Geometric Large Deformation Research Articles

On energy mechanism of rate-dependent failure mode evolution in plain weave composite

The intricate failure modes and the yet unclear rate dependency of carbon fiber reinforced plain weave composite materials pose a challenge to mechanics researchers. This study establishes an energy-based evolution mechanism for the compressive failure modes of plain weave composite materials as the strain rate varies. This mechanism illustrates how the rate dependency of failure modes arises from the competitive relationship between strain potential energy and deformation kinetic energy. At low loading rates, the specimen exhibits a progressive crushing failure mode characterized by low peak stress and significant geometric deformation. As the loading strain rate increases, the energy required for this geometric deformation also increases. When the energy expenditure surpasses that needed to elevate the stress level of the specimen, it transitions to an instantaneous failure mode with high peak stress. In this mode, the specimen fractures into multiple small fragments immediately upon failure, lacking the large geometric deformations observed at lower rates. Through calculating this energy mechanism, a transition strain rate of 180 s−1 was determined for both failure modes. The accuracy of this mechanism was further verified by tests conducted near the critical strain rate. The energy-based evolution mechanism for failure modes provides a simplified and concise framework for simplifying complex models of composite material failures.

Nonlinear Deflection Characteristics of Weakly Bonded Curved Composite Structure Under Hygro-Thermo-Mechanical Loadings

A customized MATLAB algorithm is developed for internally separated laminated composite panels experiencing large geometric deformations. The algorithm is designed to calculate nonlinear deflection responses under the effect of combined hygro-thermo-mechanical (HTM) loading. The hygrothermal (HT) load on the panel is in-plane, whereas the mechanical load acts upon the structure transversely. The analysis has adopted various kinematic theories and finite element (FE) techniques to determine the deformations computationally. The deflection behavior of the composite is characterized through a macro mechanical model considering the nonlinearity in geometry with and without accounting for the stretching effects across the panel thickness. Additionally, the changes in composite properties due to the environment and/or loadings are adopted to achieve a realistic response, preserving continuity assumptions between the individual layers of the weakly bonded structure. Moreover, various numerical examples are examined through different models to illustrate the influences of environmental factors and design-specific parameters on the flexural strength of weakly bonded structures. The findings strongly emphasize the necessity of employing diverse kinematic models when examining laminated structures, both with and without HT loading, while also acknowledging the potential for debonding.

Assessing geometrical uncertainties in geological interface models using Markov chain Monte Carlo sampling via abstract graph

Uncertainty assessment is a common requirement in 3D modeling applications. The Markov chain Monte-Carlo (MCMC) method is a practical way to generate multiple realizations of 3D models to evaluate model uncertainty. However, when probing high-dimensional target distributions related to the detailed geometry of 3D geological interfaces, the generating 3D models by existing MCMC methods always suffer from the presence of artifacts in large geometrical deformation that modeling deformed geometries in stochastic perturbation, which limits their effectiveness and efficiency. This paper presents an abstract graph-based MCMC method for the uncertainty assessment of 3D geological interfaces. An abstract graph is used to represent the reasonable shape of the geological interface. In proposing new candidate 3D models via the MCMC iterations, the 3D models are perturbed such that the energy function measuring the distortion of the abstract graph is minimized in a least-squares sense. This can preserve the plausible geometry of the 3D models against high perturbations and provide artifact-free 3D models as candidates for MCMC sampling. The resulting MCMC iterations enable the drawing of probable realizations of 3D models while maintaining a high acceptance rate in probing the complicated target distributions of 3D geological interface models. The proposed method was applied to the assessment of uncertainties in three regional faults in the Jiaodong Peninsula, eastern China. The uncertainty assessment was carried out based on a complex probability distribution with consideration of geological-geophysical observations and prior knowledge of fault geometry. The results show that the proposed MCMC method could reasonably locate the uncertainties in free-form fault models defined by thousands of constraints. And the abstract graph-based MCMC method can sample highly-perturbed and geometrically plausible 3D models in high-resolution, which is crucial to the effectiveness and efficiency of the geometrical uncertainty assessment.

