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2020 Vol. 41, No. 1
Published: 2020-02-28
 
1 Data-driven Computational Mechanics: a Review
DOI: 10.19636/j.cnki.cjsm42-1250/o3.2020.001
The concept of big data with digital twin and artificial intelligence is profoundly influencing the fourth industrial revolution. At the same time, facing severe challenges in advanced manufacturing and safety assessment of high-performance materials and structures, classical computational mechanics has more and more limitations in achieving the goal of ‘half-time and half-cost’ of R&D cycle. Data-driven computational mechanics emerged in this context and showed great vitality. This paper aims to discuss and analyze the trend of data-driven computational mechanics by reviewing recent research achievements. In this paper, the algorithms in the framework of data-driven computational mechanics are summarized into two categories: the first one is based on energy functional, the key point of which is to construct the constitutive relationship by using material data; while the second category is based on distance functional, the specificity of which lies in directly embedding the material data into mechanical simulations. Several related data-driven algorithms of each category are briefly recalled, and the challenges and prospects of data-driven computational mechanics are discussed.
2020 Vol. 41 (1): 1-14 [Abstract] ( 1323 ) HTML (1 KB)  PDF   (0 KB)  ( 274 )
15 Analysis of Flexural Vibrations of Laminated Piezoelectric Semiconductor Plates
DOI: 10.19636/j.cnki.cjsm42-1250/o3.2019.039
We theoretically study the flexural vibration of a laminated piezoelectric semiconductor (PS) composite plate. Based on the two-dimensional (2D) equations for the laminated thin-film PS plates, the analytical s of the electromechanical fields and distribution of electrons in the thin-film PS plate subjected to a steady-state flexural vibration are obtained. We numerically investigated the effects of the amplitude and excitation frequency of mechanical loading and the initial concentration of carriers on the macroscopic responses of the PS structure. Numerical results show that the amplitudes of all physical quantities in the plate have the largest values under the first-order natural frequency. Under the second/third and other-higher order natural frequencies, each physical field has many local maximum or minimum regions. The carriers move to or leave these local regions. In addition, due to the screening effect of carriers, only the initial carriers with certain concentrations have a tuning effect on the PS plate.
2020 Vol. 41 (1): 15-29 [Abstract] ( 267 ) HTML (1 KB)  PDF   (0 KB)  ( 220 )
30 Elastoplastic Mechanical Analysis Based on the Virtual Element Method
DOI: 10.19636/j.cnki.cjsm42-1250/o3.2019.042
The virtual element method (VEM) with the features of finite difference method (FDM) can be regarded as an extension procedure of the finite element method (FEM) to arbitrary polygonal elements. Similar to the FEM, the VEM is also a Galerkin method that discretizes the entire physical domain into polygonal meshes, including non-convex shapes. The difference is that there is no need to calculate the interpolation function inside the element. In terms of the nonlinear properties such as meso-mechanical properties and mechanical analysis of heterogeneous materials, e.g., the particle-reinforced composite materials, traditional elastoplastic finite elements have many deficiencies, such as the great number of meshes and low efficiency. The virtual element method makes the mesh division more flexible, and can observe the real structure of the reaction material more closely, which provides a new idea for nonlinear problems such as the elastoplastic analysis of materials. In this research, a new procedure for elastoplastic mechanical problems with the VEM is proposed by considering the specialties of incremental elastoplastic calculation and bilinear projection operator. Then the scheme for updating the stress of elastoplastic mechanical problems with the VEM is provided. Based on the above-mentioned techniques, the accuracy and convergency of VEM for elastoplastic mechanical problems are studied. The mesh dependence of VEM for elastoplastic mechanical problems are discussed as well. Finally, some numerical experiments of arbitrary polygonal and concave polygonal elements are carried out. The triangle or quadrilateral mesh is not necessary in the VEM, and the stiffness matrix is constructed by the projection operator on the element. Only the degree of freedom of nodes is employed to build up the element stiffness matrix and the stress equivalent load. The research shows that the procedure of VEM is simple to implement and has high accuracy. At the same time, the mesh dependence and singularity of the plastic region are improved accordingly.
