Large Deformation Research Articles

Effect of whey protein on the formation, structure and gastrointestinal breakdown of quinoa flour-based composite gels

Whole grain flour has captured increasing attention due to its health benefits. Herein, the quinoa flour-based composite gels were fabricated by heating quinoa flour dispersions containing 0-7 w/w% whey protein isolate (WPI). The thermal properties and gel formation of the dispersions were determined, along with the large deformation and fracture properties, microstructure, and molecular reorganization of the resulting gels. Protein hydrolysis, solid loss, glucose release and microstructural changes were monitored to characterize the gastrointestinal breakdown of the gels. Results showed that quinoa starch was gelatinized at 60-70 °C. Upon heating, quinoa starch was segregated into microparticles of ∼ 3 μm, which aggregated into the starch phase, whereas protein aggregates filled the gap of the starch gel network. A bicontinuous structure was formed with increasing WPI concentration to 7 w/w%. Meanwhile, the storage modulus, gel hardness and fracture stress of the gels increased by 5-8 times. The addition of WPI inhibited gel disintegration during in vitro digestion. However, intestinal glucose release was not delayed because of the phase-separated structure of the gels. With increasing WPI concentration, larger protein aggregates survived after 5 min of intestinal digestion, demonstrating that the enhanced protein network was the main contributor slowing down gel disintegration during in vitro digestion. This work would promote the development of quinoa flour-based products with controlled digestion.

Simplified inverse distance weighting-immersed boundary method for simulation of fluid-structure interaction

When simulating fluid-structure interaction (FSI) problems involving moving objects, the implicit inverse distance weighting-immersed boundary method (IDW-IBM) developed by Du et al. [1] has to construct a large square correlation matrix and solve its inversion at each time step. In this work, a simplified inverse distance weighting-immersed boundary method (SIDW-IBM) is proposed to eliminate the intrinsic limitations in the original implicit IDW-IBM. Through error analysis using Taylor series expansion, a second order approximation can be derived, which allows us to approximate the large square correlation matrix into a diagonal matrix; thereby, we proposed the SIDW-IBM based on this second order approximation to explicitly evaluate the velocity corrections, where the needs to assemble the large correlation matrix and inverse it are circumvented. Owing to the fact that the inverse distance weighting interpolation removes the limitations in the Dirac delta function, the proposed SIDW-IBM has been successfully implemented on the non-uniform meshes to further improve the computational efficiency. The proposed SIDW-IBM is integrated with the reconstructed lattice Boltzmann flux solver (RLBFS) [2] to simulate some classic incompressible viscous flows, including flow past an in-line oscillating cylinder, flow past a heaving airfoil, and flow past a three-dimensional flexible plate. The good agreement between the present results and reference data demonstrates the capability and feasibility of the SIDW-IBM for simulating FSI problems with moving boundaries and large deformations.

Design and analysis of hundred-meter wind turbine blade trailing edge based on finite element method (FEM)

Abstract The trailing edge region of composite wind turbine blades usually has a large deformation under wind load and the accidents caused by the damage of blade trailing edge accounts for a large proportion among blade accidents. With the development of large blade size, higher requirements are put forward for the stability of wind turbine blade trailing edge. Therefore, the trailing edge region is critical in the design of blade. A detailed study of the design and analysis for wind turbine blade trailing edge region was carried out in which the structure stability was regarded as the key. The influence of auxiliary spar cap and auxiliary spar web on the stiffness distribution and stability of the trailing edge were studied based on focus and finite element method (FEM). The respiratory effect of different structures due to deformation were analyzed and compared. The results showed that the structure of the auxiliary spar cap and auxiliary spar web can significantly increase stiffness, stability and decrease respiratory deformation at the trailing edge of blade compared to the traditional three webs structure. The structure of auxiliary spar and auxiliary spar web is the best design scheme for hundred-meter composite blade trailing edge.