Self-equilibrium, stability, and accuracy degradation of imperfect prismatic tensegrities with additional cable nets

Prismatic tensegrity is an attractive structure due to the unique advantages of self-equilibrium, lightweight, small compression volume, specific super stability, ease of deployment, and functional extension. However, it is subject to geometric large deformation when suffering from imperfect factors like manufacturing errors, thermal deformation, slips of tensioning knots, and mechanical relaxation of members, which will eventually reduce the accuracy and reliability. We develop a kind of prismatic tensegrities with additional cable nets for space deployable constructions. For the specific requirements of high accuracy and high reliability, we fully consider the influence of imperfect factors, and explore their environment- and time-dependent characteristics from the view of self-equilibrium, stability, and accuracy. First, a preload optimization method is established for high-accuracy determination of the shape and uniform distribution of preload. Then, a high-fault-tolerance accuracy estimation method is proposed for accuracy degradation research, for which nonlinear force density equations and time-dependent tangential stiffness matrix are formulated to obtain deformation shapes and stability criteria beforehand. Eventually, the characteristics of the prismatic tensegrities with additional cable nets, under the influence of imperfect factors, are fully revealed and forecasted. The methods and some conclusions of this study can also be applied to other complex tensegrities or prestressed pin-jointed systems.

A novel series of mechanical metamaterials with sign-changing coefficient of thermal expansion and their parameter analysis

Mechanical metamaterials show great application prospects in many fields such as aerospace, biomedical engineering, energy and transportation. The development of mechanical metamaterials with multiple peculiar properties is an important prerequisite for the development of intelligent sensors with excellent performance and the realization of multifunctional integration of structures. In this paper, a series of novel mechanical metamaterials are designed by adding rhomboid negative thermal expansion units into re-entrant hexagonal honeycombs, which have different signs of the coefficient of thermal expansion when the temperature rises or falls, and the analytical formula of their equivalent thermal expansion coefficient are derived. Parameter analysis and numerical simulations show that the metamaterial can realize the sign-changing properties of thermal expansion coefficient without entering the range of large geometric deformation under specific constituting materials and geometric parameters. In addition, this design idea is extended to three-dimensional form.

An analytical formulation to extract the capacity curve of steel structures

Among the methods for evaluating the nonlinear performance of structures, pushover analysis is an appropriate alternative instead of direct time history analysis. To accurately extract the capacity curve of a structure, according to the loading regulations/protocols such as FEMA-356 and ATC-40, lateral loads are incrementally applied to the structure in experimental tests until the structural failure occurs. Because of the cost and time-consuming nature of experimental tests, proposing mathematical/analytical methods could be the appropriate tools to predict the capacity curves of a system. The present study proposes a new method to find the capacity curves of cantilever steel beams based on mathematical formulations, structural analysis, and material properties. The reason to select a simple beam in this study is to shed more light on the unknown aspects of the system’s behavior. Therefore, in this research, the effect of axial load is ignored to clarify the nonlinear behavior of complicated systems such as frames. The strains, stresses, and other responses corresponding to large geometric deformations have been extracted in two cases with and without strain hardening by considering changes in the behavior of materials. The proposed method has been verified using the finite-element method with Abaqus software. The results indicate that the proposed method has acceptable accuracy and could be applied in the pushover analysis of steel structures.

Turbulent-degraded image restoration via improved principal component analysis method

It is challenging to removing atmospheric turbulence-induced geometric distortion and blurry degradation simultaneously. The improved principal component analysis (i-PCA) method is proposed in this paper. The image set selection strategy is implemented by the Euclidean distance between each sub-module image and its corresponding reference image to remove large geometric deformations and blurs directly. The eigenvector representing the original image data is uniquely determined by combining the maximum correlation with the original image and the maximum variance of the corresponding principal component for resolving the direction issue of the eigenvector. The algorithm is tested using synthetic and real turbulence-distorted images. The experimental results show that the i-PCA method proposed can effectively alleviate the atmospheric turbulence effects and significantly enhance visual quality, promising for its application to turbulence-distorted image.

An analytic solution for form finding of GFRP elastic gridshells during lifting construction

The GFRP elastic gridshell is a type of spatial structure composed of long continuous hollow GFRP members and has been used in large-span roof structures. The elastic gridshell achieves its shape as the result of elastic deformations during the construction process of lifting or pushing. The shape-forming mechanism of such structures is very complicated due to significant geometric non-linearity. This research aims to propose analytic formulations to estimate the structural features of the GFRP elastic gridshell under lifting construction. An analytical theory, considering the large geometric deformations, is first presented for analyzing single lifted member. Based on the given theory and an iteration process, a form-finding method is further proposed for predicting the deformation, nodal forces and bending moment of biaxial symmetrical GFRP elastic gridshells during the lifting construction. The form-finding method is realized on the Matlab platform and a case study is carried out. Finite element analysis is further conducted to validate the accuracy and practicability of the proposed method. Results show that, the analytic theory is highly accurate for the analysis of lifted members, and the proposed form-finding method is applicable in predicting the structural behaviors of GFRP elastic gridshells for which the lifting construction is adopted.

