Abstract
This paper represents a first attempt to derive one-dimensional models with non-convex strain energy starting from “genuine” three-dimensional, nonlinear, compressible, elasticity theory. Following the usual method of obtaining beam theories, we show here for a constrained kinematics appropriate for long cylinders governed by a polyconvex, objective, stored energy function, that the bar model originally proposed by Ericksen [3] is obtainable but enriched by an additional term in the strain gradient. This term, characteristic of nonsimple grade-2 materials, penalizes interfacial energies and makes single-interface two-phase solutions preferred. The resulting model has been proposed by a number of authors to describe the phenomenon of necking and cold drawing in polymeric fibers and, here, we discuss its suitability to interpret also the elastic-plastic behavior of metallic tensile bars under monotone loading.
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Buonsanti, M., Royer-Carfagni, G. From 3-D Nonlinear Elasticity Theory to 1-D Bars with Nonconvex Energy. Journal of Elasticity 70, 87–100 (2003). https://doi.org/10.1023/B:ELAS.0000005633.22491.af
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DOI: https://doi.org/10.1023/B:ELAS.0000005633.22491.af