Spring-slider Model Research Articles

Inertial flow-induced fluid pressurization enhances the reactivation of rate-and-state faults

We reveal that inertial flow can introduce additional pressure perturbations which accelerate the instability of critically stressed faults. We integrate a poroelastic spring-slider model with rate-and-state friction (RSF), a nonlinear flow model characterized by the improved Izbash equation, and a universal visco-inertial permeability model. The effect of inertial flow depends on the fracture network properties, proximity to faults, and injection parameters. Significant inertial flow results in higher pressure magnitudes and pressurization rates, causing notable differences in predictions between linear and nonlinear flow models, as well as aging and slip laws. The impact of inertial flow is particularly pronounced within a specific permeability range and is enhanced by high-rate injections. The fault reactivation is delayed due to fault strengthening with RSF in response to increased pressurization rates. Conversely, the presence of inertial flow enhances fault reactivation and promotes unstable slip behaviors. Furthermore, the results demonstrate that cyclic injection increases the critical stiffness of faults without an adequate release of pore pressure in each cycle. The time interval of the cyclic injection is prolonged as inertial flow generates higher pressure levels. This study highlights the importance of inertial flow in the stability analysis of critically stressed faults.

Analysis of Fluid-Injection-Induced Seismicity Using a Dynamic Sliding Model Incorporating the Rate- and State-Dependent Friction Law

Summary Earthquakes can be triggered by fluid injection into underground formations. Fluid injection can cause large changes in the underground volume that exert stresses on nearby preexisting faults, leading to seismic activity. Assuming an increase in underground development activities in the future, our understanding of the mechanism underlying induced seismicity must be improved, and methods must be developed to properly assess the risk of seismic events. The objective of this study is to develop a seismicity prediction model that calculates the magnitude and timing of triggered earthquakes or seismic events occurring during various subsurface fluid injection activities. We developed an injection-induced seismicity analysis model that predicts the dynamic earthquake nucleation caused by changes in stress and pore pressure that occur during various subsurface activities. The governing equations consisting of the dynamic motion of the poroelastic spring-slider system, rate and state friction laws and pore pressure diffusion equation were solved using the embedded semi-implicit Runge-Kutta (SIRK) method. The dynamic sliding model was also incorporated into the finite element method (FEM) model, considering the variations in the stresses and pore pressures in the formation. A field case study was also conducted to compare the model results with typical microseismicity responses observed from hydraulic fracturing treatments in shale fields. Contrary to the popular understanding derived from Amonton’s law, the dynamic friction model revealed that a large normal stress on the fault leads to rapid sliding. A larger normal stress accumulates a large amount of elastic energy until it slips owing to fluid injection, nucleating large seismic waves. The poroelastic spring-slider model estimated reasonable microseismic magnitudes for hydraulic fracturing treatment but overestimated the time required to trigger a microseismic event under field conditions. To improve the analysis results, the poroelastic spring-slider model was coupled with a linear elastic FEM that considered the complex interplay of stress changes from hydraulic fracturing and the associated pore pressure variation in the formation. Compared with the field data, the coupled simulation model estimated a reasonable timing for the induced microseismic events when the increasing pore pressure during hydraulic fracturing penetrated deep into the formation. These findings suggest the existence of permeable natural fractures in the formation, which intensify early frictional sliding during treatment. The seismicity prediction model presented in this study simulates the magnitude and timing of seismic nucleation, helping to manage and mitigate the environmental impacts of induced seismicity during various subsurface development activities, such as oil and gas extraction, hydraulic fracturing, geothermal, and carbon dioxide sequestration. Moreover, the case study results imply that the time series of seismic events predicted by the model can be used to understand the possible fracture geometry and extent of fluid invasion for field applications. Key Terms and Phrases induced seismicity, subsurface fluid injection, rate- and state-dependent friction law, embedded semi-implicit Runge-Kutta method, finite element analysis

Elasto-viscoplastic material modelling using the multiaxial Prandtl operator approach

The closed-form solution for Prandtl model implemented into the finite element method is presented which enables elasto-viscoplastic simulations of engineering materials. A nonlinear temperature-dependent damper is combined in series with the temperature-dependent spring-slider model for the description of the material stress–strain behaviour. The simulation capabilities allow a separate study of influence due to plastic or viscous properties of the material. Several load cases are studied, including constant temperature relaxation and variable thermomechanical loads. The simulation results are then compared to the Abaqus-implemented material model for elasto-viscoplastic simulations. The models provide similar solutions for simpler load cases whereas higher discrepancies can be observed for more complex load histories since the positions of the nonlinear damper in the models differ.