2020 Vol. 41 (1): 30-40 [Abstract] ( 441 ) HTML (1 KB)  PDF   (0 KB)  ( 208 )
41 The Interaction between Parallel Screw Dislocations and a Finite Crack in One-dimensional Hexagonal Quasicrystals
DOI: 10.19636/j.cnki.cjsm42-1250/o3.2019.033
By using the famous complex variable function method introduced by Muskhelishvili and the analytic function theory in this paper, the analytical solutions of the interaction of many parallel screw dislocations with a finite crack in infinitely large one-dimensional hexagonal quasicrystals are studied. The field intensity factors at the crack tip and the imaged force acting on one dislocation with the existence of crack and other dislocations are obtained. The numerical examples are given to discuss the influence of the dislocation position on the field intensity factors and the imaged force. And the position and distribution of the dislocations also effect the generalized stress field.
2020 Vol. 41 (1): 41-49 [Abstract] ( 192 ) HTML (1 KB)  PDF   (0 KB)  ( 202 )
50 Stress Intensity Factor Calculation of Friction Contact Cracks Based on Complementary Theory and Extended Finite Element Method
DOI: 10.19636/j.cnki.cjsm42-1250/o3.2019.037
The extended finite element method is a numerical method for modeling discontinuities within the classical finite element framework. This method can treat arbitrary cracks independent of the mesh and crack growth with minimal remeshing. Based on the principle of virtual work equation, and combined with the nonlinear complementary for contact conditions and the extended finite element discrete technique, a nonlinear complementary model for frictional contact crack problem with the extended finite element method is presented. First, the conditions that describe frictional contact are formulated as a system of non-smooth equations based on variational inequality theory, and the non-smooth damped newton method is given based on the definitions of generalized derivative to directly solve the system of equations without any extra parameters and iteration. Then, take the finite plane with a single inclined crack, edge-cracked plate as examples. The stress intensity factor of finite plane with closed crack was calculated by the interaction integral approach. The numerical solution calculated by the extended finite element method is basically consistent with the theory solution. Finally, the propagation of inclined crack under uniaxial compression is simulated by the extended finite element method. The calculation result shows that the numerical result is agreement with the experimental result and this method can accurately simulate the crack growth under uniaxial compression. Numerical example is presented to demonstrate the correctness and effectiveness of this method.
2020 Vol. 41 (1): 50-58 [Abstract] ( 260 ) HTML (1 KB)  PDF   (0 KB)  ( 242 )
59 Conversion between Two Types of Parameters in Viscoelastic Combination Model for Common Hypotheses and its Applicability
DOI: 10.19636/j.cnki.cjsm42-1250/o3.2019.038
The viscoelastic combination model usually has two forms. One is the form based on the Young’s modulus and the coefficients of tensile viscosity, the other is the form based on the shear modulus and the coefficients of shear viscosity. The conversion relationship between two types of parameters has been established for the Generalized Kelvin model. However, there still exists some problems such as the theoretical foundation is still relatively weak and the scope and conditions of application are not clear. Considering two kinds of three dimensional hypothesis commonly used in geotechnical engineering (constant Poisson's ratio hypothesis and constant volume modulus hypothesis), the conversion relationship between two types of parameters for creep compliance and complex compliance in viscoelasticity model is given based on the linear viscoelastic theory. Then the conversion relationship was applied to the generalized Kelvin model and the Poynting-Thomson model, and the conversion formulas between two types of parameters for these two models are established respectively. The scope and conditions of application for the conversion are put forward, and the problems are pointed out which should be paid attention to in practical engineering application in the end.
