Computational Contact and Impact Mechanics: Fundamentals of by Tod A. Laursen

By Tod A. Laursen

This ebook comprehensively treats the formula and finite aspect approximation of touch and effect difficulties in nonlinear mechanics. meant for college kids, researchers and practitioners drawn to numerical reliable and structural research in addition to engineers and scientists facing applied sciences during which tribological reaction has to be characterised, the ebook contains an introductory yet designated assessment of nonlinear finite aspect formulations prior to facing touch and impression particularly. issues encompassed comprise continuum mechanics, mathematical constitution, variational framework and finite aspect implementations linked to contact/impact interplay. also, very important and at present rising examine themes in computational touch mechanics are brought, encompassing such issues as tribological complexity, conservative therapy of inelastic impression interplay and novel spatial discretization ideas.

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Additional resources for Computational Contact and Impact Mechanics: Fundamentals of Modeling Interfacial Phenomena in Nonlinear Finite Element Analysis

Example text

92), taking the time derivative of it and then transforming produces an objective object. This idea is appropriately generalized mathematically by the concept of the Lie derivative. 116) where 'Pt* denotes the push-forward operation, and 'Pt denotes the pullback operation. In this case, the tensor m is pulled back to the reference configuration, time differentiated, and then pushed back forward to the spatial frame. The resulting quantity is guaranteed to be frame indifferent, for the same reasons exemplified above (with the pull-back and push-forward being to the reference configuration rather than to the rotated one) for the Green-Naghdi rate.

Finally, owing to the two configurations that must be considered when formulating the finite strain problem, a distinction will be made within the indices associated with coordinates in the reference configuration, and their counterparts in the current configuration. Specifically, uppercase roman indices I, J, K, .. will be used in association with the reference configuration, and lowercase ones i, j, k, ... will be used for spatial components. Thus, one may write X = {XJ}, and:1; = {Xi}. 18 2.

91) c(t) is a relative rigid body translation between the original frame and observer *, while a relative rotation is produced by the proper orthogonal tensor Q(t). To observer *, the motion appears as defined by 3:* = cp*(X,t) = c(t) + Q(t)cp(X,t). 95) would be present. Clearly, I is not objective. 98) which shows us that d is objective. So, we have a spatial rate of strain object, d, which is objective. The question arises whether corresponding reference measures of rate are objective. It turns out that such material rates are automatically objective, since they do not change when superimposed rigid body motions occur spatially.

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