International Journal of Applied Mechanics

We propose a machine learning embedded method of parameters determination in the constitutional models of hydrogels. It is found that the developed logistic regression-like algorithm for hydrogel swelling allows us to determine the fitting parameters based on known swelling ratio and chemical potential. We also put forward the neural networks-like algorithm, which, by its own property, can converge faster as the layer deepens. We then develop neural networks-like algorithm for hydrogel under uniaxial load for experimental application purpose. Finally, we propose several machine learning embedded potential applications for hydrogels, which would provide directions for machine learning-based hydrogel research.

The mechanical properties and deformation of Origami structures are studied in this paper. Usually, it is a coupling problem of crease rotation and shell deformation. Here, the creases are simplified as torsional springs, whose rotational stiffness $k$ is obtained by the experiment of compressing a creased shell. While the shells that may have large deformation are simplified as rigid plates connected by virtual creases, whose rotational stiffness is roughly expressed as bending stiffness divides width of the shell. Hence, a coupling factor $C$ is defined to evaluate the coupling effect of creases and shells. Implementing the obtained rotational stiffnesses of real and virtual creases into the expression of strain energy, an improved Virtual Crease Method (VCM) is proposed. By analyzing the bi-stability of creased shell and Miura-Ori structure, the accuracy and convergence of this improved VCM is proved.

This study concerns the effect of applied velocity on the energy state and stress state related to the puncture-cutting of soft material. A finite element modeling (FEM) of combined puncture and cutting of neoprene rubber by a pointed blade was established at 17 velocities (from 10mm/min to 1500mm/min). The proposed FEM takes into consideration, the nonlinear material behavior of the elastomeric substrate. First, puncture-cutting tests are conducted and the evolution of puncture-cutting force with increased velocity is investigated. Second, the commonly used puncture-cutting energy criterion, including the fracture toughness of material and the friction energy occurring between the material and the pointed blade, are summarized and analyzed. Finally, an analysis of the stress state in the fracture process zone is proposed. Results show that the puncture-cutting force increases significantly with increasing insertion velocity. A low velocity of the pointed blade is dominated by a uniaxial tension with a constant energy, while a medium velocity causes a dominant biaxial tension with increasing energy, which may be the source of the viscoelastic deformation involved around the crack tip. However, an increase of the velocity increases the shear stress up to a maximum value and, therefore, shows a toughening of material.

This paper proposes an interval finite element method based on function decomposition for structural static response problems with large-scale unknown-but-bounded parameters. When there is a large number of uncertain parameters, it will lead to the curse of dimensionality. The existing Taylor expansion-based methods, which is often employed to deal with large-scale uncertainty problems, need the sensitivity information of response function to uncertain parameters. However, the gradient information may be difficult to obtain for some complicated structural problems. To overcome this drawback, univariate decomposition expression (UDE) and bivariate decomposition expression (BDE) are deduced by the higher-order Taylor series expansion. The original structure function with $n$-dimensional interval parameters is decomposed into the sum of several low-dimensional response functions by UDE or BDE, each of which has only one or two interval parameters while the other interval parameters are replaced by their midpoint values. Therefore, solving the upper and lower bounds of the $n$-dimensional function can be converted into solving those of the one- or two-dimensional functions, which savethe calculation costs and can be easily implemented. The accuracy and efficiency of the new method are verified by three numerical examples.

The space flexible arm has the characteristics of large flexibility and size, and external excitation will cause harmful vibration. In this paper, the dynamic response of flexible arms is analyzed, and the vibration control is studied when nonlinear factors are considered. First, the vibration equation is established according to the Hamilton’s principle, and the generalized force is derived by using rod model and beam model, respectively. Then the Runge–Kutta method is used to solve the vibration equation, and the dynamic response is obtained. Finally, the PD and fuzzy control simulations of three arms are established, and the dead zone and saturation nonlinearities are applied in the programs. The numerical results show that the external force causes significant response, and the vibration control method is effective. Besides, in order to achieve vibration control effect, it is necessary to reduce the dead zone nonlinear range.