2020 Vol. 41 (1): 59-70 [Abstract] ( 264 ) HTML (1 KB)  PDF   (0 KB)  ( 195 )
71

Effect of Surface Modification by Direct Fluorination on Bending Fatigue Behaviors of Poly (Methyl Methacrylate)

Effect of Surface Modification by Direct Fluorination on Bending Fatigue Behaviors of Poly (Methyl Methacrylate)[J]. journal1, 2020,41(1): 71-82')" href="#">
DOI: 10.19636/j.cnki.cjsm42-1250/o3.2019.036
The surface direct fluorination was utilized in this paper to improve the bending fatigue behavior of Poly (methyl methacrylate) (PMMA). The effect of the surface direct fluorination on the fracture toughness and bending strength of PMMA were firstly tested. Then the bending fatigue behaviors, including the fatigue life as well as the fatigue crack propagation process of PMMA with different types of pre-notch before and after surface direct fluorination were comprehensively studied. The experimental result of the bending fatigue life showed that the fatigue performance of PMMA was improved significantly after surface direct fluorination, which was accounted for the structural constraining effect of the fluorinated surface layer. In addition, the evolution of the regular striation morphology on the fatigue fracture surface was found to be correlated to the occurrence of the craze at the crack tip. As another evidence of the improvement of the fatigue life of PMMA, the propagation rate of fatigue striation decreased obviously after the surface direct fluorination. This work showed that the surface direct fluorination is a feasible approach to improve the fatigue property of PMMA, which provided useful guidance for substantial industrial application.
2020 Vol. 41 (1): 71-82 [Abstract] ( 250 ) HTML (1 KB)  PDF   (0 KB)  ( 194 )
83 Symplectic Superposition Solutions of a Free Orthotropic Rectangular Thin Plates Bending Problem on Winkler Foundation
DOI: 10.19636/j.cnki.cjsm42-1250/o3.2019.034
The orthotropic plates have widely applications in engineering problems. But due to the complexity of the orthotropic plate problems, it is generally difficult to obtain their analytical solutions, especially for fully free orthotropic rectangular plates on elastic foundations. At present, there are few methods to study this kind of problems. However, all these methods belong to traditional inverse or semi-inverse methods, with which it is rather difficult to seek a trial function satisfying corresponding boundary conditions. This shortcoming limits the scope of the application of the semi-inverse methods. Recently, a novel symplectic superposition method for elasticity has been rapidly developed in isotropic plate problems. Unlike the semi-inverse methods with predetermined trial functions, the symplectic superposition method is rigorously rational without any guess functions. However, because of the complexity of fully free orthotropic rectangular plates on elastic foundations, this kind of problems has not been solved by the symplectic superposition method. Based on the above, in this paper, the analytical bending solution of a fully free orthotropic rectangular thin plate, subjected to a concentrated load, resting on Winkler foundation is studied by the Symplectic superposition method. Firstly, the original bending equation is rewritten as a Hamiltonian canonical equations based on the known results. And the eigenvalues and eigenfunctions of the Hamiltonian operator matrix for the plate problem with two opposite edges slidingly supported are calculated. Then it is proved that the eigenfunctions are symplectic orthogonal and complete in the sense of Cauchy's principal value. Based on the completeness of the eigenfunctions, the general solution of the orthotropic rectangular thin plate with two opposite edges slidingly supported is derived. Secondly, the bending problem of fully free orthotropic rectangular thin plate, subjected to a concentrated load, resting on Winkler foundation is solved by superposing three sub-problems, which are all the bending problems of the orthotropic rectangular thin plates with two opposite edges slidingly supported. Finally, the deflection values of an isotropic rectangular thin plate and an orthotropic rectangular thin plate at some specific points are calculated by the obtained symplectic superposition solution respectively. Then we find that the numerical results obtained in this paper are in excellent agreement with the numerical results in the existing literature. Here, we only consider a concentrated load problem for the orthotropic rectangular thin plate, but the analytical solutions of the orthotropic rectangular thin plates under arbitrary loads can be calculated by using symplectic superposition method. Furthermore, the method can also be used to solve the problems of bending and vibration of orthotropic rectangular thin plates under more boundary conditions.
2020 Vol. 41 (1): 83-92 [Abstract] ( 281 ) HTML (1 KB)  PDF   (0 KB)  ( 196 )
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