The deformation of an initially straight elastic strip can be determined by prescribing the two end angles and the distance between the two ends. At certain end angles and end distance, snapping motion of the elastica may occur. A collection of these end angle pairs is called the snap boundary of the planar elastica. In the snap boundary theory developed previously (Cazzolli and Corso, 2019) self-intersection of the elastica was admitted. In this paper we extend the theory in Cazzolli and Corso (2019) by excluding self-intersection and admitting only self-contact. We define a dimensionless end distance as the ratio between the physical end distance and the total length of the planar elastica. When the dimensionless end distance is great than 0.246, the planar elastica does not involve self-intersection or self-contact. Therefore, the snap boundary theory previously developed in Cazzolli and Corso (2019) still holds. On the other hand, when the dimensionless end distance is smaller than 0.246 the snap boundaries for self-intersection and self-contact will be different. In this range one of the two stable configurations inside the snap boundary may contact itself. When the dimensionless end distance is further reduced to smaller than 0.151, both of the two stable equilibrium configurations may involve self-contact.

可以通过规定两个端角和两端之间的距离来确定最初笔直的弹性条的变形。在某些端角和端距处，可能会发生弹性体的弹跳运动。这些端角对的集合称为平面弹性的捕捉边界。在先前开发的捕捉边界理论中（Cazzolli和Corso，2019），弹性体的自相交被接受。在本文中，我们通过排除自相交并仅允许自接触来扩展Cazzolli和Corso（2019）中的理论。我们将无量纲的末端距离定义为物理末端距离与平面弹性的总长度之比。当无因次端距大于0.246时，平面弹性不涉及自相交或自接触。所以，之前在Cazzolli和Corso（2019）中发展的捕捉边界理论仍然成立。另一方面，当无量纲的末端距离小于0.246时，自相交和自接触的捕捉边界将不同。在此范围内，捕捉边界内的两个稳定配置之一可能会与其自身接触。当无量纲的末端距离进一步减小到小于0.151时，两个稳定的平衡构型都可能涉及自接触。