scholarly journals Wrinkling Phenomena in Neo-Hookean Film/Substrate Bilayers

2012 ◽  
Vol 79 (3) ◽  
Author(s):  
Yanping Cao ◽  
John W. Hutchinson
Keyword(s):  
Finite Element ◽  
Critical Strain ◽  
Full Range ◽  
Period Doubling ◽  
Modulus Ratio ◽  
Layer System ◽  
Mountain Ridge ◽  
Compliant Substrates ◽  
Film Substrate

Wrinkling modes are determined for a two-layer system comprised of a neo-Hookean film bonded to an infinitely deep neo-Hookean substrate with the entire bilayer undergoing compression. The full range of the film/substrate modulus ratio is considered from the limit of a traction-free homogeneous substrate to very stiff films on compliant substrates. The role of substrate prestretch is considered wherein an unstretched film is bonded to a prestretched substrate with wrinkling arising as the stretch in the substrate is relaxed. An exact bifurcation analysis reveals the critical strain in the film at the onset of wrinkling. Numerical simulations carried out within a finite element framework uncover advanced post-bifurcation modes including period-doubling, folding and a newly identified mountain ridge mode.

scholarly journals The role of nonlinear substrate elasticity in the wrinkling of thin films

2013 ◽  
Vol 371 (1993) ◽  
pp. 20120422 ◽  
Author(s):  
John W. Hutchinson
Keyword(s):  
Thin Films ◽  
Substrate Stiffness ◽  
Modulus Ratio ◽  
Compliant Substrates ◽  
Wide Range ◽  
The Stability ◽  
Film Substrate ◽  
Film Stiffness ◽  
Substrate Elasticity

The role of substrate nonlinearity in the stability of wrinkling of thin films bonded to compliant substrates is investigated within the initial post-bifurcation range when wrinkling first emerges. A fully nonlinear neo-Hookean bilayer composed of a thin film on a deep substrate is analysed for a wide range of the film–substrate stiffness ratio, from films that are very stiff compared with the substrate to those only slightly stiffer. Substrate pre-stretch prior to film attachment is shown to have a significant effect on the nonlinearity relevant to wrinkling. Two dimensionless parameters are identified that control the stability and mode shape evolution of the bilayer: one specifying arbitrary uniform substrate pre-stretch and the other a stretch-modified modulus ratio. For systems with film stiffness greater than about five times that of the substrate the wrinkling bifurcation is stable, whereas for systems with smaller relative film stiffness bifurcation can be unstable, especially if substrate pre-stretch is not tensile.

scholarly journals Multimodal Surface Instabilities in Curved Film–Substrate Structures

2017 ◽  
Vol 84 (8) ◽  
Author(s):  
Ruike Zhao ◽  
Xuanhe Zhao
Keyword(s):  
Thin Films ◽  
Mechanical Properties ◽  
Numerical Simulation ◽  
Period Doubling ◽  
Tubular Structures ◽  
Modulus Ratio ◽  
Future Design ◽  
Mismatch Strain ◽  
Curved Structures ◽  
Film Substrate

Structures of thin films bonded on thick substrates are abundant in biological systems and engineering applications. Mismatch strains due to expansion of the films or shrinkage of the substrates can induce various modes of surface instabilities such as wrinkling, creasing, period doubling, folding, ridging, and delamination. In many cases, the film–substrate structures are not flat but curved. While it is known that the surface instabilities can be controlled by film–substrate mechanical properties, adhesion and mismatch strain, effects of the structures’ curvature on multiple modes of instabilities have not been well understood. In this paper, we provide a systematic study on the formation of multimodal surface instabilities on film–substrate tubular structures with different curvatures through combined theoretical analysis and numerical simulation. We first introduce a method to quantitatively categorize various instability patterns by analyzing their wave frequencies using fast Fourier transform (FFT). We show that the curved film–substrate structures delay the critical mismatch strain for wrinkling when the system modulus ratio between the film and substrate is relatively large, compared with flat ones with otherwise the same properties. In addition, concave structures promote creasing and folding, and suppress ridging. On the contrary, convex structures promote ridging and suppress creasing and folding. A set of phase diagrams are calculated to guide future design and analysis of multimodal surface instabilities in curved structures.

scholarly journals Towards a quantitative understanding of period-doubling wrinkling patterns occurring in film/substrate bilayer systems

