5:15 PM - 6:45 PM
[SSS05-P10] Proposal of super/subloading elastoplastic friction model and numerical simulation of stick-slip phenomenon
Keywords:friction, stick-slip , fault, elastoplastic costitutive law, numerical analysis, time-dependency
The development of friction constitutive laws is indispensable for elucidating frictional phenomena at plate boundaries and faults. In this paper, we propose a super/subloading elastoplastic friction model1), 2). The model is characterized by the following two points: (1) the state in which the static friction coefficient is larger than the kinetic friction coefficient is considered as the "structure" of friction coefficient, and (2) the decay and healing of the structure is described by an evolution rule for capturing state transition from static to kinetic friction. In the present manuscript, we indicate that the model can reproduce both stick-slip and steady slip phenomena in a mass-spring system.
The fundamental equations are listed in Fig. 1. The superloading surface concept was originally proposed by Asaoka et al.2) to describe the typical behavior of naturally deposited soils. As shown in Fig. 2, sensitive clays have a higher strength than its remolded and normally consolidated sample due to the presence of soil skeleton structure. Based on the analogy between the softening behavior of soil and the transition process from static to kinetic friction (Fig. 3), we analogically describe friction-induced phenomena using the superloading surface concept. In the proposed model, Coulomb's criterion (gray line) is regarded as a normal yield surface, as shown in Fig. 4. Then, a superloading surface (orange line), and a subloading surface (blue line) are introduced assuming their similarities. While the installation of the superloading surface allows a state above the normal yield surface (the blue region in Fig. 4), the subloading surface describes cyclic plasticity inside the superloading surface. The non-associated flow rule restricts only tangential plastic displacements. The evolution rule for R conformed to the previous model1). The evolution rule for R* consists of two terms (Fig. 5): The first term represents the softening from static to kinetic friction due to plastic slip (degradation of the structure), and the second term represents the healing from kinetic to static friction with time (contact surface adhesion and aging effect). This model can explain the continuous change of frictional force within the framework of elastoplasticity theory and provide coherent description on the stick/slip state. Detailed formulation can be seen in Toyoda et al.3).
Next, we solved the stick-slip phenomenon of a mass-spring system (Fig. 6) using the proposed model. The one-dimensional rate-type equation of motion was implicitly solved. The constitutive parameters of the contact surface are prescribed in Fig. 6, the analysis was conducted using the five cases listed in Table 1.
First, the slip displacement - time relation for Cases 1 - 3 with different coefficients κ and ξ in the evolution rule of R* is shown in Fig. 7(a). As a result of calculations, in Case 1, where the friction coefficient was not changed, a steady slip was obtained. In Case 3, where both decay and healing of structure were considered, a staircase-like slip-displacement - time relation (stick-slip phenomenon) was obtained.
Next, we discuss the effect of normal stress variation on the stick-slip phenomenon. Figure 7(b) shows the results of Cases 4 and 5, where the normal stress gradually decreased/increased with time relative to Case 3. While the initial slip was hindered/promoted in Case 4/Case 5 due to the increase/decrease of normal stress, the amount of slippage and stress drop became larger/smaller in Case 4/Case 5.
(Acknowledgement) We received Grant-in-Aid for Scientific Research (Grant-in-Aid for Scientific Research (B), 22H01586).
1) Ozaki, O. and Hashiguchi, K. (2010): Numerical analysis of stick-slip …, Tribology International, Vol. 43, 21020-2133
2) Asaoka, A., Nakano, M. and Noda, T. (2000): Superloading yield surface concept …, Soils Found, 40(2), 99-110.
3) Toyoda, T., Yasuike, R., Noda, T. (2024): Super/sub-loading surface model …, Tribology International, 191, 109080.
The fundamental equations are listed in Fig. 1. The superloading surface concept was originally proposed by Asaoka et al.2) to describe the typical behavior of naturally deposited soils. As shown in Fig. 2, sensitive clays have a higher strength than its remolded and normally consolidated sample due to the presence of soil skeleton structure. Based on the analogy between the softening behavior of soil and the transition process from static to kinetic friction (Fig. 3), we analogically describe friction-induced phenomena using the superloading surface concept. In the proposed model, Coulomb's criterion (gray line) is regarded as a normal yield surface, as shown in Fig. 4. Then, a superloading surface (orange line), and a subloading surface (blue line) are introduced assuming their similarities. While the installation of the superloading surface allows a state above the normal yield surface (the blue region in Fig. 4), the subloading surface describes cyclic plasticity inside the superloading surface. The non-associated flow rule restricts only tangential plastic displacements. The evolution rule for R conformed to the previous model1). The evolution rule for R* consists of two terms (Fig. 5): The first term represents the softening from static to kinetic friction due to plastic slip (degradation of the structure), and the second term represents the healing from kinetic to static friction with time (contact surface adhesion and aging effect). This model can explain the continuous change of frictional force within the framework of elastoplasticity theory and provide coherent description on the stick/slip state. Detailed formulation can be seen in Toyoda et al.3).
Next, we solved the stick-slip phenomenon of a mass-spring system (Fig. 6) using the proposed model. The one-dimensional rate-type equation of motion was implicitly solved. The constitutive parameters of the contact surface are prescribed in Fig. 6, the analysis was conducted using the five cases listed in Table 1.
First, the slip displacement - time relation for Cases 1 - 3 with different coefficients κ and ξ in the evolution rule of R* is shown in Fig. 7(a). As a result of calculations, in Case 1, where the friction coefficient was not changed, a steady slip was obtained. In Case 3, where both decay and healing of structure were considered, a staircase-like slip-displacement - time relation (stick-slip phenomenon) was obtained.
Next, we discuss the effect of normal stress variation on the stick-slip phenomenon. Figure 7(b) shows the results of Cases 4 and 5, where the normal stress gradually decreased/increased with time relative to Case 3. While the initial slip was hindered/promoted in Case 4/Case 5 due to the increase/decrease of normal stress, the amount of slippage and stress drop became larger/smaller in Case 4/Case 5.
(Acknowledgement) We received Grant-in-Aid for Scientific Research (Grant-in-Aid for Scientific Research (B), 22H01586).
1) Ozaki, O. and Hashiguchi, K. (2010): Numerical analysis of stick-slip …, Tribology International, Vol. 43, 21020-2133
2) Asaoka, A., Nakano, M. and Noda, T. (2000): Superloading yield surface concept …, Soils Found, 40(2), 99-110.
3) Toyoda, T., Yasuike, R., Noda, T. (2024): Super/sub-loading surface model …, Tribology International, 191, 109080.