Wrinkle Strain Research Articles

Superhydrophobic gradient wrinkle strain sensor with ultra-high sensitivity and broad strain range for motion monitoring

A graphene-based gradient wrinkle strain sensor with a broad range and ultra-high sensitivity was fabricated by a simple pre-stretching method. It can be applied to the detection of full-range human body motions.

Experimental verification on wrinkling behavior given by wrinkling analysis using the tension field theory

This study investigates the physical meaning of membrane surface features given by a wrinkling analysis based on tension field theory and wrinkle strain, which releases the compressive stress in membranes in tension field theory. A rectangular membrane was subjected to shear loading, and the wrinkle geometry and strain field were measured by photogrammetry using a direct linear transformation method. The experimental model was then subjected to a wrinkling analysis based on tension field theory, and the calculated wrinkled membrane behavior was quantitatively compared to the measured results. The analyzed membrane surface features approximately represented the neutral curved surface bisecting the actual wrinkle geometry (the difference was approximately 10% of the maximum wrinkle amplitude), even when the membrane surface feature was not initially flat. The wrinkle strain, defining an in-plane shrinkage strain that releases compressive stress on the membrane in tension field theory, agreed with the experimentally observed in-plane shrinkage strain regardless of the formation process of the wrinkles. The relation between the in-plane shrinkage strain and ratio of the wrinkle amplitude to the half-wavelength of the wrinkles was then derived from inextensional theory. This relation appropriately described the relation measured in the experiment, confirming that inextensional theory describes the wrinkle formation. The results of this study will assist the evaluation of the simulation results using tension field theory for the development of future lightweight, membrane-based space structures such as sunshields and solar sails.

Experimental verification on simplified estimation method for envelope curve of wrinkled membrane surface distortions

The effectiveness of a simplified method for estimating an envelope curve of wrinkled-membrane-surface distortion, which was recently proposed by the author, was experimentally assessed. The equation is formulated using three physical quantities regarding wrinkles: the length of the wrinkle line, the major principal strain in wrinkled regions, and the in-plane shrinkage strain appearing in the orthogonal direction of the wrinkle line. Since these three physical quantities are attributed to two-dimensional problems, the formula makes it possible to simply estimate wrinkle amplitude without a cumbersome bifurcation analysis. Applying a wrinkle strain in tension-field theory instead of the in-plane shrinkage strain in the formula, a simplified method to estimate an envelope curve of a wrinkled membrane with a low computational cost was developed using the wrinkling analysis with tension-field theory. Wrinkling phenomena appearing on two membrane models subjected to an in-plane shear and a corner-tension load were experimentally measured by photogrammetry using the direct linear-transformation method and a laser-displacement sensor. The experiment model was then subjected to a finite element analysis using tension-field theory, and an envelope curve of the wrinkled membrane was estimated using the method. The estimated envelope curves appropriately captured the actual wrinkle amplitude appearing on the membrane surface regardless of the formation process of wrinkles. From the result, the validity of the proposed estimation method was confirmed. This paper offers an effective method to predict the magnitude of the wrinkled-membrane-surface distortion with a low computational cost, and will assist the development of future gossamer space structures incorporating membranes.

Approximate estimation of wrinkle wavelength and maximum amplitude using a tension-field solution

Membrane-based space structures such as solar sails, inflatable antennas and sunshields have attracted attention for use on future advanced space science and engineering missions. Since these membrane-based space structures are easily deformed by small disturbances, a practical calculation method for the surface configuration of the deformed membranes is required to realize the membrane structures without failure. This study formulates an equation to estimate the wrinkle wavelength and maximum amplitude appearing on thin membranes based on a tension-field solution. The equation calculates the wrinkle wavelength and maximum amplitude using three wrinkling parameters, which are the major principal stress in the wrinkled region, the length of the wrinkle line, and the wrinkle strain. Because these wrinkling parameters are given by a traditional wrinkling analysis using tension-field theory, the formulated equation reveals an approximate wrinkle wavelength and a maximum amplitude appearing on the thin membranes without cumbersome bifurcation analysis and has characteristics applicable to various types of structures. By conducting a wrinkling analysis using tension-field theory for the two classical membrane models, which have wrinkling phenomena appearing across the entire membrane and in part of the membrane, a wrinkle wavelength and maximum amplitude are estimated from the formula. Comparing the estimated results with those given by wrinkling analysis using shell theory, it is observed that the estimate appropriately captures the wrinkle wavelength and maximum amplitude in the wrinkled region where tension-field theory is applicable. The equation presented in this study offers a new, practical approach to estimate the wrinkled membrane surface configuration.