Mechanism-based and data-driven approach to developing the constitutive model of viscoelastic elastomers

Constitutive modeling of viscoelastic elastomers has been an active field for decades. In this work, we develop a mechanism-based and data-driven method to develop constitutive models of viscoelastic elastomers under large deformation. Based on the theory of finite deformation viscoelasticity, the feature of strain energy density function is utilized when we design the machine learning architecture, which allows for fast generation of qualified artificial data to train artificial neural networks (ANNs). According to the typical microstructures of elastomers, three groups of ANNs are established to determine the strain energy density functions of the hyperelastic and viscous polymer networks, which are further tested by experimental data of our own and those in the literature. The machine learning architecture also allows for flexible expansion of the ANN database to consider newly-developed elastomers. The developed constitutive model of the material automatically satisfies the laws of thermodynamics and can be easily implemented in finite element analysis for more complex structures and loading conditions. The developed numerical and experimental framework provides an efficient paradigm for constitutive modeling of viscoelastic elastomers.

A data-driven approach to analyze bubble deformation in turbulence

Bubble deformation and breakup from turbulence is present in many engineering applications and in nature, yet the physical mechanisms still remain poorly understood. Depending on the local turbulence intensity or Weber number, a bubble may either deform without breakup, suffer a violent breakup, or exhibit a resonant behavior, where the turbulent eddies excite the bubble's natural frequencies. Recent studies have used spherical harmonic decomposition to analyze bubble interaction with turbulence, quantifying the deformation energy of each eigenmode. However, this approach is only applicable for small levels of deformation (linear regime), while the bubble shape remains close to a sphere. In the present work, we present a novel data-driven approach combining large deformation diffeomorphic metric mapping and proper orthogonal decomposition, which is more robust for large deformations. The method is tested on a set of validation cases and applied to turbulent bubble deformation cases obtained from direct numerical simulations data.

Nonlinear elasticity tailoring and failure mode manipulation of functionally graded honeycombs under large deformation

Design of lattice metamaterials with tailored mechanical properties at a relatively higher (macro) length scale by architecting lower (micro) length scale geometric and material configurations leads to achieving unprecedented mechanical properties for fulfilling advanced multi-functional structural demands. In the design space of innovative microstructural configurations, we propose a novel class of lattice metamaterials with cell walls made of optimally designed functionally graded intrinsic materials. Under different modes of remotely applied mechanical stresses, two different intuitive architectures of functional gradations for the intrinsic cell wall materials are proposed. The large-deformation nonlinear lattices result in broadband modulation of effective stiffness, and an unprecedented manipulation capability of failure modes and corresponding strengths covering ductile and brittle types depending on architected material gradation. For estimating the nonlinear elasticity and microstructural stresses as a measure of failure mode for the proposed functionally graded lattices undergoing large deformation, a multi-scale mechanics-based semi-analytical framework is developed. Geometrically nonlinear functionally graded beams with generalized material gradation, integrated with unit cell architectures, are analyzed through iterative variational energy principle-based Ritz approach. Based on the developed physically insightful computational framework, effective nonlinear elastic properties and failure modes of the functionally graded honeycomb lattices are tailored as a function of the intrinsic material gradation at the lower length scale. The proposed novel class of lattices with optimally designed functionally graded intrinsic materials and coupled unit cell architectures would open up innovative avenues for designing advanced multi-functional engineering structures and mechanical systems.

An accurate and locking-free geometric exact beam formulation on the special orthogonal group SO(3)

An accurate and locking-free geometric exact beam formulation (GEBF) on the special orthogonal group SO(3) is developed for slender beams with large deformations and large rotations. Due to the nonlinear nature of the spatial rotations, the classical GEBFs usually have a non-constant mass matrix and complex expressions of inertia forces; meanwhile, the singularity and locking issues are also key matters of concern. Aiming at resolving these drawbacks, two main contributions are achieved in the present work. First, the angular velocity is independently interpolated, resulting in a constant mass matrix and explicitly representable inertial forces, which can offer significant advantages for efficient dynamic simulations. Second, inspired by the assumed natural strain method in shell theory, the stretch-shear strain is interpolated to obtain simplified and locking-free elastic forces, which is a new attempt to alleviate the locking problems for the GEBFs. In addition, the special orthogonal group SO(3) is utilized for updating incremental rotation vectors to eliminate singularities, and objective strain measurement is achieved by employing relative rotation vector interpolation. The effectiveness and superiority of the developed low-order and high-order elements are demonstrated through numerical simulations of standard benchmark examples. The present work contributes to the advancement of accurate and reliable formulation for slender beams; the constant mass matrix, the locking-free characteristics, and the elegant form of the formulation make it particularly suitable for multibody dynamic analysis.

