10 research outputs found
An Existence Theorem for a Class of Wrinkling Models for Highly Stretched Elastic Sheets
We consider a class of models motivated by previous numerical studies of
wrinkling in highly stretched, thin rectangular elastomer sheets. The model
used is characterized by a finite-strain hyperelastic membrane energy perturbed
by small bending energy. Without bending energy, the stored-energy density is
not rank-one convex for general spatial deformations but reduces to a
polyconvex function when restricted to the plane, i.e., two-dimensional
hyperelasticity. In addition, it grows unbounded as the local area ratio
approaches zero. The small-bending component of the model is the same as that
in the classical von K\'arm\'an model. Here we prove the existence of energy
minima for a general class of such models
The Mullins effect in the wrinkling behavior of highly stretched thin films
Recent work demonstrates that finite-deformation nonlinear elasticity is
essential in the accurate modeling of wrinkling in highly stretched thin films.
Geometrically exact models predict an isola-center bifurcation, indicating that
for a bounded interval of aspect ratios only, stable wrinkles appear and then
disappear as the macroscopic strain is increased. This phenomenon has been
verified in experiments. In addition, recent experiments revealed the following
striking phenomenon: For certain aspect ratios for which no wrinkling occurred
upon the first loading, wrinkles appeared during the first unloading and again
during all subsequent cyclic loading. Our goal here is to present a simple
pseudo-elastic model, capturing the stress softening and residual strain
observed in the experiments, that accurately predicts wrinkling behavior on the
first loading that differs from that under subsequent cyclic loading. In
particular for specific aspect ratios, the model correctly predicts the
scenario of no wrinkling during first loading with wrinkling occurring during
unloading and for all subsequent cyclic loading.Comment: 15 pages, 9 figure
Disappearance of stretch-induced wrinkles of thin sheets: a study of orthotropic films
A recent paper (Healey et al., J. Nonlin. Sci., 2013, 23:777-805.) predicted
the disappearance of the stretch-induced wrinkled pattern of thin, clamped,
elastic sheets by numerical simulation of the F\"oppl-von K\'arm\'an equations
extended to the finite in-plane strain regime. It has also been revealed that
for some aspect ratios of the rectangular domain wrinkles do not occur at all
regardless of the applied extension. To verify these predictions we carried out
experiments on thin 20 micrometer thick adhesive covered), previously
prestressed elastomer sheets with different aspect ratios under displacement
controlled pull tests. On one hand the the adjustment of the material
properties during prestressing is highly advantageous as in targeted strain
regime the film becomes substantially linearly elastic (which is far not the
case without prestress). On the other hand a significant, non-ignorable
orthotropy develops during this first extension. To enable quantitative
comparisons we abandoned the assumption about material isotropy inherent in the
original model and derived the governing equations for an orthotropic medium.
In this way we found good agreement between numerical simulations and
experimental data.
Analysis of the negativity of the second Piola-Kirchhoff stress tensor
revealed that the critical stretch for a bifurcation point at which the
wrinkles disappear must be finite for any aspect ratio. On the contrary there
is no such a bound for the aspect ratio as a bifurcation parameter. Physically
this manifests as complicated wrinkled patterns with more than one highly
wrinkled zones on the surface in case of elongated rectangles. These
arrangements have been found both numerically and experimentally. These
findings also support the new, finite strain model, since the F\"oppl-von
K\'arm\'an equations based on infinitesimal strains do not exhibit such a
behavior.Comment: 16 pages, 5 figure
Disappearance of stretch-induced wrinkles of thin sheets: a study of orthotropic films
A recent paper [Healey et al., J. Nonlin. Sci., 2013, 23, 777-805.] predicted the disappearance of the stretch-induced wrinkled pattern of thin, clamped, elastic sheets by numerical simulation of the Föppl-von Kármán equations extended to the finite in-plane strain regime. It has also been revealed that for some aspect ratios of the rectangular domain wrinkles do not occur at all regardless of the applied extension. To verify these predictions
we carried out experiments on thin (20 µm thick adhesive covered) elastomer sheets with different aspect ratios under displacement controlled pull tests. We found that the wrinkled shapes are strongly influenced by the emerging
orthotropy during the extension. To carry out quantitative comparisons we abandoned the assumption about material isotropy and derived the governing equations for an orthotropic medium. In this way we found good agreement
between numerical simulations and experimental data.
Analysis of the negativity of the second Piola-Kirchhoff stress tensor showed that the critical stretch for a bifurcation point at which the wrinkles disappear must be finite for any aspect ratio. On the other hand, there
is no such a bound for the aspect ratio as a bifurcation parameter. Physically this manifests as complicated wrinkled patterns with more than one highly wrinkled zones on the surface in case of elongated rectangles. These arrangements have been found both numerically and experimentally. These findings also support the new, finite strain model, since the Föppl-von Kármán equations based on infinitesimal strains do not exhibit such a behavior