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 引用本文: 彭向峰, 李录贤. 超弹性材料本构关系的最新研究进展[J]. 力学学报, 2020, 52(5): 1221-1234.
Peng Xiangfeng, Li Luxian. STATE OF THE ART OF CONSTITUTIVE RELATIONS OF HYPERELASTIC MATERIALS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(5): 1221-1234.
 Citation: Peng Xiangfeng, Li Luxian. STATE OF THE ART OF CONSTITUTIVE RELATIONS OF HYPERELASTIC MATERIALS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(5): 1221-1234.

## STATE OF THE ART OF CONSTITUTIVE RELATIONS OF HYPERELASTIC MATERIALS

• 摘要: 超弹性材料是工程实际中的常用材料, 具有在外力作用下经历非常大变形、在外力撤去后完全恢复至初始状态的特征. 超弹性材料是典型的非线性弹性材料, 其性能可通过材料的应变能函数予以表征. 近几十年来, 围绕应变能函数形式的构造, 已提出许多超弹性材料本构关系研究的数学模型和物理模型, 但适用于多种变形模式和全变形范围的完全本构关系仍是该领域期待解决的重要问题. 本文从3个不同角度, 对超弹性材料本构关系研究的最新进展进行了总结和分析: (1)不同体积变化模式, 包含不可压与可压两种; (2)多变形模式, 包含单轴拉伸、剪切、等双轴以及复合拉剪等多个种类; (3)全范围变形程度, 包含小变形、中等变形到较大变形范围. 超弹性材料本构关系研究的最新进展表明, 为了全面描述具体材料的实验数据并在实际问题中应用超弹性材料, 需要建立适合于多种变形模式和全变形范围的可压超弹性材料的完全本构关系. 对实际超弹性材料完全本构关系的建立及可压超弹性材料应变能函数的构造, 笔者还提出了相应的实施步骤和研究方法.

Abstract: Hyperelastic materials are commonly used in practical engineering with the prominent feature that a very large deformation may be produced under a force but the initial state can be completely recovered when the force is removed. Hyperelastic materials are typically nonlinear elastic ones, whose behaviors are in general characterized by their strain energy functions. For several decades, a lot of mathematical models and physical models have been proposed to study their constitutive relations through constructing the form of energy functions. However, a complete constitutive relation suitable for varied deformation modes and the entire deformation range is still the significant issue to expect in this field. This paper summarizes and analyzes the latest research status of constitutive relations of hyperelastic materials from three perspectives: (1) volume change modes including incompressible and compressible ones; (2) deformation modes such as uniaxial tension, shearing, biaxial tension and combined stretch and shear; (3) the entire range of deformation including small deformation, moderate deformation and large deformation. The latest progresses indicate that, in order to comprehensively describe experimental data of a given hyperelastic material and to apply it in practical problems, it is necessary to establish a complete constitutive relationship of compressible hyperelastic materials, which is suitable for varied deformation modes and the entire range of deformation. The authors suggest an implementation procedure for establishing the complete constitutive relationship of an actual hyperelastic material and an approach to construct the strain energy function of a compressible material.

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