A Preliminary Two-Dimensional Palpation Mechanics for Detecting a Hard Inclusion by Indentation of a Soft Matrix Under Large Strain

2019 ◽  
Vol 86 (5) ◽  
Author(s):  
Shengchen Liu ◽  
Kai-tak Wan
Keyword(s):  
Large Strain ◽  
Soft Materials ◽  
Finite Depth ◽  
Two Dimensional ◽  
Soft Layer ◽  
Element Analysis ◽  
Hard Inclusion ◽  
Soft Matrix ◽  
Indentation Axis ◽  
The Matrix

A rigid inclusion is embedded at a finite depth in a soft layer resting on a rigid substrate. A spherical indenter presses vertically onto the surface, deforming the matrix and displacing the inclusion. A subsurface inclusion initially near the indentation axis moves primarily downward, until an unstable lateral jump occurs to minimize the energy stored in the elastic medium. Such an instability is unique to soft materials undergoing large deformation. A two-dimensional plane-strain finite element analysis is used to simulate the 3D phenomenon.

Fracture Analyses of Soft Materials With Hard Inclusion

2018 ◽  
Vol 85 (11) ◽  
Author(s):  
Pengyu Pei ◽  
Yan Shi ◽  
Guang Yang ◽  
Cunfa Gao
Keyword(s):  
Soft Materials ◽  
Stress Concentrations ◽  
Element Analysis ◽  
Hard Inclusion ◽  
Applied Loading ◽  
Fracture Behaviors ◽  
Theoretical Predictions ◽  
Key Factor ◽  
Fracture Theory ◽  
Line Inclusion

This paper presents a detailed study on the fracture behaviors of soft materials with hard inclusion. Stress concentrations on the interfaces of hard and soft materials are considered as the key factor for structure fracture. Based on linear fracture theory, the fracture behaviors of soft materials with elliptical hard inclusion are investigated. Stress concentrations, consisting of tensile, hoop, and compressive stress, are observed with changes of inclusion geometries and the modulus ratio of hard and soft materials. And their influences on the categories of principal stress concentration are shown in a phase diagram in the current paper. Finite element analysis is carried out with consideration of the large deformation of soft material, which demonstrates the effectiveness of the theoretical predictions in a great scope of applied loading. Finally, the predictions based on theoretical and simulation results are validated by experiments. This work points out that the hard line inclusion is the source of danger in soft materials just like the crack in brittle materials.

scholarly journals Tunable characteristics of low-frequency bandgaps in two-dimensional multivibrator phononic crystal plates under prestrain

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Hai-Fei Zhu ◽  
Xiao-Wei Sun ◽  
Ting Song ◽  
Xiao-Dong Wen ◽  
Xi-Xuan Liu ◽  
...  
Keyword(s):  
Phononic Crystal ◽  
Real Life ◽  
Low Frequency ◽  
Acoustic Vibration ◽  
Crystal Plate ◽  
Frequency Noise ◽  
Two Dimensional ◽  
The Matrix ◽  
Noise Frequency ◽  
Realtime Control

AbstractIn view of the influence of variability of low-frequency noise frequency on noise prevention in real life, we present a novel two-dimensional tunable phononic crystal plate which is consisted of lead columns deposited in a silicone rubber plate with periodic holes and calculate its bandgap characteristics by finite element method. The low-frequency bandgap mechanism of the designed model is discussed simultaneously. Accordingly, the influence of geometric parameters of the phononic crystal plate on the bandgap characteristics is analyzed and the bandgap adjustability under prestretch strain is further studied. Results show that the new designed phononic crystal plate has lower bandgap starting frequency and wider bandwidth than the traditional single-sided structure, which is due to the coupling between the resonance mode of the scatterer and the long traveling wave in the matrix with the introduction of periodic holes. Applying prestretch strain to the matrix can realize active realtime control of low-frequency bandgap under slight deformation and broaden the low-frequency bandgap, which can be explained as the multiple bands tend to be flattened due to the localization degree of unit cell vibration increases with the rise of prestrain. The presented structure improves the realtime adjustability of sound isolation and vibration reduction frequency for phononic crystal in complex acoustic vibration environments.

Two-Dimensional Full-Vectorial Finite Element Analysis of NRD Guide Devices

2021 ◽  
Vol 31 (4) ◽  
pp. 345-348
Author(s):  
Yasuhide Tsuji ◽  
Keita Morimoto ◽  
Akito Iguchi ◽  
Tatsuya Kashiwa ◽  
Shinji Nishiwaki
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Two Dimensional ◽  
Element Analysis ◽  
Nrd Guide

scholarly journals Divergent ⇒ complex amplitudes in two dimensional string theory

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Ashoke Sen
Keyword(s):  
Scattering Amplitudes ◽  
String Theory ◽  
Matrix Model ◽  
Two Dimensional ◽  
Full Matrix ◽  
Instanton Contribution ◽  
The Matrix ◽  
Theory Result ◽  
The One ◽  
Remarkable Agreement

Abstract In a recent paper, Balthazar, Rodriguez and Yin found remarkable agreement between the one instanton contribution to the scattering amplitudes of two dimensional string theory and those in the matrix model to the first subleading order. The comparison was carried out numerically by analytically continuing the external energies to imaginary values, since for real energies the string theory result diverges. We use insights from string field theory to give finite expressions for the string theory amplitudes for real energies. We also show analytically that the imaginary parts of the string theory amplitudes computed this way reproduce the full matrix model results for general scattering amplitudes involving multiple closed strings.

