Analysis of wrinkled membrane structures using a Plane Stress projection procedure and the Dynamic Relaxation method

Meitour, H. Le; Rio, Gérard; Laurent, Hervé; Lectez, Anne-Sophie; Guigue, Pascale

doi:10.1016/j.ijsolstr.2020.10.026

Cited by 15 publications

(9 citation statements)

References 61 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In 2009, Zheng [45] uncovered the restabilization phenomenon in a highly stretched sheet, showing that wrinkles appear first, then decrease, and eventually disappear with the continuous increase of applied stretching. To consider large deformations of soft films, some plate/shell theories accounting for finite in-plane strain [62][63][64][65] and advanced numerical methods [32,[66][67][68][69][70] for capturing multiple bifurcations in nonlinear post-buckling paths were developed. General mechanics models to characterize large deformations of thin films can be placed into three categories: extended Föppl-von Kármán plate model (EFvK) [32][33][34], finite-strain plate model derived from three-dimensional nonlinear elasticity [71][72][73][74], and consistent finite-strain plate model [64,65,70,75].…”

Section: Introductionmentioning

confidence: 99%

Mechanics of tension-induced film wrinkling and restabilization: a review

Wang

Yang

2022

Proc. R. Soc. A.

View full text Add to dashboard Cite

Wrinkling of thin films under tension is omnipresent in nature and modern industry, a phenomenon which has aroused considerable attention during the past two decades because of its intricate nonlinear behaviours and intriguing morphology changes. Here, we review recent advancements in the mechanics of tension-induced film wrinkling and restabilization, by identifying three major stages of its progress: small-strain (less than 5 % ) wrinkling of stiff sheets, finite-strain (up to 30 % ) wrinkling and restabilization (isola-centre bifurcation) of soft films, and the effects of curved configurations and material properties on pattern formation. Growing demand for fundamental understanding, quantitative prediction and precise tracking of secondary bifurcation transitions in morphological evolution of thin films helps to advance finite-strain plate/shell theories and sophisticated modelling methods. This progress not only promotes our insightful understanding of complex instability behaviour but also reveals novel phenomena and sheds light on developing wrinkle-tunable membrane structures and functional surfaces.

show abstract

Section: Introductionmentioning

confidence: 99%

Mechanics of tension-induced film wrinkling and restabilization: a review

Wang

Yang

2022

Proc. R. Soc. A.

View full text Add to dashboard Cite

show abstract

“…Instead, some works using the explicit solution method, coupled with dynamic relaxation 39,40 for the equilibrium, have been studied to overcome these problems due to geometric instabilities.…”

Section: Application To Neurosurgical Simulation Of Brain Deformationsmentioning

confidence: 99%

“…Compared to NH, TI incurred additional computation for I 4 terms, OT incurred additional computation for I 4 and I 6 terms, and MR incurred additional computation for I 2 terms. The computation of I 2 terms was more expensive than computing I 4 or I 6 terms, which was mainly due to the extra computational operations in ( t ĝT ⋅ I 2m ) (see Equations [39][40][41][42]). Table 6 presents the average computational overheads.…”

Section: Cpu Computational Performancementioning

confidence: 99%

“…In such a mechanical unstable region, the implicit (iterative) scheme may fail to obtain a converged solution or produce a solution with excessive numerical dissipation that in many cases precludes fine, local details of wrinkles. Instead, some works using the explicit solution method, coupled with dynamic relaxation 39,40 for the equilibrium, have been studied to overcome these problems due to geometric instabilities.…”

Section: Application To Neurosurgical Simulation Of Brain Deformationsmentioning

confidence: 99%

See 1 more Smart Citation

A direct Jacobian total Lagrangian explicit dynamics finite element algorithm for real‐time simulation of hyperelastic materials