Estimation of time-variable friction parameters using machine learning

SUMMARY The laboratory-derived rate- and state-dependent friction (RSF) law governs rock friction. Although a number of studies have investigated the RSF friction parameters, they are not fully understood yet within a physical framework. In this study, we estimated the variation of RSF parameters during stick-slip cycles, in order to have insights into the temporal variation of fault conditions during slipping, which may help understand the relation between the change in friction parameters and the generation of gouge particles. To get a more refined understanding of the evolution of RSF parameters, we estimated these parameters for each of the hundreds of stick-slip events that occurred on laboratory faults during an experiment. We used experiment data for which the gouge particles were removed from the laboratory faults at the beginning of each experiment; this procedure made possible to evaluate the influence of the gouge layer evolution on the variation of the RSF parameters. Since the amount of data was very large, we adopted a random forest (RF) machine learning approach for data analysis. The RF model was trained on simulated friction data and then applied to the experiment stick-slip event data to estimate the RSF parameters. To generate simulated friction data of stick-slip events, a one-degree-of-freedom spring-slider model governed by the RSF law was assumed. From plots of friction change as a function of displacement, some representative features were extracted to account for the RSF parameters and were used as input to the RF algorithm. Using the RF approach, we captured the variation of the RSF parameters a, $b - a$ and ${D}_{\mathrm{c}}\ $defined in the RSF law. The results show that during a first transient phase, the parameter a becomes smaller, while parameters $b - a$ and ${D}_{\mathrm{c}}$ become larger, as the gouge layer becomes thicker. The variation of the RSF parameters becomes less pronounced during the following steady-state phase. These results suggest that the variation of RSF friction parameters may be related to the evolution of the gouge layer.

Experimental and Numerical Calculation of the Friction Performance of a Concrete Surface.

The presented self-developed high-precision contact friction test device conducts experimental research on the friction characteristics of concrete pavement. First, the error analysis of the test device is carried out. The structure shows that the test device meets the test requirements. Subsequently, the device was used to carry out experimental research on the friction performance of concrete pavement under different roughness and temperature changes. The results showed that the friction performance of concrete pavement increased with the increase in surface roughness, and decreased with the increase in temperature. It has a small volume and significant stick-slip properties. Finally, the spring slider model is used to simulate the friction characteristics of the concrete pavement, then the shear modulus and viscous force of the concrete material are adjusted to achieve the calculation of the friction force over time under temperature changes, which is consistent with the experimental structure.

Can the Nucleation Phase be Generated on a Sub-fault Linked to the Main Fault of an Earthquake?

We study the effects of seismic coupling, friction, viscous, and inertia on earthquake nucleation based on a two-body spring-slider model in the presence of thermal- pressurized slip-dependent friction and viscosity. The stiffness ratio of the system to represent seismic coupling is the ratio of coil spring K between two sliders and the leaf spring L between a slider and the background plate and denoted by s=K/L. The s is not a significant factor in generating the nucleation phase. The masses of the two sliders are m1 and m2, respectively. The frictional and viscous effects are specified by the static friction force, fo, the characteristic displacement, Uc, and viscosity coefficient, h, respectively. Numerical simulations show that friction and viscosity can both lengthen the natural period of the system and viscosity increases the duration time of motion of the slider. Higher viscosity causes lower particle velocities than lower viscosity. The ratios g=h2/h1, f=fo2/fo1, y=Uc2/Ucl, and m=m2/m1 are four important factors in influencing the generation of a nucleation phase. When s>0.17, g>1, 1.15>f>1, y<1, and m<30, simulation results exhibit the generation of nucleation phase on slider 1 and the formation of P wave on slider 2. The results are consistent with the observations and suggest the possibility of generation of nucleation phase on a sub-fault. Results exhibit independence of P wave at slider 2 on the shape and duration time of nucleation phase at slider 1.

