## 1 Introduction
The first condition is only satisfied when employing structures similar to the generalized Kelvin model. This implies the necessity of knowing the creep compliance beforehand, which requires providing corresponding data through creep tests. The second condition typically applies only to some incompressible materials. However, meeting both conditions in practical engineering can be challenging due to many problems. For example, in the viscoelastic analysis of solid rocket motor propellants [10; 11], which are polymer materials, relaxation tests rather than creep tests are usually conducted. These tests provide data on the relaxation modulus varying with time instead of the creep compliance [12]. Additionally, Poisson's ratio is not constant. In such cases, the direct application of the initial strain method is not feasible. Another approach is to employ an integral constitutive relationship [13]. This approach considers the stress-time history sum of a series of rectangular pulses over small time intervals. Utilizing the Boltzmann superposition principle, the following form of the hereditary integral is derived [14]:  
\[\sigma(t)=E(t)\varepsilon_{0}+\int_{0}^{t}E(t-\tau)\frac{d\varepsilon(\tau)}{ d\tau}d\tau \tag{2}\]  
where \(\sigma(t)\) and \(\varepsilon(\tau)\) represent stress and strain, respectively, both of which are functions of time; \(E(t)\) represents the relaxation modulus of the viscoelastic material; and \(\varepsilon_{0}\) representsthe initial strain. Current commercial software packages such as ABAQUS 2022 and ANSYS 2023 utilize this constitutive relationship [15; 16]. However, these commercial programs require the input of shear relaxation modulus \(G(t)\) and bulk relaxation modulus \(K(t)\), which decompose deformation at any given time into volumetric and shear components. Typically, these two relaxation moduli are assumed to follow a Prony series, with material parameters fitted from experimental data. Once these relaxation modulus expressions are determined, the remaining process is similar to the elastic finite element method. Time is discretized into a series of intervals, and numerical integration methods are used to obtain displacement and strain for each time interval. The advantage of this method lies in its generality. Regardless of the specific constitutive model used, as long as the Prony series of the relaxation modulus is obtained, the analysis can be completed following steps similar to those of traditional finite element methods. However, the drawback is apparent: forming the stiffness matrix must be repeated for each time step, resulting in high computational complexity and lower efficiency. Another drawback is the requirement for shear and bulk relaxation tests to obtain corresponding material parameters for these commercial software packages. Since these tests are operationally complex, they are rarely conducted in practical engineering. Most relaxation tests involve tension or compression [17], providing the relaxation modulus \(E(t)\) over time [18; 19]. Then, assuming a constant Poisson's ratio, the bulk and shear moduli are derived from these parameters and input into the commercial software. However, this conversion process inevitably introduces additional errors. Therefore, while this method uses shear relaxation and bulk relaxation moduli, it relies solely on the elastic relaxation modulus and a constant Poisson's ratio [20; 21; 22]. In summary, it is clear that whether developing custom finite element programs or using commercial software for analysis, it is commonly assumed that Poisson's ratio remains constant throughout the entire analysis process. However, this assumption is inaccurate for many practical viscoelastic problems. For example, experimental results on Poisson's ratio of viscoelastic materials like polymers show that it is not constant throughout the testing. It tends to increase towards \(1/2\) with rising temperature and prolonged loading time, while it decreases towards \(1/3\) with decreasing temperature and shorter loading time.