The CoCrFeMnNi high-entropy alloy (HEA) is a potential structural material, whose cyclic plasticity is essential for its safety assessment in service. Here, the effects of twin boundaries (TBs) and temperature on the cyclic plasticity of CoCrFeMnNi HEA were studied by the molecular dynamics (MD) simulation. The simulation results showed that a significant amount of lattice disorders were generated due to the interactions between partial dislocations in CoCrFeMnNi HEA during the cyclic deformation. Lattice disorder impeded the reverse movement of dislocations and then weakened Bauschinger’s effect in the HEA. The cyclic plasticity of CoCrFeMnNi HEA, especially Bauschinger’s effect, depends highly on the temperature and pre-existing TBs. Such dependence lies in the effects of temperature and pre-existing TBs on the extent of lattice disorder. This study helps further understand the cyclic plasticity of CoCrFeMnNi HEA from the atomic scale.

This paper investigates the nonlinear bending analysis of a hyperelastic plate via neo-Hookean strain energy function. The first-order shear deformation plate theory (FSDPT) is used for the formulation of the field variables. Also, the nonlinear Lagrangian strains are considered via the right Cauchy–Green tensor. The governing equations and nonlinear boundary conditions are derived using Euler–Lagrange relations. The meshless collocation method based on radial basis function is used to discretize the governing equations of the hyperelastic plate. Square and circular plates are studied to evaluate the accuracy of the meshless collocation method based on thin-plate spline (TPS) and multiquadric (MQ) and logarithmic thin-plate spline (LTPS) radial basis function. Also, the results of the meshless method are compared to those of the finite element method. In some cases, the meshless method is more efficient than the finite element method due to no meshing. The linear and nonlinear natural boundary conditions are directly imposed on the stiffness matrix and are compared to each other. The maximum differences between linear and nonlinear natural boundary conditions are 1.43%. The von-Mises stress using meshless collocation method based on TPS basis function is compared to those of the finite element method.

This paper conducts theoretical study on the mechanical, thermal and electrical properties of graphene reinforced composites by effective medium theory (EMT). Considering the imperfect bonding between the reinforcing fillers and the matrix, an interphase surrounding the graphene fillers is introduced during the EMT modeling. The coated graphene fillers are homogenized as effective reinforcements dispersed in a matrix. The EMT model is validated by comparing the predicted material properties with previously reported results. Parametric study is carried out to investigate the influences of several parameters, including concentration and geometry of graphene fillers, the attributes of the introduced an interphase and the alternating current (AC) frequency, upon the effective material properties of the reinforced composites. The results demonstrate that the increase of the thickness of the interphase results in the decrease of Young’s modulus, thermal conductivity and electrical conductivity of the composites while it is favorable to enhance the dielectric properties of the composites. The increase in the aspect ratio of the graphene filler enhances all material properties involved. Percolation behaviors are observed for the dielectric properties of the composites. Moreover, the dielectric properties of the composites are very sensitive to the change of the AC frequency within a certain range, which suggests the achievement of active tuning of material properties.

The morphology of a bleb and its changes are critical to the amoeboid migration of a cell. By releasing bonds between the membrane and the cortex of a cell, the formation of a bleb can be observed experimentally, but the mechanism that affects the size and shape of a bleb during amoeboid migration requires further study. In this study, by adapting the governing equations and discrete equations of the two-dimensional fluid–solid coupling model recommended by Strychalski and Guy [2013 “A computational model of bleb formation,” Mathematical Medicine and Biology 30(2), 115–130], we overcome the defect that the bleb by traditional means is always too small compared with experimental results, and simulate the behaviors of cell blebs successfully. The effects of various parameters such as the number of broken bonds, the viscosity coefficient of the cortex, and the cell’s membrane modulus on the size and the shape of the bleb are investigated. Numerical results show that the model effectively simulates the formation and evolution of a bleb, thus, the contributions of several factors to bleb shape and size are successfully derived.

In this paper, an improved conforming AFEM (C-AFEM) for efficient modeling of arbitrary crack propagation and branching is proposed and validated. An explicit formulation for branching cracks has been derived within the C-AFEM framework. The conjugate gradient method is integrated into the C-AFEM formulation to solve the local problem that consists of all elements traversed by single or multiple cracks. Multiple numerical evidences show that this new approach can substantially improve the modeling efficiency. The solution accuracy and numerical robustness are also significantly improved.

