Large deformation and wrinkling analyses of bimodular structures and membranes based on a peridynamic computational framework

Li, Hui; Zheng, Yonggang; Zhang, Y. X.; Ye, H. F.; Zhang, H. W.

doi:10.1007/s10409-019-00894-7

Cited by 14 publications

(5 citation statements)

References 49 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…al. [36] used an implicit bond-based peridynamic formulation to analyse quasi-static large deformation, wrinkling and fracture of membranes. Bang and Madenci [37] developed peridynamic strain energy functions for a Non-Hookean type membrane under equibiaxial, planar, and uniaxial loading conditions.…”

Section: Introductionmentioning

confidence: 99%

Analytical Solution of the Peridynamic Equation of Motion for a 2-Dimensional Rectangular Membrane

Yang

Öterkuş

et al. 2022

J Peridyn Nonlocal Model

View full text Add to dashboard Cite

In order to analyse the deformation response of materials and structures, various continuum mechanics theories have been proposed. Peridynamics is a new non-local continuum mechanics formulation which has governing equations in integro-differential equation form. Analytical solution of these integro-differential equations is limited in the literature. In this study, analytical solution of the peridynamic equation of motion for a 2-dimensional membrane is presented. Analytical solutions are obtained for both static and dynamic conditions. Various numerical cases are considered to validate the derived analytical solution by comparing peridynamic results against classical continuum mechanics results. For both static and dynamic cases, both solutions agree very well with each other. Moreover, the influence of the size of the length scale parameter in peridynamics, horizon, is investigated. According to the numerical results, it is concluded that as the horizon size becomes larger, peridynamic solution captures nonlocal characteristics and peridynamic results deviate from classical continuum mechanics results.

show abstract

Section: Introductionmentioning

confidence: 99%

Analytical Solution of the Peridynamic Equation of Motion for a 2-Dimensional Rectangular Membrane

Yang

Öterkuş

et al. 2022

J Peridyn Nonlocal Model

View full text Add to dashboard Cite

show abstract

“…45,46 Besides, other important works such as combining the PD with traditional methods or analyzing engineering problems have been performed. [47][48][49][50][51][52][53][54] However, transient problems involving discontinuous or sharp gradient characteristics are currently not well addressed.…”

Section: Introductionmentioning

confidence: 99%

“…Ren et al later developed a dual‐horizon PD formulation that naturally includes varying horizon sizes with minimal spurious wave reflection and eliminate the "ghost force. " 45,46 Besides, other important works such as combining the PD with traditional methods or analyzing engineering problems have been performed 47‐54 . However, transient problems involving discontinuous or sharp gradient characteristics are currently not well addressed.…”

Section: Introductionmentioning

confidence: 99%

A time‐discontinuous peridynamic method for transient problems involving crack propagation

Liu

Qian

et al. 2021

Numerical Meth Engineering

View full text Add to dashboard Cite

A time-discontinuous peridynamic method (TDPD) for modeling transient problems of wave and crack propagation in solids is presented in this article. The main features of the TDPD are that the displacement field and the velocity field are independently interpolated in the temporal domain by using cubic and linear functions, respectively. Jump terms representing discontinuities of the variables are introduced between the adjacent time steps. The weak form and a new time integration scheme are derived by combining the peridynamic governing equations with the time-discontinuous method. The displacement field is continuous while discontinuous jumps are introduced into the velocity field. Those characteristics enable the TDPD to accurately capture the sharp gradient in stress and effectively control the spurious numerical oscillation. The effectiveness of the TDPD is first demonstrated through two representative numerical examples of wave propagation. Three additional examples are presented to show the advantages of the TDPD in the simulation of dynamic crack propagation problems. It is shown that TDPD provides more accurate and satisfactory results when compared with the traditional time integration scheme.

show abstract

“…Surface topological features have wide applications in surface property tuning [1][2][3][4][5][6], optical devices [7,8], stretchable electronics [9][10][11], precision metrology [12,13], and assembly templates [14]. Compressing a stiff thin film on a soft substrate leads to surface wrinkling, which serves as a convenient approach to introduce topological features on the surface.…”

Section: Introductionmentioning

confidence: 99%

“…They fabricated wrinkled metal films on polydimethylsiloxane (PDMS) substrates using mismatch of thermal expansion, which introduced compression strain in the film and led to the formation of wrinkling. Both experimental and theoretical studies have shown that stiff thin film-soft substrate bilayer system and compression strain beyond a critical value in the film are required to form thin film wrinkling [3,11,[15][16][17][18][19][20][21][22][23][24][25]. It is a process to balance the bending energy of the thin film and the strain energy of the substrate by adopting specific wrinkling wavelength and amplitude [17,23,26,27].…”

Section: Introductionmentioning

confidence: 99%

Confined thin film wrinkling on shape memory polymer with hybrid surface morphologies

Wang

Xiao

2021

Acta Mech. Sin.

View full text Add to dashboard Cite

With appropriate stimuli, such as heat, humidity, or magnetic field, shape memory polymers (SMPs) can recover to their original shapes from temporary, programmed states. Using thermal responsive SMPs as substrates, we demonstrate a simple method to realize hybrid surface morphologies through confined thin film wrinkling in localized areas. The bilayer system was fabricated by depositing a layer of aluminum thin film on top of a SMP substrate programmed with a tensile strain. After the system was heated by a heating wire, hybrid wrinkling patterns were formed in a confined circular area around the heat source, with an inner spoke pattern and an outer ring pattern. Wrinkling patterns showed good symmetry, and the size of the wrinkling area can be tuned by controlling the heat input. This study offers a simple but effective approach to fabricate hybrid morphological features in micro-scale.

show abstract

Large deformation and wrinkling analyses of bimodular structures and membranes based on a peridynamic computational framework

Cited by 14 publications

References 49 publications

Analytical Solution of the Peridynamic Equation of Motion for a 2-Dimensional Rectangular Membrane

Analytical Solution of the Peridynamic Equation of Motion for a 2-Dimensional Rectangular Membrane

A time‐discontinuous peridynamic method for transient problems involving crack propagation

Confined thin film wrinkling on shape memory polymer with hybrid surface morphologies

Contact Info

Product

Resources

About