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Published January 1, 2017 | public
Journal Article

Local and nonlocal continuum modeling of inelastic periodic networks applied to stretching-dominated trusses


We present a nonlocal continuum model and its numerical implementation to describe the macroscale response of periodic discrete networks via second-order homogenization. The scale-bridging technique is applied to the specific example of stretching-dominated elastic and inelastic periodic truss networks. Experiments on small-scale truss structures have highlighted the importance of nodal connections on the effective stiffness and strength. Therefore, we describe the mechanics of trusses by accounting for the stretching of truss members and the deformation of nodes. For the representative 2D examples of lattices having square and triangular architectures and for example bar and nodal constitutive laws, we show that a simple continuum model based on affinely deforming a representative unit cell is sufficient to reproduce the nonlinear elastic behavior of discrete trusses. By contrast, localization that arises, e.g., from inelastic deformation requires a refined model. This is where the presented nonlocal continuum model is capable of accurately capturing details of localized deformation. We illustrate the performance of the model by comparing the results of example finite element simulations using the continuum constitutive model to discrete lattice calculations with elastic–plastic bars. Optimal performance is achieved when the representative unit cell of the continuum model agrees with the actual size of the discrete truss unit cell, which accounts for size effects even in regimes where a separation of scales between finite element size and unit cell size does not strictly apply.

Additional Information

© 2016 Elsevier B.V. Received 10 April 2016; received in revised form 22 September 2016; accepted 23 September 2016. Available online 29 September 2016. Support from the National Science Foundation (NSF) through CAREER award CMMI-1254424 is gratefully acknowledged.

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