“闲倚胡床，庾公楼外峰千朵。与谁同坐。明月清风我。
别乘一来，有唱应须和。还知么。自从添个。风月平分破。”
《点绛唇》- 苏轼 (宋)
”莫听穿林打叶声，何妨吟啸且徐行。竹杖芒鞋轻胜马，谁怕？一蓑烟雨任平生。
料峭春风吹酒醒，微冷，山头斜照却相迎。回首向来萧瑟处，归去，也无风雨也无晴。”
《定风波》- 苏轼 (宋)
“庐山烟雨浙江潮，未至千般恨不消。
到得还来别无事，庐山烟雨浙江潮。”
《庐山烟雨浙江潮》- 苏轼 (宋)
“夜饮东坡醒复醉，归来仿佛三更。家童鼻息已雷鸣。敲门都不应，倚杖听江声。
长恨此身非我有，何时忘却营营。夜阑风静縠纹平。小舟从此逝，江海寄余生。”
《临江仙》- 苏轼 (宋)
Single crystal silicon (SCS) is widely used in the design of semiconductors. In order to better understand and predict its fracture behavior, a 3D phase-field approach is proposed to simulate its brittle fracture. A modified phase-field model is proposed by incorporating anisotropic fracture toughness of SCS into its formulation. The critical energy release rate is determined by finding the most probable cleavage direction (i.e., the direction of the maximum tensile principal strain component of the local strain tensor). An iso-parametric monolithic finite element algorithm is then developed using 4-node tetrahedral elements and 8-node hexahedral elements to predict crack initiation and crack growth direction in a SCS brick specimen under uniaxial extension. The result agrees well with the analytical solution. In addition, brittle fracture of a SCS tapered double cantilever beam is simulated. Analysis result agrees well with the experiment, such as compliance v.s. crack length, and the crack growth direction.
The paper can be found here:
=> Paper
=> Simulation
I hope this paper is helpful to your research and other academic activities.
本书从理论解析和数值模拟两方面入手探讨了振动式陀螺（也称谐振式陀螺）相关的动力学理论和基于有限元的数值模拟方法，分为两章介绍。主要的创新之处在于：
希望对您的学习和工作有所帮助！
Micro-electromechanical system (MEMS) vibratory gyroscopes are inertial sensors for measuring angular velocity based on a micro-machined proof-mass that can detect rotating-induced inertial force (i.e., Coriolis force). During the past several decades, great advancement has been achieved in the fields of design and fabrication of MEMS vibratory gyroscopes, however, little investigation on understanding and improving their measurement range could be found in the literature. We find that most of the commercial single-axis force-rebalance MEMS vibratory gyroscopes have a measurement range of the order 10^2 . A question naturally arises: is there any physical reasoning to the limit of the measurement range? To answer this question, we propose a theoretical method to investigate the limit by creating a mathematical model for typical single-axis force-rebalance MEMS vibratory gyroscopes. A deeper analysis gives the answer to the question, for the first time.
The paper can be found here:
=> Paper
I hope this paper is helpful to your research and other academic activities.
While the subject of ballistics has been investigated for several centuries, nowadays, the design of a ballistic component or device is still not an easy task, but usually a process of trial and error, or an iterative process of analysis, testing and tweaking. Concerning the design of a gun with a gas-operated piston system, it is challenging to accurately determine how a gas-operated piston system would affect the interior ballistic performance of the gun (e.g., muzzle velocity) due to gas loss and how large the chamber/gas-room pressure would be for safety purpose. To address this problem, a numerical approach based on the coupled Euler-Lagrange technique and a constitutive model for the combustion gas mixture of solid propellants is presented, where the constitutive model is developed by combining Vieille’s law for combustion and the equation of state for gas mixture. The model is validated by experiments for a double base propellant. The approach is then applied to study the effect of a gas-operated piston system on the interior ballistic performance of typical gun designs with different gas port radiuses. The interior ballistic parameters like the muzzle velocity and the highest barrel pressure are computed. Results show that these designs of gas ports influence the interior ballistic parameters very little. In addition, a larger gas port radius results in a larger gas room pressure, which indicates a faster operation of the gas-operated piston.
The paper can be found here:
=> Paper
=> Animation based on SPH method
=> Animation based on CEL method
I hope this paper is helpful to your research and other academic activities.
The lecture notes were prepared for an undergraduate course on the fundamentals and applications of the finite element method in solid mechanics.
You may make copies of these notes for education and research.
The lecture notes can be found here:
Silicon multi-ring structures connected by spokes are ideal candidate to carry circumferential traveling waves in the design of MEMS vibratory gyroscope. However, these structures are prone to instability at high-speed rotation. This paper presents an efficient approach to determine the critical and flutter speeds of these structures for their various natural modes, and thereby to predict their in-plane instability. Through extensive parametric study, the effects of various design parameters on the instability of these structures are obtained and discussed. The results show that stability of these structures could be enhanced by increasing number of spokes, reducing number of rings, and reducing gaps between rings. Furthermore, it is found that these structures are more stable with circumferential traveling waves with a larger nodal diameter.
Based on a continuum theory that accounts for the underlying molecular physics of polar elastomers (PEs), a typical boundary value problem (BVP) is developed to analyze the electro-mechanical instability (EMI) of PEs with randomly distributed dielectric particles. Through extensive numerical simulations, the effects of various parameters such as particle volume fraction, particle size and enhancement factor related to polar groups on the critical voltage leading to EMI of PEs are investigated. The results are presented in 3D phase diagrams, which may better help researchers to understand EMI of PEs and guide them in synthesis, design, and application of PEs in the fields of chemistry, physics, bio-engineering, etc.
MMASC is a nonlinear finite element package for simulating mechanical behaviors of soft composites subjected to external stimuli in a multi-physics context.
The main features of the package are as following:
It supports Tet/Hex meshes.
It is coded in modern Fortran and has an interface for UMAT/VUMAT, UEL/VUEL etc.
It supports multi-physics nonlinear analysis, either static or dynamic, either implicit or explicit.
It supports two-scale analysis with options of 3 different homogenization methods.
It has a unique math-core and is independent of external libraries.
The current released version is only for electromechanical coupling problems.
The following is an example about coupling electric field and displacement field analysis for rubber-like materials (such as elastomers and gels). The problem is defined as shown in Fig. 1.
Four different analyses procedures (see Fig. 2) are incorporated into this version of MMASC, and each of the procedure defines two analysis steps.
The first step is controlled by mechanical pre-stress and the second step is controlled by electric potential or charge. In order to compare the two-scale procedure and one-scale procedure, this example just assumes that both macroscale domain and microscale unit cell are uniform. The results are shown in Fig. 3. While this example is simple, its extension to cases for heterogeneous materials is natural. Please consult to the user manual of MMASC.
You can find the program(Windows) here:
The input files for the example here:
You may download these 3 files in a folder and then open a terminal to run the program.
You are free to redistribute this version of MMASC. And I hope the program is helpful to your research.