Development of Johnson-Cook-Distinct Lattice Spring Model and its application in projectile penetration into metal targets

Projectile penetration into metal targets plays an important role in modern protective structure engineering, damage assessment in terrorist attacks, and car clash accident analysis, etc. The penetration process of metal target has been characterized by large deformation, high temperature, high pressure, and dynamic damage, which can be classified as a continuous-discontinuous dynamical process. To capture the dynamic responses of metal materials subjected to high-speed penetration, Johnson-Cook model has been implemented in a continuum-discrete model, namely, Distinct Lattice Spring Model (DLSM). This is achieved by redefining the constitutive model in DLSM, with plasticity hardening (plastic strain effects), strain rate, temperature, damage evolution, equation of state, etc., being taken into account, thus developing a new numerical model called JC-DLSM model. This model is validated through studying Taylor rod high-speed impact experiments, thin metal plate penetration experiments, and projectile impact experiments on titanium alloy targets. Good agreement between numerical modelling and experimental data has been achieved for all cases considered, thereby demonstrating the capability of JC-DLSM to reproduce the damage characteristics and ballistic limits of metals under high-speed impact/penetration. Then, the impacts of projectile shape, metal target surface configuration on the characteristics of penetration damage patterns have been investigated. This contributes to a better understanding of the damage mechanisms of metal targets upon penetration or impact, facilitating the computational means for analysing and optimizing the penetration resistance of protective engineering structures.

The superior ballistic performance of highly stretchable and flexible double-face knitted fabrics (DFKF): An experimental investigation

When the protective and protected systems are detached, the former can be allowed to absorb the kinetic energy of the impacting projectile through large deformation without considering the back face signature of the latter. This paper presents a novel double-face knitted fabric (DFKF) designed for this very impacting scenario. Shooting tests equipped with high-speed camera were used to characterize the ballistic performance with the impact velocities ranging from 100∼450 m/s. The results showed that the ballistic limits (Vbl) of DFKF are approximately triple and double that of its counterpart UD and plain fabrics, respectively. For mass-normalized metrics, the specific energy absorption (SEA) is 250% and 350% greater than the UD and plain fabrics at their corresponding Vbls. The quasi-static tests showed that the DFKF displayed greater resilience, crease recovery properties, and flexibility, which also made it an especially better candidate than UD and plain weaves for the design of umbrella surface cloth. It was also found that DFKF is dependent on yarn count and the incorporation of spandex. A prototype anti-ballistic umbrella is manufactured using DFKF made of 200D multi-filament yarn. The ballistic performance is also sensitive to the impact site when the umbrella is subjected to impact.

Modelling nematic liquid crystal in fractal dimensions

In this paper we present a fractal Berreman's model which account for azimuthal surface anchoring of nematic liquid crystals which play a leading role nowadays in biomedical field and pharmaceutical controlled release dosage forms. The model is based on the concept of "product-like fractal measure" in anisotropic media which permits to describe liquid crystals formation in terms of fractal dimensions. It was observed that fractal dimensions affect both the polar azimuthal angle and the Franck excess elastic energy density of the distortion. For fractal dimensions close to unity, our analysis reveals the emergence of fluctuations and large deformations in the dynamical variables of the theory which suggest the presence of non-linear elastic instabilities or emergence of defect structures in liquid crystals. These fluctuations fade away for fractal dimensions much less than unity. We have evaluated the elastic energy per unit of area which is found to depend on the square of the fractal dimension. This leads to a decrease of the saturation voltage which is necessary to reduce the elastic energy of liquid crystals films in order to minimize the elastic energy. This reduction may describe nematic liquid crystals free from deformations, singularities or weak anchoring surfaces.

