6 research outputs found
C1-continuous space-time discretization based on Hamilton's law of varying action
We develop a class of C1-continuous time integration methods that are
applicable to conservative problems in elastodynamics. These methods are based
on Hamilton's law of varying action. From the action of the continuous system
we derive a spatially and temporally weak form of the governing equilibrium
equations. This expression is first discretized in space, considering standard
finite elements. The resulting system is then discretized in time,
approximating the displacement by piecewise cubic Hermite shape functions.
Within the time domain we thus achieve C1-continuity for the displacement field
and C0-continuity for the velocity field. From the discrete virtual action we
finally construct a class of one-step schemes. These methods are examined both
analytically and numerically. Here, we study both linear and nonlinear systems
as well as inherently continuous and discrete structures. In the numerical
examples we focus on one-dimensional applications. The provided theory,
however, is general and valid also for problems in 2D or 3D. We show that the
most favorable candidate -- denoted as p2-scheme -- converges with order four.
Thus, especially if high accuracy of the numerical solution is required, this
scheme can be more efficient than methods of lower order. It further exhibits,
for linear simple problems, properties similar to variational integrators, such
as symplecticity. While it remains to be investigated whether symplecticity
holds for arbitrary systems, all our numerical results show an excellent
long-term energy behavior.Comment: slightly condensed the manuscript, added references, numerical
results unchange
Contact with coupled adhesion and friction: Computational framework, applications, and new insights
Contact involving soft materials often combines dry adhesion, sliding
friction, and large deformations. At the local level, these three aspects are
rarely captured simultaneously, but included in the theoretical models by
Mergel et al. (2019). We here develop a corresponding finite element framework
that captures 3D finite-strain contact of two deformable bodies. This framework
is suitable to investigate sliding friction even under tensile normal loads.
First, we demonstrate the capabilities of our finite element model using both
2D and 3D test cases, which range from compliant tapes to structures with high
stiffness, and include deformable-rigid and deformable-deformable contact. We
then provide new results on the onset of sliding of smooth elastomer-glass
interfaces, a setup that couples nonlinear material behavior, adhesion, and
large frictional stresses. Our simulations not only agree well with both
experimental and theoretical findings, they also provide new insights into the
current debate on the shear-induced reduction of the contact area in
elastomeric contact
Continuum contact models for coupled adhesion and friction
We develop two new continuum contact models for coupled adhesion and
friction, and discuss them in the context of existing models proposed in the
literature. Our new models are able to describe sliding friction even under
tensile normal forces, which seems reasonable for certain adhesion mechanisms.
In contrast, existing continuum models for combined adhesion and friction
typically include sliding friction only if local contact stresses are
compressive. Although such models work well for structures with sufficiently
strong local compression, they fail to capture sliding friction for soft and
compliant systems (like adhesive pads), for which the resistance to bending is
low. This can be overcome with our new models. For further motivation, we
additionally present experimental results for the onset of sliding of a smooth
glass plate on a smooth elastomer cap under low normal loads. As shown, the
findings from these experiments agree well with the results from our models. In
this paper we focus on the motivation and derivation of our continuum contact
models, and provide a corresponding literature survey. Their implementation in
a nonlinear finite element framework as well as the algorithmic treatment of
adhesion and friction will be discussed in future work
Amtsblatt des GroĂherzoglich Hessischen Oberschulraths No 32. Darmstadt am 4. April 1838
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