Supersonic aerodynamic piezoelectric energy harvesting performance of functionally graded beams

In this study, a novel multifunctional nonlinear composite structure consisting of functionally graded beams and piezoelectric sheets is proposed. This structure exhibits excellent supersonic aerodynamic energy harvesting performance under heating conditions. Referring to the geometric large deformation theory, the electromechanical coupling dynamics equation of the whole structure under supersonic aerodynamic force and the thermal environment is established by Hamilton’s principle. The energy harvesting effect of piezoelectric sheets is simulated by Runge–Kutta algorithm. The correlation parameters of the length-to-fine ratio, gradient index, resistance, airflow speed, and temperature were compared and analyzed. Results show that this new multifunctional nonlinear composite structure can achieve the ideal energy harvesting effect and proper adjustment of parameters can improve the energy harvesting effect under the thermal environment. This study provides new ideas for related research on nonlinear energy harvesting under heating conditions.

Optimization design of chiral hexagonal honeycombs with prescribed elastic properties under large deformation

Flexible chiral honeycomb cores generally exhibit nonlinear elastic properties due to large geometric deformation. The effective elastic moduli and Poisson’s ratio typically vary with an increase in deformation. Here, the size and shape optimization of the chiral hexagonal honeycombs was performed to keep the Young’s moduli and Poisson's ratio unchanged under large deformations. The size of the honeycomb unit cell and the position coordinates of the key points were defined simultaneously as design variables. The equivalent Young's modulus and Poisson’s ratio of chiral honeycombs were calculated through geometric nonlinear analysis. The objective was to minimize the allowable tolerance between the prescribed and actual properties within the range of the target strain. A genetic algorithm was then adopted. The optimal results demonstrate that the chiral honeycombs can maintain effective elastic properties that do not vary under large deformation. These results are meaningful to morphing aircraft designs.

Comparative study of wind resistance of a 2D stack of featured ocean containers and a 3D forty feet unit

ABSTRACTPreviously the effect of configuration of containers as well as wind angle of attack on the wind resistance of a container ship was studied by using simple blocks to represent the containers. However, in field observations, the authors testified large geometric deformations in statistically significant numbers of containers. Using ANSYS CFX, the outer side of the stacking configuration is modelled as a thin plate comprising several bays and tiers. Frictional resistance of the plate with corrugations and damages is compared to that of a flat plate. Moreover, using unsteady RANS with K-ω, SST turbulence model, a computer model of a single featured 3D unit is studied and compared with the simple block. In this case, viscous pressure drag is significant and results for simple block and real container are surprisingly different. In summary, differences in wind resistance between simple blocks and real containers are considerable and must be taken into account in future studies.

Nonlinear thermal free vibration frequency analysis of delaminated shell panel using FEM

The current research reported the thermal free vibration characteristics of the debonded composite shell structure considering the large geometrical deformation. The delaminated composite panel structural model is derived using two different higher-order polynomial kinematics. The nonlinear structural geometry has been modeled via Green-Lagrange relations in conjunction with temperature loading. The separation between the adjacent layers of the composite has been incurred through a sub-laminate approach and the corresponding displacement continuity imposed at the boundaries (laminated and delaminated). Moreover, the isoparametric Lagrangian type of element (eighty-one and ninety degrees of freedom) is adopted for the discretization of the physical shell structure. The nonlinear governing equation of motion of heated shell (healthy and debonded) structure derived using Hamilton principle and the nonlinear frequency responses computed using the direct iterative technique for the computational purpose. The solution (numerical) stability and the accuracy have been established as a priori by solving a series of examples available in the literature. The conclusions regarding the model applicability for debonded (size, location and position) structural analysis represented with or without temperature effect.

Effective elastic properties of flexible chiral honeycomb cores including geometrically nonlinear effects

Flexible chiral honeycomb cores generally exhibit nonlinear elastic properties in response to large geometric deformation, which are suited for the design of morphing aerospace structures. However, owing to their complex structure, it is standard to replace the actual core structure with a homogenized core material presenting reasonably equivalent elastic properties in an effort to increase the speed and efficiency of analyzing the mechanical properties of chiral honeycomb sandwich structures. As such, a convenient and efficient method is required to evaluate the effective elastic properties of flexible chiral honeycomb cores under conditions of large deformation. The present work develops an analytical expression for the effective elastic modulus based on a deformable cantilever beam under large deformation. Firstly, Euler–Bernoulli beam theory and micropolar theory are used to analyze the deformation characteristics of chiral honeycombs, and to calculate the effective elastic modulus under small deformation. On that basis, the expression for the effective elastic modulus is improved by including the stretching deformation of the chiral honeycomb structure for a unit cell under conditions of large deformation. The effective elastic moduli calculated by the respective analytical expressions are compared with the results of finite element analysis. The results indicate that the analytical expression obtained under consideration of the geometric nonlinearity is more suitable than the linear expressions for flexible chiral honeycomb cores under conditions of high strain and low elastic modulus.