Large deformation problem of hyperbolic shallow shells with bimodular effect: A perturbation‐variation method

AbstractAs an important analytical method, the perturbation‐variation method combines the advantages of perturbation method and variational method, and is widely used for the solution of nonlinear plate and shell problems. In this study, the perturbation‐variation method is used to solve the large deformation problem of a flexible hyperbolic thin shallow shells with different moduli in tension and compression (bimodular effect). First, we establish the governing equations expressed in terms of three displacement components, in which the bimodular effect of materials is considered in physical equations and the large deformation of shell is considered in geometrical equations. Next, we use the perturbation‐variation method to solve the governing equations established, obtaining the perturbation‐variation solution up to third‐order. During the application of the method, the displacements are expressed into perturbation formulas of all levels first, and the unknown constants and functions in the perturbation formulas are determined by the extreme value conditions of the functional established (variational principle), hence the perturbation‐variation method gets its name from this practice. The numerical results from FEM basically agree with the perturbation‐variation solution obtained. The method proposed may be extended into the solution of similar partial differential equations established in applied fields.

Research on the ultra-low temperature tensile deformation mechanism of Al-Mg-Si alloys in different heat treatment states

The susceptibility of Al-Mg-Si alloy to cracking during room temperature large plastic deformation poses a significant obstacle to its widespread application. Cryogenic temperature forming of aluminum alloys has emerged as a prominent research topic. However, the precise mechanisms underlying the enhancement of aluminum alloy plasticity in different states remain elusive. In order to elucidate this matter, a series of uniaxial tensile experiments were conducted on Al-Mg-Si alloy featuring diverse initial states, under varying temperature conditions. The results show that when the deformation temperature is reduced from 25℃ to -196℃, the tensile strength and elongation of the wrought material are increased by 48MPa and 5.42%, and the tensile strength and elongation of the annealed material are increased by 118MPa and 5.65%. In contrast, while the T4 state sample exhibited a significant improvement in tensile strength (103MPa), no substantial enhancement in elongation was observed. This disparity can be primarily attributed to the absence of second-phase precipitation in the as-forged and annealed states. As the temperature decreased, the critical shear stress increased, resulting in increased resistance to deformation. Consequently, an increased degree of lattice rotation and activation of dislocations in various slip systems ensued, thereby improving the deformation uniformity. The formation of initial microvoids predominantly occurred close to grain boundaries. Therefore, compared with room temperature deformation, low temperature deformation caused by the accumulation of dislocations and hole sprouting concentrated at a single location was less likely. As a result, the dislocation distribution was more uniform and fracture was less likely to occur. Conversely, in the T4 state, the aging process resulted in the precipitation of a substantial amount of the soluble second phase (Mg5Si6). Consequently, microvoid nucleation transpired at the phase boundaries, leading to an elevated tensile strength. However, because of the increased dislocation hindrance when the deformation temperature was lowered, no significant enhancement in plasticity was observed.

Adaptively remeshed multiphysical modeling of resistance forge welding with experimental validation of residual stress fields and measurement processes

Welding processes used in the production of pressure vessels impart residual stresses in the manufactured component. Computational modeling is critical to predicting these residual stress fields and understanding how they interact with notches and flaws to impact pressure vessel durability. In this work, we present a finite element model for a resistance forge weld and validate it using laboratory measurements. Extensive microstructural changes, near-melt temperatures, and large localized deformations along the weld interface pose significant challenges to Lagrangian finite element modeling. The proposed modeling approach overcomes these roadblocks in order to provide a high-fidelity simulation that can predict the residual stress state in the manufactured pressure vessel; a rich microstructural constitutive model accounts for material recrystallization dynamics, a frictional-to-tied contact model is coordinated with the constitutive model to represent interfacial bonding, and adaptive remeshing is employed to alleviate severe mesh distortion. An interrupted-weld approach is applied to the simulation to facilitate comparison to displacement measures. Several approaches are employed for residual stress measurement in order to validate the finite element model: neutron diffraction, the contour method, and the slitting method. Model-measurement comparisons are supplemented with detailed simulations that reflect the configurations of the residual-stress measurement processes themselves. The model results show general agreement with experimental measurements, and we observe some similarities in the features around the weld region. Factors that contribute to model-measurement differences are identified. Finally, we conclude with some discussion of the model development and residual stress measurement strategies, including how to best leverage the efforts put forth here for other types of related weld problems.