Experimental study on erosion behavior of fracturing pipelines involving fluctuating stress

Erosive wear due to particle impact serves as the main cause of pipeline failure. During hydraulic fracturing, fracturing pipelines inevitably suffer erosion damage under high fluctuating stress. In this study, a novel erosion test rig was developed in order to reproduce erosion scenes under complicated fracturing conditions. Then the erosion experiments involving fluctuating stress were carried out for the first time, and the erosion characteristics under varying conditions were obtained. In the erosion tests, the impact angles of the slurry flow varied from 15° to 90°, the flow velocities varied from 7.5 m/s-20 m/s, the solid particle concentration was 10% (in wt.%). The target material was 35CrMo steel, and the flat tensile specimens of 4 mm thickness were used in all erosion tests. Furthermore, the erosion mechanism with consideration of applied stress was subsequently revealed according to micro-structural characterization as well as the rheological spring-slider model. The complex erosion behavior of fracturing pipelines under severe conditions was well unraveled at the laboratory scale.

Mechanical behavior analysis of fully grouted bolt under axial load

Based on the idea of discretization and the force balance analysis of each mass spring element, a spring-element analysis method for bolt is proposed. By analyzing the mechanical behavior of the bond interface of the fully grouted bolt, three coupling models of the bond interface, the slider model, the spring model and the spring-slider model, are proposed. Using the spring-element method, five load transfer models, namely the slider model, the spring model, the modified spring model, the spring-pulled slider model, and the spring-slider model, were deduced. And get the bolt displacement distribution function, axial force distribution function and shear stress distribution function under each model. The five proposed models are verified, analyzed and discussed by using the pull-out test of the smooth steel bolt and the threaded steel bolt. It is verified by experiments that this study is helpful to comprehensively understand the mechanical behavior of fully grouted bolts under axial load. The proposed spring element analysis method is simple and easy to understand and the results are reasonable.

A 1D Spring-Slider Model with a Simple Poly-Linear Failure Law Produces Rich Variations in Slip Behavior

ABSTRACT The failure law prescribed along the fault surface and the elastic stiffness of the surrounding medium play important roles in determining the characteristics of earthquakes. Here we use a 1D spring-slider model that includes inertia, along with a simple poly-linear failure law composed of multiple linear segments to provide insight into earthquake initiation and growth. The poly-linear failure law, which parameterizes shear resistance as a function of slip, allows analytical solutions describing the system for each failure law segment. Analytical solutions facilitate investigation of the effects of the slopes of the different failure law segments in relation to the slope of the elastic loading curve determined by the spring stiffness. Depending on the relation between the slope of the failure law segment and the elastic loading slope, there are three stability regimes in the system: harmonic oscillations, exponential growth, and cubic growth. By combining the different solution regimes within one earthquake cycle, we observe a wide range of behaviors of this simple system: interseismic oscillatory creep, precursory signals before the main event, a shorter or a much longer acceleration phase before the onset of instability, and varying durations of the preseismic and coseismic phases. These results provide a potential explanation for some seismic observations, including increased levels of “seismic noise” prior to an earthquake, precursory events, tremor and low-frequency earthquakes.

Stick-slip behavior of a clayey crustal fault

Recent studies have revealed that slip on clay-rich fault planes, which develop in the shallow crust and can cause huge earthquakes, is controlled by their flow properties rather than their frictional properties. Here, we simulate a seismogenic crustal fault and show that such a fault plane may behave as a thixotropic yield stress fluid. We then conduct numerical experiments using a simple spring-slider model that incorporates this thixotropic property, and we successfully reproduce spontaneous stick-slip behaviors that correspond to a variety of seismogenic processes, ranging from regular earthquakes with high slip rates to slow earthquakes with lower slip rates. This finding suggests that the seismic activity on a shallow clay-rich crustal fault may be governed by the time-evolving microstructure of the clay-water system that exists along the fault plane.

Failure of Rock Slope with Heterogeneous Locked Patches: Insights from Numerical Modelling

Rock slope stability is commonly dominated by locked patches along a potential slip surface. How naturally heterogeneous locked patches of different properties affect the rock slope stability remains enigmatic. Here, we simulate a rock slope with two locked patches subjected to shear loading through a self-developed software, rock failure process analysis (RFPA). In the finite element method (FEM)-based code, the inherent heterogeneity of rock is quantified by the classic Weibull distribution, and the constitutive relationship of the meso-scale element is formulated by the statistical damage theory. The effects of mechanical and geometrical properties of the locked patches on the stability of the simulated rock slope are systematically studied. We find that the rock homogeneity modulates the failure mode of the rock slope. As the homogeneity degree is elevated, the failure of the locked patch transits from the locked patch itself to both the interfaces between the locked patched and the slide body and the bedrock, and then to the bedrock. The analysis of variance shows that length and strength of locked patch affect most shear strength and the peak shear displacement of the rock slope. Most of the rock slopes exhibit similar failure modes where the macroscopic cracks mainly concentrate on the interfaces between the locked patch and the bedrock and the slide body, respectively, and the acoustic events become intensive after one of the locked patches is damaged. The locked patches are failed sequentially, and the sequence is apparently affected by their relative positions. The numerically reproduced failure mode of the rock slope with locked patches of different geometrical and mechanical properties are consistent with the laboratory observations. We also propose a simple spring-slider model to elucidate the failure process of the rock slope with locked patches.