Adhesion of carbon nanotubes on elastic substrates with finite thickness

How carbon nanotubes (CNTs) interact with substrates is fundamental for understanding their physical properties. In existing theoretical and modeling studies, the substrates are considered to be rigid with semi-infinite thickness. In this work, the effects of finite substrate thickness and elasticity are analyzed theoretically and numerically for free boundary conditions. Based on the energy-variational approach, considering the interfacial van der Waals interactions and bending strain energies stored in CNTs and substrates, the governing equations and boundary conditions are derived analytically. The theoretical predictions are in reasonable agreement with the results of molecular dynamics simulations. When the substrate is sufficiently thick, the results of the present theoretical model are entirely consistent with previous models for the infinite-thickness substrate. However, for relatively thin substrates, the effect of substrate thickness is significant due to the geometric large deformation. Three stable adhesive states (initial non-adhesive, partially adhesive, and fully wrapping states) can be achieved, dependent on the substrate thickness, the number of CNT walls, and the interfacial adhesion work. The stability of adhesive configurations is explored by analyzing the energy variations corresponding to the adhesive deformation. We show that there exist several modes of energy variations, depending on the adhesion work and the substrate-CNT bending stiffness ratio, which exhibit linear and nonlinear influences, respectively. Our results could serve as guidelines to design CNT-on-substrate systems.

Effect of temperature on the mechanical behaviours of a single-ply weave-reinforced shape memory polymer composite

Single-ply weave-reinforced shape memory polymer composites (SpWR_SMPCs) are promising materials for deployable space structures because they have high deformability, stiffness and strength and exhibit variable mechanical properties at different external temperatures. Thus, understanding their sensitivity to temperature has been a significant concern for better application. This paper presents comprehensive experimental investigations of temperature effects on the mechanical behaviours of a recently developed SpWR_SMPC. With the aid of newly modified compressive and shear test fixtures, the mechanical behaviours dissimilar to those of laminated composites were experimentally investigated: below the glass transition temperature (Tg), the composite was in a solid state, and the modulus relationship was observed as tension > compression > flexural > shear; however, above Tg, the relationship changed significantly due to the transition to a rubbery state and the obvious existence of weft skew. During tension and compression, a large geometric deformation was easily exhibited owing to the weave microstructure. All the mechanical properties showed decreasing trends with the rise in temperature, and the most decline was shown in the resin-dominated compressive and shear properties. Based on the test data, Correia's empirical formula was validated to characterize the thermo-mechanical behaviours as an explicit function of temperature. In general, the present work provides basic observations and comprehensive test guidelines for understanding the effects of temperature on the mechanical properties of SpWR_SMPCs.

Efficient and Robust Direct Image Registration Based on Joint Geometric and Photometric Lie Algebra.

This paper considers the joint geometric and photometric image registration problem. The inverse compositional (IC) algorithm and the efficient second-order minimization (ESM) algorithm are two typical efficient methods applied to the geometric registration problem. Their efficiency stems from the utilization of the group structure of geometric transformations. To allow for photometric variations, the dual IC algorithm (DIC) proposed by Bartoli performs joint geometric and photometric image registration by extending the IC algorithm. The group structures of both geometric and photometric transformations are exploited. Despite the robustness to large photometric variations, DIC is vulnerable to large geometric deformations. The ESM algorithm is extended by Silveira et al. to address photometric variations. In their approach, the photometric transformations are modeled in Euclidean space. Their approach is robust to relatively large geometric and photometric transformations; however, it is not efficient for large photometric variations. We propose a new efficient and robust image registration method by exploiting the non-Euclidean Lie group structure of joint geometric and photometric transformations for both grayscale and color images. The image registration is formulated as a nonlinear least squares problem. In our method, the geometric and photometric transformations are jointly parameterized by their corresponding Lie algebras. Based on this parameterization approach, the second-order approximation strategy of ESM is employed to optimize the joint geometric and photometric parameters. The error function in the nonlinear least squares problem is approximated by a second-order Taylor expansion with respect to joint geometric and photometric parameters without computing the Hessian matrix. For further efficiency, independent convergence criteria for geometric and photometric parameters are used in the iterative optimization process. The superiority of our proposed method over the previous methods, in terms of efficiency, accuracy, and robustness, is demonstrated through extensive experiments on synthetic and real data.