Wrinkling of Orthotropic Membranes: An Analysis by the Polar Method

In the present paper, a simple membrane model based on the wrinkle strain approach is revisited with the aim of examining how the material elastic constants affect the static response of anisotropic membranes when wrinkling is taken into account.

Efficient Modification Scheme of Stress-Strain Tensor for Wrinkled Membranes

A new modification scheme of the stress-strain tensor for wrinkled membranes is presented on the basis of the tension field theory. The scheme is applicable to finite element analysis of partly wrinkled membranes with arbitrary shapes. Derivation of the modification scheme rests on an introduction of the so-called wrinkle strain and a simplification of the virtual work equation of wrinkled membranes. Because all of the modifications required to account for wrinkling are totally confined within the stress-strain relations of membranes, the scheme can be easily implemented with existing finite element codes. Furthermore, the modified stress-strain tensor automatically leads to the consistent tangent stiffness matrix, where changes in both the wrinkling direction and the amount of wrinkliness are taken into account. Three numerical examples are treated to show the accuracy and effectiveness of the proposed modification scheme.

Complementarity problem formulation for the wrinkled membrane and numerical implementation

A linear complementarity formulation has been developed to analyze a wrinkled membrane problem which involves the nonlinearities caused by large deformitions and unilateral behavior due to wrinkling. A kinematic quantity called wrinkle strain is introduced as a measure of the physical wrinkliness of the surface by modifying the deformation gradient tensor. The wrinkle strain tensor when substituted in the constitutive equation expresses the physical stress field of the wrinkled membrane. An incremental method is adopted and numerically implemented with a finite element setting.

The transition zone near wrinkles in pulled spherical membranes

The unwrinkled transition zone between the rigid boundaries and the wrinkled portion of a spherical membrane subjected to a pulling force is analyzed. The strains are first assumed to be small, and two cases are considered: (a) a spherical membrane barrel pulled into a wrinkled cylinder and (b) a hemispherical membrane pulled into a wrinkled cone. It is shown that in both cases the angular size of the transition zone is O(ε), where ε is the prevailing strain, rather then o(√ε) as in the usual nonlinear membrane edge effect problem. Large rotations and substantial variations in the circumferential stresses and strains take place in this narrow zone. The extension to the case of “moderate” strains is then made for the spherical barrel, using a power series approach. It follows from the results that the size of the transition zone becomes O(√ε) as the wrinkled region shrinks to zero. Finally, a complete large strain analysis of a partly wrinkled spherical barrel membrane is made. Included are both the transition zone and the interior wrinkled region. The analysis establishes the ranges of validity of the previous solutions and demonstrates the deterioration of the “edge effect”. A formula for the “wrinkle strain” in the interior is included. Interestingly, the deviation of the slope ᾱ of the deformed membrane from the winkled direction is shown to be always small, so that the problem can be assumed to be geometrically linear in cot ᾱ, but materially nonlinear.

Nonlinear Wrinkling of Nonlinear Membranes of Revolution

The general problem of nonlinear wrinkling of nonlinear membranes of revolution is considered. The theory is applicable to membranes made of any nonlinear material although only Mooney material is considered in this paper. A smooth psuedo deformed surface is introduced to give a gross representation of the true deformed surface, and a kinematic quantity called wrinkle strain is introduced to measure the wrinklyness of the surface. The wrinkly regions are determined by the usual assumption that a thin membrane cannot take any compressive stress. A stretching problem is solved as an example.