Computational adhesion - Numerical methods for adhesive contact problems at multiple length scales.
Final Report Abstract
This section summarizes the achievements that have been made within project, both within the originally proposed subprojects (P1 – P4) and in additional fields that turned out to be important. In P1 two novel energy-momentum schemes were developed for the time integration of dynamic adhesion problems. Both schemes are considerably more accurate than existing methods adapted to adhesion. The second scheme further turns out to be computationally not significantly more expensive than classical Newmark’s method, while being more robust. Besides, a contact criterion was formulated to distinguish between adhesion- and impact-dominated problems. In addition, a C 1 -continuous time integration method was developed, which was originally intended for adhesive contact problems. It turned out that instead, this method is ideally suited for temporally smooth mechanical problems that require high accuracy especially for long-term simulations. In P2 an unbiased, robust, and accurate contact algorithm was developed, denoted the two-half pass algorithm. Additionally, a general, both theoretical and computational framework was formulated to capture various classes of contact based on surface formulations. These include classical frictionless and frictional contact, van der Waals adhesion, cohesive zone models, and electrostatic interactions. The framework was also applied in P4 to combine dry adhesion and friction. Besides, the contact algorithm was applied to investigate self-cleaning properties of gecko setae, self-adhesion of thin strips and 3D solids, and facile detachment (or non-sticking) of insect acanthae. To increase both the accuracy and efficiency further, in P3 different surface enrichment techniques were proposed that are based either on high-order Lagrangian, Hermite, or NURBS shape functions. In particular for adhesive and frictional contact, C 1-continuously enriched (e.g., NURBS) elements lead to considerably more robust contact algorithms. They were applied, for instance, to peeling of gecko spatulae from rough surfaces, rubber friction, dynamic adhesion, and to various problems involving combined friction and adhesion. Also, different strategies were proposed for adaptive mesh and quadrature refinement. Moreover, an automatic mesh generation method was developed, which combines accurate T-spline surface meshes (obtained from a commercial CAD software) with a conventional, linear bulk element mesh. Within a multiscale modeling framework, a reduced spatula model has been developed that is based on an efficient beam finite element formulation. As a comparison with the original, solid model reveals, the reduced model requires less than 1 % of the computational degrees of freedom, while remaining remarkably accurate. This model was also used to construct a refined model of an entire gecko seta. Also, directional adhesion was studied for both individual spatulae (modeled as a beam) and setal lamellae (modeled as an anisotropic continuum). In P4 a cohesive zone model was adjusted to capture the behavior of the van der Waals model for mode I debonding. It was then applied to tangential peeling of gecko spatulae. To include also frictional sliding, a general framework was developed that can incorporate various phenomenological sliding laws. Inspired by existing theoretical and experimental studies, different laws were proposed for frictional sliding. One of these laws seems to be especially promising for the modeling of frictional sliding in bio-adhesive fibrils. In addition, it can be applied to model friction of smooth rubber surfaces. Besides the points mentioned above, it was possible to work on numerous related topics, especially because of the good progress of the research group. In cooperation with a research laboratory of École Centrale de Lyon, preliminary experiments were performed for frictional adhesion of smooth rubber spheres. Also, a collaboration was started to further investigate bio-mechanic systems like friction of insects. Other important topics include: membrane and capillary adhesion; a post-processing scheme for adhesive contact; and shape optimization of flexible adhesive systems at various length scales. In total, the research funded by this project resulted in more than 20 publications in renowned journals, two doctoral dissertations, and about 45 presentations at international conferences.
Publications
- (2011). Enriched contact finite elements for stable peeling computations. Int. J. Numer. Methods Eng., 87:593–616
Sauer, R. A.
- (2011). The peeling behavior of thin films with finite bending stiffness and the implications on gecko adhesion. J. Adhesion, 87(7–8):624–643
Sauer, R. A.
- (2013). A computational contact formulation based on surface potentials. Comput. Methods Appl. Mech. Eng., 253:369–395
Sauer, R. A. and De Lorenzis, L.
(See online at https://doi.org/10.1016/j.cma.2012.09.002) - (2013). An energy-momentum-conserving temporal discretization scheme for adhesive contact problems. Int. J. Numer. Methods Eng., 93(10):1057–1081
Gautam, S. S. and Sauer, R. A.
(See online at https://doi.org/10.1002/nme.4422) - (2014). A geometrically exact finite beam element formulation for thin film adhesion and debonding. Finite Elem. Anal. Des., 86:120–135
Sauer, R. A. and Mergel, J. C.
(See online at https://doi.org/10.1016/j.finel.2014.03.009) - (2014). Computational optimization of adhesive microstructures based on a nonlinear beam formulation. Struct. Multidiscip. Optim., 50(6):1001– 1017
Mergel, J. C., Sauer, R. A., and Saxena, A.
(See online at https://doi.org/10.1007/s00158-014-1091-1) - (2014). NURBS-enriched contact finite elements. Comput. Methods Appl. Mech. Eng., 275:55–75
Corbett, C. J. and Sauer, R. A.
(See online at https://doi.org/10.1016/j.cma.2014.02.019) - (2015). An unbiased computational contact formulation for 3D friction. Int. J. Numer. Methods Eng., 101(4):251–280
Sauer, R. A. and De Lorenzis, L.
(See online at https://doi.org/10.1002/nme.4794) - (2015). Three-dimensional isogeometrically enriched finite elements for frictional contact and mixed-mode debonding. Comput. Methods Appl. Mech. Eng., 284:781–806
Corbett, C. J. and Sauer, R. A.
(See online at https://doi.org/10.1016/j.cma.2014.10.025) - (2016). A survey of computational models for adhesion. J. Adhesion, 92(2):81–120
Sauer, R. A.
(See online at https://doi.org/10.1080/00218464.2014.1003210)