Localization in anisotropic elastoplastic micropolar media: Application to fiber reinforced composites

In this paper, an anisotropic elastoplastic constitutive model is formulated for fiber reinforced composites, undergoing large geometric deformation. The composite material is modeled as a micropolar continuum, which unlike a classical or a Cauchy continuum, takes into account the higher order fiber bending and twisting modes of deformation. In micropolar theory, the rotational degree of freedom is independent of the displacement field. This is utilized to express the microrotation tensor that represents the rotation of the fibers. An anisotropic micropolar yield criterion is introduced by extending Hill’s criterion in classical elastoplasticity and including couple-stresses. The geometric and materially nonlinear theoretical model is derived. The corresponding updated Lagrangian (UL) finite element formulation is discussed. In literature, micropolar theory has been applied to problems associated with localized deformation, where classical theories fail to capture this phenomenon due to the loss of ellipticity of the governing equations. These previous analyses have been done on isotropic micropolar media, and in order to initiate the onset of localization, a softening relationship between the equivalent stress and strain has been introduced. Since the introduction of material softening into the constitutive relation has been a topic of contention in the field of continuum mechanics, it is shown to be unnecessary. Instead, localization is induced due to geometric and material nonlinearity, along with misalignment of the principal material directions with respect to the dominant loading directions that introduce axial-shear coupling. In fiber reinforced composites, localization occurring from compressive loading is representative of fiber kink banding, which is associated with a snap-back behavior in the macroscopic stress-strain response.

Template Matching for Wide-Baseline Panoramic Images from a Vehicle-Borne Multi-Camera Rig

Automatic detection and locating of objects such as poles, traffic signs, and building corners in street scenes captured from a mobile mapping system has many applications. Template matching is a technique that could automatically recognise the counterparts or correspondents of an object from multi-view images. In this study, we aim at finding correspondents of an object from wide baseline panoramic images with large geometric deformations from sphere projection and significant systematic errors from multi-camera rig geometry. Firstly, we deduce the camera model and epipolar model of a multi-camera rig system. Then, epipolar errors are analysed to determine the search area for pixelwise matching. A low-cost laser scanner is optionally used to constrain the depth of an object. Lastly, several classic feature descriptors are introduced to template matching and evaluated on the multi-view panoramic image dataset. We propose a template matching method combining a fast variation of a scale-invariant feature transform (SIFT) descriptor. Our method experimentally achieved the best performance in terms of accuracy and efficiency comparing to other feature descriptors and the most recent robust template matching methods.

Highly Sensitive Two-Axis Bending Sensor Based on Arc-Induced Long Period Fiber Grating in Dual Side-Hole Fiber

A highly sensitive two-axis bending sensor based on long period fiber grating (LPFG) in a dual side-hole fiber (DSHF) is presented and experimentally investigated. The LPFG is fabricated by periodically collapsing a piece of DSHF with automatic arc discharge technology. The existence of the two air holes in the DSHF makes the cladding modes, regardless of the polarization state, concentrate in the area perpendicular to the connection of the two holes. Such a feature leads to quite different bending responses at the directions perpendicular and parallel to the connection of the air holes, which makes the DSHF-based LPFG suitable for two-axis bending measurement. The bending sensitivity of the LPFG are 21.03 nm/m -1 and 15.77 dB/m -1 at the orthogonal directions, respectively. Besides, compared with the general arc-induced LPFGs in solid fibers, the size of the DSHF-based LPFG is effectively reduced because the periodic air hole collapse in the DSHF causes a large geometric deformation of the fiber core and increases coupling coefficient between the core and cladding modes. The sensing characteristics of strain, polarization, surrounding refractive index, and temperature are also investigated in our experiment.

Analysis Method of Stiffness and Load Capacity of Euler Spring with High Static Stiffness and Low Dynamic Stiffness

A large number of studies have shown that nonlinear passive control devices have good vibration attenuation and isolation effect. And vibration isolation systems with nonlinear stiffness have more advantages than linear systems. The paper addresses the stiffness and load capacity design problem of Euler springs with varying cross-sections. Firstly, in order to analyze nonlinear behavior of curved beams due to large geometric deformations, a set of first-order differential equations are established, which can be easily solved by numerical integration. Secondly, a curved beam is taken for example to compare analytical results calculated by using the first-order differential equations and ANSYS simulation results. Then the influence of geometric parameters of curved beams with varying cross-sections on structural stiffness and load capacity is investigated by using ANSYS. Finally, a design strategy for stiffness and load capacity of curved beams is summed up.