As one of the most popular 3D printed metamaterials, the auxetic structure with its tunable Poisson’s ratio has attracted huge amount of attention recently. In this study, we designed an auxetic shape-memory metamaterial, which showed designable buckling responses by using the thermomechanically coupled in-plane instability. The influence of viscoelasticity on in-plane moduli and Poisson’s ratios of shape-memory auxetic metamaterial was experimentally investigated. Based on the generalized Maxwell model and finite-element method, the buckling behaviors and their main influence factors were studied. The analytical results and experimental ones showed a good agreement. Thermomechanical properties of the printed metamaterials govern the temperature and strain rate-dependent buckling, and a controllable transition from the negative to positive Poisson’s ratio in the metamaterials can be achieved. Based on the shape memory effect, the buckled state and the Poisson’s ratio of the metamaterials can be tuned by programmed thermomechanical processes. This study provides a simple and efficient way to generate morphing structures using the designable buckling effect.

In this paper, elastic wave scattering in hollow pipes with non-axisymmetric and inclined angle defects is studied using finite element (FE) simulations. A comb array transducer is employed in the FE code to excite the pipe in its first longitudinal mode using a 10-cycle sine modulated excitation signal at 120kHz central frequency. Defects with variations in geometrical shapes such as depths, axial and circumferential lengths, and inclined angles are investigated to provide detailed analysis of wave propagation patterns and mode conversions in a 12-in diameter pipe. The influence of each geometrical parameter and also possible newborn modes is studied both in time and wavenumber-frequency domain via circumferential order identification approach and dispersion curves. Results show that the depth of a non-axisymmetric circumferential defect has the minimum influence on the propagating mode while crack’s width can influence the measured longitudinal mode in a sinusoidal pattern which is a function of excitation signal’s wavelength. Further, the propagating mode can exhibit higher contribution of either axisymmetric or non-axisymmetric modes based on the reflection patterns, depending on its angle and axial length.

A mid-node mass lumping scheme is proposed to formulate the lumped mass matrices of serendipity elements for accurate structural vibration analysis. Since the row-sum technique leads to unacceptable negative lumped mass components for serendipity elements, the diagonal scaling HRZ method is frequently employed to construct lumped mass matrices of serendipity elements. In this work, through introducing a lumped mass matrix template that includes the HRZ lumped mass matrix as a special case, an analytical frequency accuracy measure is rationally derived with particular reference to the classical eight-node serendipity element. The theoretical results clearly reveal that the standard HRZ mass matrix actually does not offer the optimal frequency accuracy in accordance with the given lumped mass matrix template. On the other hand, by employing the nature of non-negative shape functions associated with the mid-nodes of serendipity elements, a mid-node lumped mass matrix (MNLM) formulation is introduced for the mass lumping of serendipity elements without corner nodal mass components, which essentially corresponds to the optimal frequency accuracy in the context of the given lumped mass matrix template. Both theoretical and numerical results demonstrate that MNLM yields better frequency accuracy than the standard HRZ lumped mass matrix formulation for structural vibration analysis.

In this paper, a new approach for stress-softening of an isotropic, incompressible, hyperelastic and rectangular beam that undergoes cyclic bending-unbending deformation, is presented. Employing an exponential softening function, damage response of the hyperelastic beam due to cyclic finite bending is investigated. The stress-softening phenomenon occurs in elastomeric materials when they deform for the first time. Under the same deformation, the stress required in reloading is smaller than the initial loading stage. This is known as the Mullins effect. To verify the accuracy of the proposed solution, finite element analysis of the same problem is carried out. In this study, a principal stretch-based strain energy function i.e., Ogden model and an invariant-based function such as a newly introduced Exp–Exp model are used for all bending, unbending and re-bending procedures. The proposed method needs a much shorter time compared to FEM simulations. Thus, in design and optimization of the structures under bending that requires a large number of analyses, the proposed semi-analytical solution can be considered as an efficient tool for studying the effects of different material and geometrical parameters.