2015 ◽  
Vol 471 (2173) ◽  
pp. 20140695 ◽  
Author(s):  
Yan Zhao ◽  
Yanping Cao ◽  
Wei Hong ◽  
M. Khurram Wadee ◽  
Xi-Qiao Feng
Keyword(s):  
Potential Energy ◽  
Critical Strain ◽  
Deformation Behaviour ◽  
Compressive Strain ◽  
Period Doubling ◽  
Careful Examination ◽  
Deformation State ◽  
Quantitative Understanding ◽  
Surface Patterns ◽  
Film Substrate

Compression of a stiff film on a soft substrate may lead to surface wrinkling when the compressive strain reaches a critical value. Further compression may cause a wrinkling–folding transition, and the sinusoidal wrinkling mode can then give way to a period-doubling bifurcation. The onset of the primary bifurcation has been well understood, but a quantitative understanding of the secondary bifurcation remains elusive. Our theoretical analysis of the branching of surface patterns reveals that the wrinkling–folding transition depends on the wrinkling strain and the prestrain in the substrate. A characteristic strain in the substrate is adopted to determine the correlation among the critical strain of the period-doubling mode, the wrinkling strain and the prestrain in an explicit form. A careful examination of the total potential energy of the system reveals that beyond the critical strain of period-doubling, the sinusoidal wrinkling mode has a higher potential energy in comparison with the period-doubling mode. The critical strain of the period-doubling mode strongly depends on the deformation state of the hyperelastic solid, indicating that the nonlinear deformation behaviour of the substrate plays a key role here. The results reported here on the one hand provide a quantitative understanding of the wrinkling–folding transition observed in natural and synthetic material systems and on the other hand pave the way to control the wrinkling mode transition by regulating the strain state in the substrate.

Finite element analysis of residual stress and interlayer in hard coating/interlayer/soft substrate system during nanoindentation

2008 ◽  
Vol 23 (5) ◽  
pp. 1358-1363 ◽  
Author(s):  
Liuhe Li ◽  
Lan Yin ◽  
Paul K. Chu
Keyword(s):  
Residual Stress ◽  
Finite Element ◽  
Hard Coating ◽  
The Finite Element Method ◽  
Soft Substrate ◽  
Element Analysis ◽  
Load Displacement ◽  
Thin Interlayer ◽  
Film Substrate

The mechanical properties of thin films are frequently evaluated using nanoindentation. The finite element method (FEM) is very effective for investigating the stress and strain fields of the film–substrate system during nanoindentation. However, the role of residual stress and the thin interlayer between the film and substrate is not well known, especially when the hard coating/interlayer/soft substrate are considered together. In this work, the FEM is used to investigate the load-displacement behavior of the hardness of the hard coating/interlayer/soft substrate system. The load–displacement process is simulated, and the effects of different residual stresses and interlayer thicknesses are discussed.

A More Exact Model for Predicting the Deflection of a Clamped Magnetostrictive Film-Substrate System

2011 ◽  
Vol 197-198 ◽  
pp. 552-557
Author(s):  
Ming Li
Keyword(s):  
Finite Element ◽  
Shear Stress ◽  
Shear Strain ◽  
Strain Energy ◽  
Analytical Formula ◽  
Finite Element Package ◽  
Film Substrate ◽  
Shear Strain Energy ◽  
Magnetostrictive Film

A more exact general analytical formula of preditcting the magnetostrictive coefficient is derived for any aspect ratio based the deflection difference between the x and y directions. The curvatures are found by minimizing the total energy of the system, which taking into account shear strain energy. The in-plane stress distribution including shear stress for short specimen is also given by the ANSYS® finite element package to illustrate the role of shear strain in the deformation of magnetostrictive film-substrate system.

Atomistic simulation of the uniaxial compression of black phosphorene nanotubes

2018 ◽  
Author(s):  
Van-Trang Nguyen ◽  
Minh-Quy Le
Keyword(s):  
Finite Element Method ◽  
Molecular Dynamics ◽  
Finite Element ◽  
Uniaxial Compression ◽  
Critical Stress ◽  
Atomistic Simulation ◽  
Critical Strain ◽  
Bond Breaking ◽  
Black Phosphorene ◽  
Weber Potential

We study through molecular dynamics finite element method with Stillinger-Weber potential the uniaxial compression of (0, 24) armchair and (31, 0) zigzag black phosphorene nanotubes with approximately equal diameters. Young's modulus, critical stress and critical strain are estimated with various tube lengths. It is found that under uniaxial compression the (0, 24) armchair black phosphorene nanotube buckles, whereas the failure of the (31, 0) zigzag one is caused by local bond breaking near the boundary.

