可压缩超弹性圆柱形通道内的内压和外约束不稳定性
Instabilities in a compressible hyperelastic cylindrical channel due to internal pressure and external constraints
摘要：
由软材料制成的加压圆柱形通道在生物系统、软机器人和超材料设计中无处不在。本文研究了内压作用下可压缩超弹性圆柱形厚壁长通道的大变形问题。所施加的压力可导致沿轴向或周向方向的弹性分叉。增量理论被用来推导偏微分方程，支配的分叉行为的圆柱形通道。两种情况下的外表面上的圆柱体，即，自由和约束的边界条件进行了研究，以了解其对屈曲行为的影响。采用复合矩阵法对推导的方程进行数值求解，得到临界压力。在这两种边界条件下，研究了圆柱体厚度和材料的可压缩性对临界压力的影响。结果表明，对于各向同性材料，分叉发生沿轴向方向的圆柱相比，在较低的临界压力的周向方向所考虑的所有情况。最后，我们证明了可剪裁的分叉行为的圆筒沿长度方向增加钢筋。通过改变材料参数，研究了触发周向分叉的各向异性超弹性材料行为。
英文摘要：
Pressurised cylindrical channels made of soft materials are ubiquitous in biological systems, soft robotics, and metamaterial designs. In this paper, we study large deformation of a long, thick-walled, and compressible hyperelastic cylindrical channel under internal pressure. The applied pressure can lead to elastic bifurcations along the axial or circumferential direction. Incremental theory is used to derive the partial differential equations that govern the bifurcation behaviour of the cylindrical channel. Two cases of boundary conditions on the outer surface of the cylinder, namely, free and constrained are studied to understand their influence on the buckling behaviour. The derived equations are solved numerically using the compound matrix method to evaluate the critical pressure. The effects of the thickness of the cylinder and the compressibility of the material on the critical pressure are investigated for both the boundary conditions. The results reveal that for an isotropic material, the bifurcation occurs along the axial direction of the cylinder at lower critical pressure compared to the circumferential direction for all cases considered. Finally, we demonstrate the tailorability of bifurcation behaviour of the cylinder by adding reinforcements along the length of cylinder. The anisotropic hyperelastic material behaviour for triggering the bifurcation in the circumferential direction is studied by varying the material parameters.
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