By T.A. Laursen (auth.), Peter Wriggers Professor Dr., Udo Nackenhorst Professor Dr. (eds.)
Contact mechanics was once and is a vital department in mechanics which covers a large box of theoretical, numerical and experimental investigations. during this rigorously edited booklet the reader will receive a cutting-edge evaluate on formula, mathematical research and numerical answer strategies of touch difficulties. The contributions accrued during this quantity summarize the lectures provided throughout the 4th touch Mechanics overseas Symposium (CMIS) held in Hannover, Germany, 2005, by means of top scientists within the zone of touch mechanics.
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Additional info for Analysis and Simulation of Contact Problems
Thus, in the combined ﬁnite-discrete element method a ﬁnite-strain elasticity element formulation is adopted. This is best demonstrated on a constant strain triangle. The matrix of the deformation gradient tensor for this element is obtained as follows ∂xc ∂xc ∂xi ∂yi ˆix ˆjx −1 = x1c − x0c x2c − x0c (1) F= ∂yc ∂yc ˆiy ˆjy y1c − y0c y2c − y0c ∂xi ∂yi where the transformation matrix is given by ˆix ˆiy ˆjx ˆjy = x1i − x0i y1i − y0i x2i − x0i y2i − y0i (2) and x0i ,y0i x1i ,y1i , x2i , y2i , x0c , y0c ,x1c ,y1c ,x2c , y2c are initial and current coordinates of node 0, 1 and 2 respectively.
T. Laursen. Computational Contact and Impact Mechanics. Springer Berlin Heildelberg, 2002. 11. M. Puso and T. Laursen. A mortar segment-to-segment contact method for large deformation solid mechanics. Comput. Methods Appl. Mech. , 193(68):601-629, 2004. 12. G. Stadler. Semismooth Newton and augmented Lagrangian methods for a simpliﬁed friction problem. SIAM J. , 15(1):39-62, 2004. 13. K. Willner. Kontinuums- und Kontaktmechanik. Springer, 2003. 14. P. Wriggers. Computational Contact Mechanics. J.
For the stress-strain relation of the material, we consider σ = (λ + 2/3µ) tr(ε) − 3αθ + 2µdev(ε). α denotes the thermal expansion coeﬃcient. The balance conditions are given by −div(σ) = 0 and div(q) = r, where q = −Kgrad(θ) denotes the heat ﬂux, the mass density and r the heat source. On the contact zone, we use the heat law qc = kc [θ] with the contact heat ﬂux qc = q · n. , , where λm denotes the mechanical Lagrange multiplier. Let λθ = p∈S qp ψp be the thermal part of the Lagrange multiplier representing the heat ﬂux qc .
Analysis and Simulation of Contact Problems by T.A. Laursen (auth.), Peter Wriggers Professor Dr., Udo Nackenhorst Professor Dr. (eds.)