Dilatancy stabilises shear failure in rock

Failure and fault slip in crystalline rocks is associated with dilation. When pore fluids are present and drainage is insufficient, dilation leads to pore pressure drops, which in turn lead to strengthening of the material. We conducted laboratory rock fracture experiments with direct in-situ fluid pressure measurements which demonstrate that dynamic rupture propagation and fault slip can be stabilised (i.e., become quasi-static) by such a dilatancy strengthening effect. We also observe that, for the same effective pressures but lower pore fluid pressures, the stabilisation process may be arrested when the pore fluid pressure approaches zero and vaporises, resulting in dynamic shear failure. In case of a stable rupture, we witness continued prolonged slip after the main failure event that is the result of pore pressure recharge of the fault zone. All our observations are quantitatively explained by a spring-slider model combining slip-weakening behaviour, slip-induced dilation, and pore fluid diffusion. Using our data in an inverse problem, we estimate the key parameters controlling rupture stabilisation, fault dilation rate and fault zone storage. These estimates are used to make predictions for the pore pressure drop associated with faulting, and where in the crust we may expect dilatancy stabilisation or vaporisation during earthquakes. For intact rock and well consolidated faults, we expect strong dilatancy strengthening between 4 and 6 km depth regardless of ambient pore pressure, and at greater depths when the ambient pore pressure approaches lithostatic pressure. In the uppermost part of the crust (<4 km), we predict vaporisation of pore fluids that limits dilatancy strengthening. The depth estimates where dilatant stabilisation is most likely coincide with geothermal energy reservoirs in crystalline rock (typically between 2 and 5 km depth) and in regions where slow slip events are observed (pore pressure that approaches lithostatic pressure).

Study on Nonuniform Evolution Characteristics of Rock Friction and Sliding

By means of experimental research and theoretical analysis, the nonuniform evolution characteristics of rock friction and sliding were studied. Using digital speckle correlation (DIC) as observation method, the whole process of friction and sliding of a granite specimen in double-sided shear experiment is studied. A spring slider model considering the microscopic characteristics of interface asperities was established to simulate the microscopic process of rock friction and sliding. By comparing the theoretical analysis results with the experimental results, the effect of interface nonuniformity on rock friction sliding instability is studied. The results demonstrated that, with the increase of nonuniformity of sliding interface, the degree of local instability before stick-slip decreases, the stick-slip period shortens, and the value of shear drop during stick-slip period decreases. The nonuniformity of sliding interface will increase after local instability.

Effect of Time-strengthening Static Friction on Earthquake Recurrence

he effect of time-strengthening static friction on earthquake recurrence is numerically studied based on the normalized equation of motion of a one-body spring-slider model with thermal-pressurized slip-weakening friction having the characteristic distance, Uc, which is in terms of static friction coefficient, 𝜇. Considering the time-strengthening static friction coefficient, 𝜇(𝑡) = 𝜇+𝐵×𝑙𝑜𝑔(𝑡), we assume Uc=Uco/(1+𝐵×𝑙𝑜𝑔(𝑡)). Simulation results exhibit that TR, 𝜏D, D, and Vm, which represent the recurrence time of two events, the duration time of slip of an event, the final slip of an event, and the peak value of particle velocity of an event, respectively, are all similar for five values of Uco when B&lt;0.01 and clearly different when B≥0.01. In general, Vm, D, and TR increase with B; and 𝜏D slightly decreases with increasing B and increases with Uco. An increase in D is particularly remarkable when Uco&gt;0.3. The earthquake recurrence is almost periodic for small Uco; while the degree of periodicity decreases when either Uco or B increases. Either the time-predictable model or the slip-predictable model can approximately interpret the simulated earthquake recurrences with small Uco and small B, yet not for those with large Uco and large B. Simulation results exhibit that time-strengthening static friction produce an opposite effect on earthquake recurrence from the time-widening slip zone.

