed through an integrated analytical, numerical and experimental approach. The influences of the chiral geometry and the joint rigidity on the shear resistance of the periodic auxetic chiral mechanical metamaterial were quantified. The design guidelines were verified by systematic finite element (FE) simulations.
A generalized micropolar bond-based Peridynamic model with shear deformability for linear and non-linear problems is proposed. The analytical implicit formulation is derived from the definition of a ...specific microelastic energy function for micropolar nonlocal lattices, giving particular attention to numerical implementation aspects of the model. We investigate the effectiveness of this formulation, empathizing the importance of considering particle’s rotations in enriched bond-based peridynamic models with arbitrary Poisson’s ratios. Numerical analyses show that a microelastic energy function dependent on a shear deformation measure in which rotational degrees of freedom of the particles are not included, leads to a model not capable to describe properly the elastic behavior of isotropic solids subjected to non-homogeneous deformation fields. Moreover two novel deformation-based failure criteria for micropolar peridynamics accounting for bond shear deformation, associated or not with the corresponding stretch of the ligament, are proposed. A deep investigation is carryied out on the direction dependency of the failure response of the lattice, considering different horizon/grid spacing ratios. In this way the maximum errors are estimated and the effective initial yield domains corresponding to the failure criteria presented are identified in two dimensional principal s1−s2 and generalized s−γ deformations space.
In this paper, we discuss various formats of gradient elasticity and their performance in static and dynamic applications. Gradient elasticity theories provide extensions of the classical equations ...of elasticity with additional higher-order spatial derivatives of strains, stresses and/or accelerations. We focus on the versatile class of gradient elasticity theories whereby the higher-order terms are the Laplacian of the corresponding lower-order terms. One of the challenges of formulating gradient elasticity theories is to keep the number of additional constitutive parameters to a minimum. We start with discussing the general Mindlin theory, that in its most general form has 903 constitutive elastic parameters but which were reduced by Mindlin to three independent material length scales. Further simplifications are often possible. In particular, the Aifantis theory has only one additional parameter in statics and opens up a whole new field of analytical and numerical solution procedures. We also address how this can be extended to dynamics. An overview of length scale identification and quantification procedures is given. Finite element implementations of the most commonly used versions of gradient elasticity are discussed together with the variationally consistent boundary conditions. Details are provided for particular formats of gradient elasticity that can be implemented with simple, linear finite element shape functions. New numerical results show the removal of singularities in statics and dynamics, as well as the size-dependent mechanical response predicted by gradient elasticity.
•A benchmark of cylindrical shell for investigating the effect to KDF from pure geometric imperfections is provided.•The Fourier series method is compared with the scatter points method for ...computation efficiency and prediction accuracy.•Guidance in dimensional tolerance is given for maximizing the load-carry capacity of cylindrical shells in manufacturing.
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.
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