By Sergio R. Idelsohn
This booklet offers and discusses mathematical versions, numerical tools and computational suggestions used for fixing coupled difficulties in technology and engineering. It takes a leap forward within the formula and answer of real-life issues of a multidisciplinary imaginative and prescient, accounting for the entire advanced couplings focused on the actual description. Simulation of multifaceted physics difficulties is a typical job in utilized study and undefined. usually an appropriate solver is outfitted by means of connecting jointly numerous single-aspect solvers right into a community. during this booklet, study in a variety of fields was once chosen for attention: adaptive method for multi-physics solvers, multi-physics phenomena and coupled-field strategies, resulting in computationally extensive structural research. The options that are used to maintain those difficulties computationally reasonable are of detailed curiosity, and make this a necessary book.
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Oskay C, Fish J (2007) Eigendeformation-based reduced order homogenization. Comp Meth Appl Mech Eng 196:1216–1243 30. Yuan Z, Fish J (2009) Multiple scale eigendeformation-based reduced order homogenization. Comput Methods Appl Mech Eng 198(21–26):2016–2038 31. Yuan Z, Fish J (2009) Hierarchical model reduction at multiple scales. Int J Numer Meth Eng 79:314–339 32. Fish J, Yuan Z (2008) N-scale model reduction theory. In Fish J (ed) Multiscale methods: bridging the scales in science and engineering.
Sharma A, Shukla A, Prosser RA (2002) Mechanical characterization of soft materials using high speed photography and split hopkinson pressure bar technique. J Mater Sci 37(5):1005– 1017 28. Oskay C, Fish J (2008) Fatigue life prediction using 2-scale temporal asymptotic homogenization. Comput Mech 42(2):181–195 29. Oskay C, Fish J (2007) Eigendeformation-based reduced order homogenization. Comp Meth Appl Mech Eng 196:1216–1243 30. Yuan Z, Fish J (2009) Multiple scale eigendeformation-based reduced order homogenization.
The second step begins when node p1 hits the punch surface. At this precise moment, the vertical displacement of node p2 , as well as those of all the nodes of line ( p1 , p2 ), are equaled to the one of p1 . This line follows thus the vertical motion of the punch. Concerning the former problematic line, it is remeshed at that stage using a cubic spline in order to precisely follow the boundary of the extruded material. This two-step strategy is symmetrically applied to the lower part of the billet.