A review on the nonlinear dynamics of hyperelastic structures

Abstract This paper presents a critical review of the nonlinear dynamics of hyperelastic structures. Hyperelastic structures often undergo large strains when subjected to external time-dependent forces. Hyperelasticity requires specific constitutive laws to describe the mechanical properties of different materials, which are characterised by a nonlinear relationship between stress and strain. Due to recent recognition of the high potential of hyperelastic structures in soft robots and other applications, and the capability of hyperelasticity to model soft biological tissues, the number of studies on hyperelastic structures and materials has grown significantly. Thus, a comprehensive explanation of hyperelastic constitutive laws is presented, and different techniques of continuum mechanics, which are suitable to model these materials, are discussed in this literature review. Furthermore, the sensitivity of each hyperelastic strain energy density function to coefficient variation is shown for some well-known hyperelastic models. Alongside this, the application of hyperelasticity to model the nonlinear dynamics of polymeric structures (e.g., beams, plates, shells, membranes and balloons) is discussed in detail with the assistance of previous studies in this field. The advantages and disadvantages of hyperelastic models are discussed in detail. This present review can stimulate the development of more accurate and reliable models.