Microstructure and properties controlling of Al-xGd alloys for thermal neutron absorbing

A novel lightweight thermal neutron absorbing Al-xGd alloy (x = 2.5, 5, and 10 wt.%) with tunable mechanical properties was fabricated by induction melting followed by a rolling process and an annealing treatment. During solidification, the Al3Gd phase predominantly formed and was distributed along grain boundaries. Cold rolling crushed and redistributed the Al3Gd phase throughout the matrix. Furthermore, the large deformation imposed on the material during cold rolling enhanced the work hardening effect and promoted dynamic recrystallization. The load transfer strengthening effect was influenced by the size, volume fraction, and distribution of the second phase. The spheroidization of the second phase increased rapidly and then remained stable during 5000 h long-term aging at 400°C. The thermal neutron absorbing performance of the Al-5Gd alloy is comparable to the 30%B4C/Al composite evaluated by Monte Carlo simulations. Furthermore, Al-5Gd alloy exhibited higher plasticity (> 20%). This novel Al-xGd alloy is a promising candidate for future lightweight thermal-neutron-absorbing materials.

Nonlinear free vibrations of a structurally tailored anisotropic pre-twisted thin-walled beam subjected to large deformations

It is essential to understand the nonlinear free vibration behaviour of a thin-walled composite structure as they find their applications in harsher environments prone to large deformations. Further, these structures made of fibrous materials, have directional properties for different fibre orientations resulting in a diversified and a complex nonlinear behaviour. In this regard, present work provides a comprehensive mathematical formulation on nonlinear vibration of pre-twisted thin-walled anisotropic box beam. The mathematical model is derived as coupled (flap-lag-extension-torsion) model considering shear deformation and green's strain tensor for large displacements in order to study the influence of nonlinear couplings on the dynamic behaviour. The derived energy equations are presented depending on degree of nonlinearity. These nonlinear equations those derived are nondimensionalized and solved with in the frame work of energy method using classical Ritz approximation. An iterative method is used to solve the nonlinear equations pertaining displacement terms. This nonlinear behaviour is evaluated for two important types of structural tailoring techniques available for thin-walled composite beams namely Circumferentially Asymmetric Stiffness (CAS) and Circumferentially Uniform Stiffness (CUS). It is found that CAS layup experiences significantly severe nonlinear effects compared to CUS due to the presence of 3rd degree nonlinear coupling terms. The variation of nonlinear frequency ratios over different ply angles showing the influence of nonlinearity on fibres orientation is presented for the first time for the two ply lay ups. The influence of degree of nonlinearity on the accuracy of the nonlinear frequencies is evaluated and presented. Moreover, the impact of nonlinearity on the pre-twisted beam is presented for different pre-twist angles.

Design and kinematics analysis of a cable-stayed notch manipulator for transluminal endoscopic surgery

The friction between the joints of the continuum manipulator with discrete joints brings great difficulties to kinematic modeling. The traditional driving wire arrangement limits the load capacity of the manipulator. A cable-stayed notch manipulator for transluminal endoscopic surgery is proposed, and a driving force coupling kinematic mode is established. The manipulator is fabricated from a superelastic Nitinol tube with bilaterally cut rectangular notches and is actuated by a stay cable. By applying the comprehensive elliptic integral solution (CEIS) for large deformation beams, the bending angle of each elastic beam is obtained, and the kinematics from the driving space to the joint space is formed. According to the bending angle of each elastic beam, the expression of the manipulator in Cartesian space can be obtained by geometric analysis. The kinematics from the joint space to the Cartesian space is established. The outer diameter of the manipulator is only 3.5 mm, and the inner diameter can reach 2 mm, allowing instruments to pass through. The maximum error of the manipulator movement is less than 5%. The load capacity of the manipulator has been verified through the stiffness experiments, and the maximum load of the manipulator can reach 400 g. The cable-stayed notch manipulator can be accurately modeled on the base of CEIS, and its motion accuracy can meet the needs of engineering applications. The compact size and excellent load capacity of the manipulator make it potential for application in transluminal endoscopic surgical robots.

A novel cellular structure with center-symmetric cell walls for morphing applications

Cellular structures are potential candidates for the supporting framework of flexible morphing skins. Unlike traditional zero Poisson’s ratio (ZPR) cellular structures with axisymmetric cell walls, this paper proposes a novel cellular structure with center-symmetric cell walls. The in-plane mechanical properties of this novel structure are explored through theoretical analysis and substantiated by both finite element simulations and experimental tests. Compared to the classic accordion honeycomb structure, the elastic modulus in the x-direction of the novel structure is reduced by an average of 58%, the strain amplification rate is increased by 122%, and the in-plane stiffness anisotropy is improved by 200%. These findings suggest that the proposed structure offers far superior stiffness anisotropy and large deformation potential, making it more suitable for morphing applications than the traditional ZPR cellular structures.

