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A Methodology for Characterization of Material Constants for Strain-locking Materials



Several natural materials and engineered composites exhibit a strain limiting behavior. The effective tangent modulus increases by several orders of magnitude when the strain reaches a critical range. This stiffening is produced when constituents within the composite with a higher relative modulus abruptly take on a larger percentage of the applied load after specific amount of deformation. The tangent modulus increases by an order of magnitude or more, so that the bulk composite material exhibits an effective “strain locking” behavior. A typical structure of such a material is one with a flexible matrix with wavy reinforcements. The strain locking occurs when the wavy reinforcements straighten out. Recently, implicit nonlinear constitutive models have been proposed to describe such materials with strain limits. This paper presents and validates a methodology for systematically characterizing the parameters of a strain limiting implicit constitutive model from experimentally obtained stress-strain data. The proposed methodology uses an intermediate function space to find the best fit parameters of the implicit constitutive model. The proposed characterization method employs two distinct phases. The first phase entails matching the best fit coefficients of intermediate functions that represent the experimental data and material constitutive model. This provides a good initial point for refining the coefficients of the constitutive law with a direct minimization of the error between the experimental and modeled stress-strain data. The proposed method is demonstrated using an experimental data set obtained from the literature that exhibits a highly abrupt tangent modulus shift and resembles a bilinear elastic material. The resulting parameter values are shown to be at a true minimum within the parameter space.


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