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For linear viscoelastic materials, this paper proposes a finite element analysis method based on an integral constitutive relationship that can simultaneously consider the relaxation behavior of the elastic modulus and the creep Poisson’s ratio. Firstly, the generalized Maxwell model is employed to depict the relaxation characteristics of the elastic modulus, while the generalized Kelvin model is used to represent the creep Poisson’s ratio. Subsequently, the element relaxation stiffness matrix is established, thereby forming a convolutional finite element equation. Furthermore, the recursive calculation of the convolutional integral is derived, and the calculation steps of the finite element for viscoelasticity considering the time-dependent nature of both the elastic modulus and Poisson’s ratio are established. Finally, the accuracy of the proposed algorithm is verified through two numerical examples with linear viscoelastic material. The results indicate that the proposed variable stiffness method for the finite element analysis of linear viscoelastic materials can simultaneously consider the changes in the elastic modulus and Poisson’s ratio over time, thereby establishing a new path and idea for the more accurate simulation of viscoelastic materials’ mechanical properties. Compared with the initial strain method for linear viscoelastic materials, the variable stiffness method proposed in this paper effectively avoids the assumption of constant stress during the micro time interval, thus significantly enhancing the finite element calculation accuracy of linear viscoelastic materials. The proposed method establishes a simulation algorithm that matches existing commercial software with viscoelastic material experiments by considering the elastic modulus and Poisson’s ratio as material parameters.

Anther dehiscence is an important process to release pollen and then is a critical event in pollination. In the wheat photo-thermo-sensitive genic male sterility (PTGMS) line, pollen cannot release from anther since the anther cannot dehisce during anther dehiscence stage in a sterile condition. In this study, we carried out RNA-sequencing to analyze the transcriptome of one wheat PTGMS line BS366 during anther dehiscence under fertile and sterile conditions to explore the mechanism. We identified 6306 differentially expressed genes (DEGs). Weighted gene co-expression network analysis (WGCNA) and KEGG analysis showed that DEGs were mainly related to “hormone signal transduction pathway” and “starch and sucrose metabolism”. We identified 35 and 23 DEGs related hormone signal transduction and sucrose metabolism, respectively. Compared with conventional wheat Jing411, there were some changes in the contents of hormones, including JA, IAA, BR, ABA and GA3, and sucrose, during three anther dehiscence stages in the sterile condition in BS366. We performed qRT-PCR to verify the expression levels of some critical DEGs of the hormone signaling pathway and the starch and sucrose metabolism pathway. The results showed disparate expression patterns of the critical DEGs of the hormone signaling pathway and the starch and sucrose metabolism pathway in different conditions, suggesting these genes may be involved in the regulation of the anther dehiscence in BS366. Finally, we conducted a hypothesis model to reveal the regulation pathway of hormones and sucrose on anther dehiscence. The information provided new clues to the molecular mechanisms of anther dehiscence in wheat and improved wheat hybrid breeding.