Aerostructural Analysis of a Deployable Aeroshell in Transonic Flow

The deployable aeroshell, a contemporary reentry system, utilizes a thin flexible membrane surface sustained by pressurized gas to efficiently decelerate a reentry vehicle at high altitudes while enabling low-ballistic-coefficient flight. When an in-flight aerodynamic force is applied, the membrane structure undergoes large deformation that may affect its performance. Hence, a coupled analysis that considers the feedback effect of structural deformation is essential for accurately predicting the behavior of such reentry vehicles. In this study, a numerical framework for coupled aeroelastic analysis was constructed in a partitioned manner using open-source software to elucidate the combined effect of structural deformation and compressible flow dynamics and characterize the aerodynamic performance of reentry vehicles with inflatable structures. The results revealed that the membrane surface was deformed elastically by the aerodynamic force owing to the large difference in pressure distribution between the front and back of the aeroshell. Fluctuating behavior was observed in the aerodynamic coefficients owing to the small-amplitude oscillation of the capsule. This oscillation was induced by the large wake behind the vehicle. Several wrinkles and concave-shaped depressions formed on the membrane surface, which exhibited a circumferential movement tendency with time.

Fluid–structure interaction analysis of curved wedges entering into water

The water entry of wedges with curvature differs significantly from that of linear wedges, which have been fully investigated and formulated. The safety and integrity of structures prompt an urgent investigation into the mechanism by which the curvature affects slamming loads and structural responses during water entry. This study examines the slamming force characteristics, pressure distributions, fluid jet evolutions, and structural response behaviors of two-dimensional curved wedge sections, considering five different curvatures and two panel thicknesses. A two-way coupling fluid–structure interaction (FSI) solver has been proposed within an open-source framework. The FSI solver was validated against published literature to ensure its high-fidelity. The small deadrise angle results in a more complicated time-domain characteristics for the slamming pressure, with a gradual transition from a single peak to a double peak. The half-peak pressure duration time were defined, and the quantitative results reveal that the hydroelastic effect of the linear wedge is significantly higher than the curved wedges. When considering the geometric curvature, the elastic wedges do not consistently reduce the peak slamming pressure and lengthen the pulse time. Additionally, large deformations generated by the panel vibrations alter the evolutionary pattern of the fluid jet. In contrast to the linear wedge, the structural responses of the curved wedges show distinctive two-stage behaviors.

A foundational framework for the mesoscale modeling of dynamic elastomers and gels

Discrete mesoscale network models, in which explicitly modeled polymer chains are replaced by implicit pairwise potentials, are capable of predicting the macroscale mechanical response of polymeric materials such as elastomers and gels, while offering greater insight into microstructural phenomena than constitutive theory or macroscale experiments alone. However, whether such mesoscale models accurately represent the molecular structures of polymer networks requires investigation during their development, particularly in the case of dynamic polymers that restructure in time. We here introduce and compare the topological and mechanical predictions of an idealized, reduced-order mesoscale approach in which only tethered dynamic bonding sites and crosslinks in a polymer’s backbone are explicitly modeled, to those of molecular theory and a Kremer-Grest, coarse-grained molecular dynamics approach. We find that for short chain networks (∼12 Kuhn lengths per chain segment) at intermediate polymer packing fractions, undergoing relatively slow loading rates (compared to the monomer diffusion rate), the mesoscale approach reasonably reproduces the chain conformations, bond kinetic rates, and ensemble stress responses predicted by molecular theory and the bead–spring model. Further, it does so with a 90% reduction in computational cost. These savings grant the mesoscale model access to larger spatiotemporal domains than conventional molecular dynamics, enabling simulation of large deformations as well as durations approaching experimental timescales (e.g., those utilized in dynamic mechanical analysis). While the model investigated is for monodisperse polymer networks in theta-solvent, without entanglement, charge interactions, long-range dynamic bond interactions, or other confounding physical effects, this work highlights the utility of these models and lays a foundational groundwork for the incorporation of such phenomena moving forward.