Time to seismic failure induced by repeating SSEs in a single-degree-of-freedom spring-slider model

SUMMARYSome large earthquakes may have been triggered by large slow slip events (SSEs). This paper studies the time it takes from the most recent SSE to seismic failure in a situation where earthquakes are influenced by periodic SSEs, unlike in earlier studies that investigated the impact of a single SSE imposed at an arbitrary timing during a seismic cycle. A single-degree-of-freedom (SDOF) spring-slider model obeying a rate- and state-dependent friction (RSF) law is used to study the time to failure. The results are compared with those in Ohtani et al., which simulates megathrust earthquakes triggered by large, spontaneous SSEs along the deeper extension of a seismogenic zone in a 2-D elastic medium. Suppose a model fault under steady-rate tectonic loading is also impacted by stress steps induced by periodic SSEs. In the absence of SSEs, there is only a unique value of the characteristic slip distance L of RSF for a given seismic return period T. In the presence of SSEs, by contrast, synchronization occurs, and there exists a finite range of L values that corresponds to the same T. The timing (phase difference) of earthquakes relative to the SSEs varies continuously with L within that range. This study focuses on the case where T is triple the SSE return period, TSSE, (T = 3TSSE) to allow comparison with Ohtani et al. For each value of L in that range, disturbance tests that assign random values to T0, the timing of the third SSE within the seismic cycle, are conducted to obtain a probability distribution for tf, the time from that SSE to seismic failure. The distribution is converted into P(t; L), the cumulative probability that seismic failure occurs within time t of the SSE. The P(t; L) is averaged over the different L values to produce $\bar{P}$(t), which takes account of variability in the strength excess on the seismic fault at the time of the SSE, a parameter that is generally unknown. These numerical disturbance tests are conducted for three different values of an SSE size parameter. It is found that the larger the SSEs, the more intensely seismic failure is concentrated within short time intervals following an SSE. For the largest SSE, whereby a single SSE accounts for 3/10 of the total stress accumulated during a seismic cycle, there is a 50 per cent probability that seismic failure occurs within 132 d. These results contrast with those of Ohtani et al., in which tf was found to be concentrated more intensely within even shorter time intervals following an SSE (80 per cent probability that seismic failure occurs within 2.78 d of the SSE). It is suggested the timing of SSE-triggered seismic failure is concentrated more strongly on a fault embedded in a continuum because of a factor that cannot be taken into account by an SDOF model—a spatial structure of stress concentration that is already there on the fault even before the triggering event, the SSE.

A New Semi-Analytical Method for Elasto-Plastic Analysis of a Deep Circular Tunnel Reinforced by Fully Grouted Passive Bolts

The use of fully grouted passive bolts as a reinforcement technique has been widely applied to improve the stability of tunnels. To analyze the behaviors of passive bolts and rock mass in a deep circular tunnel, a new semi-analytical solution is presented in this work based on the finite difference method. The rock mass was assumed to experience elastic–brittle–plastic behavior, and the linear Mohr–Coulomb criterion and the nonlinear generalized Hoek–Brown criterion were employed to govern the yielding of the rock mass. The interaction and decoupling between the rock mass and bolts were considered by using the spring–slider model. To simplify the analysis process, a bolted tunnel was divided into a bolted region and an unbolted region, while the contact stress at the bolted–unbolted interface and the rigid displacement of the bolts were obtained using two boundary conditions in combination with the bisection method. Comparisons show that the results obtained using the proposed solution agree well with those from the commercial numerical software and the in situ test. Finally, parametric analyses were performed to examine the effects of various reinforcement parameters on the tunnel’s stability. The proposed solution provided a fast but accurate estimation of the behavior of a reinforced deep circular tunnel for preliminary design purposes.

INFLUENCE OF VISCOSITY ON THE THERMAL ENERGY PRODUCED IN SEISMIC FAULT: ONE-DIMENSIONAL MODELING

This study is focused on thermal energy due to slip-weakening friction, but also on the temperature distribution. In this paper, we considered a one-body spring-slider model in the presence of slip-weakening friction and viscosity. We examine the effect of slip-weakening friction law and viscosity on thermal energy. We established the expression of thermal energy produced by slip-weakening friction in the case that we considered a simplified linearly slip-weakening friction law. Numerical simulation with Euler method are made for determining the thermal energy in the case of three others slip-weakening friction law, i.e., the thermal-pressurization (TP) friction law, the softening-hardening (SH) friction law and a simple slip-weakening (SW) friction law. The effect of the viscosity strongly modifies the results of the evolution of the temperature and the thermal energy. We establish that the TP friction law is better to evaluate the thermal energy in seismic fault. We solve the 1-D heat conduction equation by numerical simulation. We showed that, contrary to others frictions forces the slip-weakening friction law better illustrate the accumulation of thermal energy produced in seismic fault and temperature distribution.

