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Crossing Scales: Data-Driven Determination of the Micro-scale Behavior of Polymers From Non-homogeneous Tests at the Continuum-Scale

Article dans une revue avec comité de lecture
Author
AMORES, Víctor J.
302798 Universidad Politécnica de Madrid [UPM]
MONTÁNS, Francisco J.
302308 University of Florida [Gainesville] [UF]
302798 Universidad Politécnica de Madrid [UPM]
CUETO, Elías
161327 Aragón Institute of Engineering Research [Zaragoza] [I3A]
CHINESTA, Francisco
86289 Laboratoire Procédés et Ingénierie en Mécanique et Matériaux [PIMM]
564849 ESI Group [ESI Group]

URI
http://hdl.handle.net/10985/22235
DOI
10.3389/fmats.2022.879614
Date
2022-05
Journal
Frontiers in Materials

Abstract

We propose an efficient method to determine the micro-structural entropic behavior of polymer chains directly from a sufficiently rich non-homogeneous experiment at the continuum scale. The procedure is developed in 2 stages: First, a Macro-Micro-Macro approach; second, a finite element method. Thus, we no longer require the typical stress-strain curves from standard homogeneous tests, but we use instead the applied/reaction forces and the displacement field obtained, for example, from Digital Image Correlation. The approach is based on the P-spline local approximation of the constituents behavior at the micro-scale (a priori unknown). The sought spline vertices determining the polymer behavior are first pushed up from the micro-scale to the integration point of the finite element, and then from the integration point to the element forces. The polymer chain behavior is then obtained immediately by solving a linear system of equations which results from a least squares minimization error, resulting in an inverse problem which crosses material scales. The result is physically interpretable and directly linked to the micro-structure of the material, and the resulting polymer behavior may be employed in any other finite element simulation. We give some demonstrative examples (academic and from actual polymers) in which we demonstrate that we are capable of recovering “unknown” analytical models and spline-based constitutive behavior previously obtained from homogeneous tests.

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