Hyperelastic constitutive model for rubber-like materials based on the first Seth strain measures invariant

Dynamic analysis of rubber-like material using absolute nodal coordinate formulation based on the non-linear constitutive law

“…Materials described by this model are called Hookean material [18]. The Neo-Hookean material model is an extension of the Hookean material model for the case of a large deformation.…”

“…The beam was assumed to be subjected to only gravitational force. The material constants shown in Table 1 were used to describe the elastic force models of (15), (18), and (21). The incompressibility constant, which is used in the volumetric energy function of (12), was assumed to be α = 1000 MPa.…”

“…To describe the hyper-elastic characteristic of rubber, the strain energy density function is used. The strain energy density function of isotropic materials which satisfies the principle of objectivity is a function of the strain invariants I 1 , I 2 , and I 3 that are defined as [18] …”

“…The global position vector of a point on the beam is represented using the global shape function and absolute coordinates as [17,18] …”

“…Based on the tensile test results, the material constant of each model was calculated, and is presented in Table 1. Using the material constants, the elastic forces given by (15), (18), and (21) were determined. Figure 2 compares the stress-stretch curves of the test data and the non-linear constitutive models.…”