A novel numerical-iterative-approach for strain-softening surrounding rock incorporating rockbolts effectiveness and hydraulic-mechanical coupling based on Three-Dimensional Hoek-Brown strength criterion

The numerical solutions for strain-softening surrounding rock under 3D Hoek-Brown strength criterion are developed incorporating the influence of passive bolts and the seepage flow field. Based on 3D Hoek-Brown failure criterion, a numerical-increment-approach is reconstructed for the first time under the spatial axisymmetric conditions, in which the elastic and plastic zones are divided into a finite number of concentric annuli with constant increments of radial stress and radius between the adjacent annuli, respectively. Furthermore, the hydraulic-mechanical coupling model is improved by considering the effects of out-of-plane plastic strain and the spring-slider model is improved by considering the axial force at rockbolt head. On the basis of the reconstructed numerical-increment-approach and the improved spring-slider model, the bolt self-equilibrium conditions for five cases of passive bolts are also reconstructed (e.g., neutral point in elastic or plastic zones, neutral length in elastic, plastic or elastic-plastic zones, respectively). Ultimately, an improved numerical-iterative-approach is proposed in terms of the developed numerical-increment-approach and the reconstructed bolt self-equilibrium conditions, through which stresses and displacement of surrounding rock can be obtained by incorporating the effects of hydraulic-mechanical coupling and passive bolts. The corresponding calculation program is also presented. The reliability of the presented approach has been verified by the numerical and existed results. From a practical point of view, the proposed approach can be applied to estimate the reinforced ground response curves and optimize the length of passive bolts.

Mechanical performance and corrosion damage of steel fibre reinforced concrete – A multiscale modelling approach

This paper investigates variations in the tensile toughness of cracked steel fibre reinforced concrete (SFRC) subjected to corrosion damage, by means of a multiscale modelling framework. Experimental results were used to discretise the pull-out behaviour of single fibres using a spring-slider model, which were then upscaled to the composite level by means of a probabilistic fibre bundle approach. The model described the alteration of the residual tensile performance of the composite due to variations of the fibre-matrix bond strength and corrosion damage of the steel fibres, observed experimentally. This investigation supports recent hypotheses suggesting that corrosion damage of the steel fibres may not be the only mechanism responsible for the deterioration reported in cracked SFRC exposed to corrosive environments. The strengthening of the fibre-matrix bond over time may entail a decrease of the tensile toughness of the composite due to fibre rupture.

A new approach to finite element modelling of cyclic thermomechanical stress-strain responses

Modern finite element based structural analyses of thermomechanically loaded structures require accurate simulations with low computational times. However, increasing the complexity of material models capable of modelling cyclic phenomena of engineering materials usually also increases the computational time. Here we present the implementation of the Prandtl operator approach into a finite element solver as a new material model for the study of the stress-strain response of solids subjected to thermomechanical loading. The main advantage of this model is its high computational speed, due mainly to the implicit consideration of the Masing and memory rules by variable temperatures, either during a single load cycle or during a complex thermomechanical load history. The model enables temperature-dependent elastoplastic stress-strain modelling using the von Mises yield function, associated flow rule and multilinear kinematic hardening. The commonly used elastic predictor–plastic corrector procedure now contains an improvement in the calculation of the equivalent plastic strain increment. This includes modelling of the true stress by the time-efficient temperature-dependent spring-slider model. The second advantage of the approach is a reduced number of material parameters per temperature required by the Ramberg–Osgood-type description of the cyclic curve. These material parameters can be obtained from either uniaxial strain controlled low cycle fatigue tests or uniaxial incremental step tests. The model has been validated on several load cases of both a thermomechanically loaded single finite element under tension-compression and shear loads, and a cantilever beam subjected to bending loads. Comparisons with reference material models show almost identical behaviour of the new and the Besseling model, but with the advantage of having up to 35 percent shorter computation times.