scholarly journals A new fourth-order explicit group method in the solution of two-dimensional fractional Rayleigh–Stokes problem for a heated generalized second-grade fluid

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Muhammad Asim Khan ◽  
Norhashidah Hj. Mohd Ali ◽  
Nur Nadiah Abd Hamid
Keyword(s):  
Finite Difference ◽  
Stokes Problem ◽  
Stability And Convergence ◽  
Second Grade ◽  
Group Method ◽  
Two Dimensional ◽  
Second Grade Fluid ◽  
The Matrix ◽  
Grade Fluid ◽  
Generalized Second Grade Fluid

Abstract In this article, a new explicit group iterative scheme is developed for the solution of two-dimensional fractional Rayleigh–Stokes problem for a heated generalized second-grade fluid. The proposed scheme is based on the high-order compact Crank–Nicolson finite difference method. The resulting scheme consists of three-level finite difference approximations. The stability and convergence of the proposed method are studied using the matrix energy method. Finally, some numerical examples are provided to show the accuracy of the proposed method.

Comparison principles for free-surface flows with gravity

1991 ◽  
Vol 230 ◽  
pp. 231-243 ◽  
Author(s):  
Walter Craig ◽  
Peter Sternberg
Keyword(s):  
Solitary Waves ◽  
Finite Depth ◽  
Free Surface Flows ◽  
Immiscible Fluids ◽  
Steady Flows ◽  
Two Dimensional ◽  
Surface Flows ◽  
Ship Hulls ◽  
Geometrical Information ◽  
Supercritical Flows

This article considers certain two-dimensional, irrotational, steady flows in fluid regions of finite depth and infinite horizontal extent. Geometrical information about these flows and their singularities is obtained, using a variant of a classical comparison principle. The results are applied to three types of problems: (i) supercritical solitary waves carrying planing surfaces or surfboards, (ii) supercritical flows past ship hulls and (iii) supercritical interfacial solitary waves in systems consisting of two immiscible fluids.

scholarly journals Assessing the Flexural Properties of Epoxy Composites with Extremely Low Addition of Cellulose Nanofiber Content

2020 ◽  
Vol 10 (3) ◽  
pp. 1159 ◽  
Author(s):  
Yingmei Xie ◽  
Hiroki Kurita ◽  
Ryugo Ishigami ◽  
Fumio Narita
Keyword(s):  
Mechanical Properties ◽  
Epoxy Resin ◽  
Flexural Modulus ◽  
Strengthening Mechanism ◽  
Short Fiber ◽  
Cellulose Nanofiber ◽  
Resin Matrix ◽  
Element Analysis ◽  
Epoxy Resin Matrix ◽  
The Matrix

Epoxy resins are a widely used common polymer due to their excellent mechanical properties. On the other hand, cellulose nanofiber (CNF) is one of the new generation of fibers, and recent test results show that CNF reinforced polymers have high mechanical properties. It has also been reported that an extremely low CNF addition increases the mechanical properties of the matrix resin. In this study, we prepared extremely-low CNF (~1 wt.%) reinforced epoxy resin matrix (epoxy-CNF) composites, and tried to understand the strengthening mechanism of the epoxy-CNF composite through the three-point flexural test, finite element analysis (FEA), and discussion based on organic chemistry. The flexural modulus and strength were significantly increased by the extremely low CNF addition (less than 0.2 wt.%), although the theories for short-fiber-reinforced composites cannot explain the strengthening mechanism of the epoxy-CNF composite. Hence, we propose the possibility that CNF behaves as an auxiliary agent to enhance the structure of the epoxy molecule, and not as a reinforcing fiber in the epoxy resin matrix.

scholarly journals Lymphocyte locomotion and attachment on two-dimensional surfaces and in three-dimensional matrices

1982 ◽  
Vol 92 (3) ◽  
pp. 747-752 ◽  
Author(s):  
WS Haston ◽  
JM Shields ◽  
PC Wilkinson
Keyword(s):  
Three Dimensional ◽  
Two Dimensional ◽  
Collagen Gels ◽  
Peripheral Lymph Node ◽  
Cellulose Esters ◽  
Peripheral Lymph ◽  
The Matrix ◽  
Identical Material ◽  
Variable Morphology ◽  
Collagen Lattices

The adhesion and locomotion of mouse peripheral lymph node lymphocytes on 2-D protein- coated substrata and in 3-D matrices were compared. Lymphocytes did not adhere to, or migrate on, 2-D substrata suck as serum- or fibronectin-coated glass. They did attach to and migrate in hydrated 3-D collagen lattices. When the collagen was dehydrated to form a 2-D surface, lymphocyte attachment to it was reduced. We propose that lymphocytes, which are poorly adhesive, are able to attach to and migrate in 3-D matrices by a nonadhesive mechanism such as the extension and expansion of pseudopodia through gaps in the matrix, which could provide purchase for movement in the absence of discrete intermolecular adhesions. This was supported by studies using serum-coated micropore filters, since lymphocytes attached to and migrated into filters with pore sizes large enough (3 or 8 mum) to allow pseudopod penetration but did not attach to filters made of an identical material (cellulose esters) but of narrow pore size (0.22 or 0.45 mum). Cinematographic studies of lymphocyte locomotion in collagen gels were also consistent with the above hypothesis, since lymphocytes showed a more variable morphology than is typically seen on plane surfaces, with formation of many small pseudopodia expanded to give a marked constriction between the cell and the pseudopod. These extensions often remained fixed with respect to the environment as the lymphocyte moved away from or past them. This suggests that the pseudopodia were inserted into gaps in the gel matrix and acted as anchorage points for locomotion.

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