Zhang

2021

Numerical Meth Engineering

View full text Add to dashboard Cite

This article presents a novel direct Jacobian total Lagrangian explicit dynamics (DJ-TLED) finite element algorithm for real-time nonlinear mechanics simulation. The nodal force contributions are expressed using only the Jacobian operator, instead of the deformation gradient tensor and finite deformation tensor, for fewer computational operations at run-time. Owing to this proposed Jacobian formulation, novel expressions are developed for strain invariants and constant components, which are also based on the Jacobian operator. Resultsshow that the proposed DJ-TLED consumed between 0.70× and 0.88× CPU solution times compared to state-of-the-art TLED and achieved up to 121.72× and 94.26× speed improvements in tetrahedral and hexahedral meshes, respectively, using GPU acceleration. Compared to TLED, the most notable difference is that the notions of stress and strain are not explicitly visible in the proposed DJ-TLED but embedded implicitly in the formulation of nodal forces. Such a force formulation can be beneficial for fast deformation computation and can be particularly useful if the displacement field is of primary interest, which is demonstrated using a neurosurgical simulation of brain deformations for image-guided neurosurgery. The present work contributes towards a comprehensive DJ-TLED algorithm concerning isotropic and anisotropic hyperelastic constitutive models and GPU implementation.

show abstract

“…This approach enables architects to establish a good relationship between spatial form and structure during structural simulation, calculation, and optimization by analyzing structure stress characteristics in architectural design. Based on this, some specific structural form-finding methods were proposed, such as the force density method [ 2 ], dynamic relaxation method [ 3 ], a graphical method [ 4 ], and thrust grid analysis method [ 5 ]. Architectural design is gradually transforming to digital strategies with the continuous improvement in computational efficiency.…”

Section: Introductionmentioning

confidence: 99%

Implementation and Optimization of Reverse Suspension Structure Design Model Using Deep Learning

Wang

Wang³

2022

Computational Intelligence and Neuroscience

View full text Add to dashboard Cite

The present work aims to improve the design efficiency and optimize the results in the increasingly complex and diversified material design projects to help architects realize the better performance of building structures. According to the characteristics of comprehensive perception and intelligent processing of the Internet of Things, a reverse suspension structure design model is constructed based on the finite element method and simulated annealing algorithm. Besides, deep learning is adopted to train complex functions for performance correction and to optimize the plane structure of shell structure. Moreover, the force is transformed into shape, and the form-finding process is completed to facilitate the operation of designers. Finally, the spatial anchoring ability of the geographic information system is used to match and calculate the relevant characteristics of spatial elements. On this basis, the index construction strategy based on weight distribution is employed to realize the data fusion diagnosis framework and enhance the intelligence of architectural design. The simulation results show that the maximum tensile stress of the physical suspension experiment is 3.71 MPa and the maximum compressive stress is 14.7 MPa. The compressive stress value is much larger than the tensile stress value. The maximum deformation value’s difference between the compressive and tensile stress is 0.07 and 0.11, respectively. The error is within the acceptable range, which is similar to the compression state results obtained from the actual suspension physical experiment, indicating that the initial design model of the reverse suspension structure based on deep learning is reliable. In addition, the evolutionary optimization effect analysis results demonstrate that the load of the design structure is relatively uniform, which verifies the feasibility of the algorithm reported here. The research significance of the reverse suspension structure model constructed here is to provide an accurate and feasible design idea for the reverse design of some complex structures in the building suspension. It can also shorten the creation and improvement cycle of this kind of structure and optimize the performance and construction cycle of the building structure.

show abstract

Analysis of wrinkled membrane structures using a Plane Stress projection procedure and the Dynamic Relaxation method

Cited by 15 publications

References 61 publications

Mechanics of tension-induced film wrinkling and restabilization: a review

Mechanics of tension-induced film wrinkling and restabilization: a review

A direct Jacobian total Lagrangian explicit dynamics finite element algorithm for real‐time simulation of hyperelastic materials

Implementation and Optimization of Reverse Suspension Structure Design Model Using Deep Learning

Contact Info

Product

Resources

About