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Fractional calculus has become a potent tool for simulating the complexity of interactions in tumor-immune system dynamics. This paper investigates the existence and uniqueness of its approximation solutions of a fractional model of tumor-immune surveillance. This analysis is essential for proving the validity and dependability of the model and provides a more in-depth understanding of the dynamics of the tumor-immune surveillance system. Second, we examine the fractional model's numerical features. We utilize a numerical technique called the Laplace residual power series method to address the equations' complexity and nonlinearity. By defining the answers as a fractional power series, this method enables us to efficiently approximate the solutions. The use of this technique enables us to investigate the temporal evolution of the tumor-immune system, offering important insights into the stability and behavior of the system. We assess the effectiveness of the Laplace residual power series method in locating approximations through a series of thorough numerical simulations. To ensure the correctness and dependability of our method, we compare the numerical findings whenever possible with well-known analytical solutions. [ABSTRACT FROM AUTHOR]

Simulation of the failure process of non-intact rock containing initial cracks, voids, and other discontinuities is a research hotspot in rock mechanics and geotechnical engineering. The damage smear method has attracted wide attention due to its ability to realistically depict the complete failure processes of rock from the microscopic to the macroscopic scale. However, when portraying pre-existed discontinuities, the damage smear method suffers from major difficulties such as mesh dependency and stress singularity. To overcome the limitations of current methodology, this paper proposes a novel non-break modeling strategy inspired by the extended finite element method for dealing with embedded discontinuities, in which the discontinuity of the physical fields across crack faces or the void boundary, as well as the stress singularity at the crack tip, can be characterized by introducing appropriate enrichment functions, and the penalty method is used to impose frictional contact constraints. Applications of the combined method of the improved modeling strategy and damage smear analysis to laboratory-scale and engineering-scale numerical examples show a satisfactory approximation with the analytical solution or experimental observations, indicating that the current modeling strategy can further improve computational accuracy while retaining the advantages of the damage smear method. [ABSTRACT FROM AUTHOR]

This paper presents a theoretical solution for bond-slip behavior of SRC interface based on experiment, numerical simulation, and theoretical derivation. Push-out tests of five specimens were firstly carried out, based on which, the simplified bond-slip model was proposed. The specimen was fabricated using the Q345H-shape steel (400 mm × 200 mm×13 mm × 8 mm) and C50 concrete (350 mm × 600 mm) with a bonding length of 500 mm. A FE model was established based on the bond-slip model to analyze the nonlinear bonding stress that are difficult to obtain from the experiment. The research shows that although the bonding stress in the elastic stage is not uniformly distributed, it is basically uniformly distributed when the ultimate bearing capacity is reached. It proves that assuming the average interfacial bonding stress under ultimate load to replace the maximum bonding stress is reasonable, which is crucial for designer to estimate interface bearing capacity and maximum bonding stress. Moreover, five different stages were obtained by the FE model analysis and the theoretical equations of bonding stress nonlinear distribution were obtained based on the boundary condition of each stage. The theoretical solution clearly showed the relationship between interface nonlinear stress distribution and influencing parameters including the bond area, elasticity modulus of material, section area of specimen, bond-slip constitutive model, and the external load. Based on the theoretical model, the influences of different parameters can be directly obtained without conducting further experiments and establishing different FE models. • The simplified bond-slip model was proposed and nonlinear distributiion of interfacial bonding stress was analyzed. • Assuming the average interfacial bonding stress under ultimate load to replace the maximum bonding stress is reasonable. • Corresponding analytical formulas for the interfacial stress in five different stages were established, respectively. • The theoretical solution showed the quantitative relationship between interface nonlinear stress and influencing parameters. [ABSTRACT FROM AUTHOR]