Numerical Simulation of Tire Sliding Events Involving Impacts with Holes and Bumps

1986 ◽  
Vol 14 (2) ◽  
pp. 125-136 ◽  
Author(s):  
Y. Nakajima ◽  
J. Padovan
Keyword(s):  
Numerical Simulation ◽  
Finite Element ◽  
Finite Element Simulation ◽  
Full Range ◽  
Arbitrary Geometry ◽  
Operating Environments ◽  
Element Simulation ◽  
Simulation Scheme

Abstract This paper extends the finite element simulation scheme to handle the problem of tires undergoing sliding (skidding) impact into obstructions. Since the inertial characteristics are handled by the algorithm developed, the full range of operating environments can be accommodated. This includes the treatment of impacts with holes and bumps of arbitrary geometry.

THE ROLE OF FINITE ELEMENT METHOD IN CIVIL ENGINEERING

2018 ◽  
Vol 5 (02) ◽  
Author(s):  
Er. Hardik Dhull
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Approximate Solution ◽  
Analytical Method ◽  
Civil Engineering ◽  
The Finite Element Method ◽  
Engineering Problems ◽  
Building Components ◽  
Element Method

The finite element method is a numerical method that is used to find solution of mathematical and engineering problems. It basically deals with partial differential equations. It is very complex for civil engineers to study various structures by using analytical method,so they prefer finite element methods over the analytical methods. As it is an approximate solution, therefore several limitationsare associated in the applicationsin civil engineering due to misinterpretationof analyst. Hence, the main aim of the paper is to study the finite element method in details along with the benefits and limitations of using this method in analysis of building components like beams, frames, trusses, slabs etc.

On the Role of Marangoni Effects on the Critical Heat Flux for Pool Boiling of Binary Mixtures

1996 ◽  
Vol 118 (1) ◽  
pp. 103-109 ◽  
Author(s):  
W. R. McGillis ◽  
V. P. Carey
Keyword(s):  
Surface Tension ◽  
Heat Flux ◽  
Binary Mixtures ◽  
Critical Heat Flux ◽  
Full Range ◽  
Pool Boiling ◽  
Marangoni Effect ◽  
Restoring Force ◽  
Marangoni Effects

The Marangoni effect on the critical heat flux (CHF) condition in pool boiling of binary mixtures has been identified and its effect has been quantitatively estimated with a modified model derived from hydrodynamics. The physical process of CHF in binary mixtures, and models used to describe it, are examined in the light of recent experimental evidence, accurate mixture properties, and phase equilibrium revealing a correlation to surface tension gradients and volatility. A correlation is developed from a heuristic model including the additional liquid restoring force caused by surface tension gradients. The CHF condition was determined experimentally for saturated methanol/water, 2-propanol/water, and ethylene glycol/water mixtures, over the full range of concentrations, and compared to the model. The evidence in this study demonstrates that in a mixture with large differences in surface tension, there is an additional hydrodynamic restoring force affecting the CHF condition.

scholarly journals An Extended Finite Element Method (XFEM) Study on the Elastic T-Stress Evaluations for a Notch in a Pipe Steel Exposed to Internal Pressure

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 507
Author(s):  
K. Yakoubi ◽  
S. Montassir ◽  
Hassane Moustabchir ◽  
A. Elkhalfi ◽  
Catalin Iulian Pruncu ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Internal Pressure ◽  
Extended Finite Element Method ◽  
Research Study ◽  
Extended Finite Element ◽  
T Stress ◽  
Cracked Structures ◽  
Element Method

The work investigates the importance of the K-T approach in the modelling of pressure cracked structures. T-stress is the constant in the second term of the Williams expression; it is often negligible, but recent literature has shown that there are cases where T-stress plays the role of opening the crack, also T-stress improves elastic modeling at the point of crack. In this research study, the most important effects of the T-stress are collected and analyzed. A numerical analysis was carried out by the extended finite element method (X-FEM) to analyze T-stress in an arc with external notch under internal pressure. The different stress method (SDM) is employed to calculate T-stress. Moreover, the influence of the geometry of the notch on the biaxiality is also examined. The biaxiality gave us a view on the initiation of the crack. The results are extended with a comparison to previous literature to validate the promising investigations.

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