Fig. 2. (A) Straight horizontal segment along the body of a fish. The thick central line indicates the longitudinal axis that keeps the same length during bending. The numbered red lines represent muscle-fibre segments that are assumed to lie in the horizontal section. (B) Simple beam deformation of the body segment of A, with a lateral expansion at the concave side and a lateral compression at the convex side. Material points are assumed to have a constant dorso-ventral position and an incompressibility constraint is applied. At the concave side, the muscle-fibres segments near the skin (4 and 8) are able to shorten much more than those near the central axis (3 and 7); at the convex side, the segments directly underneath the skin (1 and 5) lengthen much more than the more medial segments (2 and 6). (C) Bending with an added shear deformation is caused by oblique muscle fibres near the medial plane (see main text). The shear deformation is maximal at the central axis and zero at the skin. This deformation enables muscle fibres near the central axis to contract at the concave side if they have a suitable orientation such as fibre segment 3, in spite of the constant length of the central axis. The strain in segments 3 and 4 is approximately the same. Segments 1 and 2 lengthen by similar percentages. Fibre segments 6 and 7 do not change more in length than in B, because they are orientated parallel to the axis. The orientations of segments 6 and 7 would result in very low strain and work output and are not present in real fish. The shear deformation causes a longitudinal shift of muscle tissue and skin relative to the central axis. The shear angle near the medial plane is denoted by .