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Physical interaction with textiles, such as assistive dressing, relies on advanced dextreous capabilities. The underlying complexity in textile behavior when being pulled and stretched, is due to both the yarn material properties and the textile construction technique. Today, there are no commonly adopted and annotated datasets on which the various interaction or property identification methods are assessed. One important property that affects the interaction is material elasticity that results from both the yarn material and construction technique: these two are intertwined and, if not known a-priori, almost impossible to identify through sensing commonly available on robotic platforms. We introduce Elastic Context (EC), a concept that integrates various properties that affect elastic behavior, to enable a more effective physical interaction with textiles. The definition of EC relies on stress/strain curves commonly used in textile engineering, which we reformulated for robotic applications. We employ EC using Graph Neural Network (GNN) to learn generalized elastic behaviors of textiles. Furthermore, we explore the effect the dimension of the EC has on accurate force modeling of non-linear real-world elastic behaviors, highlighting the challenges of current robotic setups to sense textile properties.