We present a geometric Lagrangian formulation for first-order field theories with dissipation. This is based on the $k$-contact geometry introduced in previous paper, and gathers contact mechanics $k$-symplectic theory together. also study symmetries dissipation laws these nonconservative theories, analyze some examples.

The contact mechanics of soft matters is strongly affected by short-range adhesive interactions, which can lead to large deformations and instabilities.

We provide mathematical justification of the emergence of large-scale coherent structure in a two-dimensional fluid system under small-scale random bombardments with small forcing and appropriate scaling assumptions. The analysis shows that the large-scale structure emerging out of the small-scale random forcing is not the one predicted by equilibrium statistical mechanics. But the error is ver...

This work develops a numerical methodology for predicting the performance of an automotive piston ring system by considering contact and lubrication mechanics. The rough surface mechanics occurs on scale much smaller than size rings therefore key aspect model is algorithm that simultaneously solves multiple mechanisms at different scales. finite element method will be used to mechanical deforma...

The data included here provides a basis for understanding "Interior morphology of high-performance polyethylene fibers revealed by modulus mapping" (K.E. Strawhecker, E.J. Sandoz-Rosado, T.A. Stockdale, E.D. Laird, 2016) [1], in specific: the multi-frequency (AMFM) atomic force microscopy technique and its application to ultra-high-molecular-weight Polyethylene (UHMWPE) fibers. Furthermore, the...

Kinematics are widely used in computational processes as input parameters for displacement driven models. Small errors in kinematics can lead to compounded errors in final contact results hence accuracy is of utmost importance [1]. When using registration to acquire kinematics from images, for instance magnetic resonance imaging (MRI), the initial conditions from manual registration may potenti...

Water droplets on rugged hydrophobic surfaces typically exhibit one of the following two states: (i) the Wenzel state [Wenzel RN (1936) Ind Eng Chem 28:988-994] in which water droplets are in full contact with the rugged surface (referred as the wetted contact) or (ii) the Cassie state [Cassie, ABD, Baxter S (1944) Trans Faraday Soc 40:546-551] in which water droplets are in contact with peaks ...