One-dimensional dynamically consistent gradient elasticity models derived from a discrete microstructure Part 2: Static and dynamic response

摘要

This paper is the second in a series of two that focus on gradient elasticity models retrieved from a discrete mictrostructure. In the first paper, the governing equations for a second-order model and a fourth-order model have been derived. In this paper, The proposed models are studied by means of static and dynamic examples, both from an analytical point of view and a Numerical point of view. Details on the spatial discretization are provided. Finally, an experiment is proposed by which the Newly introduced parameter can be determined that is responsible for the nonlocal relation between the continuous and the Discrete field variables.