We construct a 2-D thermo-mechanical model of upper-mantle extension in which lithospheric strength (viscosity) depends on both strain rate and temperature. The model domain is a 1200 km wide by 400 km deep rectangle composed entirely of mantle material (Table ). This mantle-only configuration is designed to isolate strain localization within the lithospheric mantle and to facilitate comparison with large-scale plate-like convection models, which commonly neglect crustal structure and employ simplified rheologies.

Accordingly, we do not model crust-mantle interactions or full continental rift mechanics. This is a deliberate simplification, as crustal layering can reduce bulk lithospheric strength and introduce rheological contrasts that enhance localization in the mantle through crust-mantle mechanical coupling e.g.. In many numerical rift models, strong coupling across rheological discontinuities favors a “narrow-rift” style of deformation e.g.. In our set-up, localization is instead controlled by mantle rheology and by the imposed yield-stress parameterization (Sect. ), allowing us to isolate how these ingredients influence the onset and evolution of localized extension.

The initial thermal structure is prescribed using the half-space cooling model for a laterally uniform plate age. Thermal boundary conditions are fixed temperatures of Ts=273 K at the surface and Tm=1600 K at the base, with thermally insulating vertical sides (Fig. ). The initial deformation state is derived from a purely horizontal velocity field, producing a nearly uniform initial strain rate in the plate (ε˙t0 = 3.73 × 10⁻¹⁶ s⁻¹ for v1/2 = 1 cm yr⁻¹, Fig. ).

Extension is imposed through symmetric, depth-dependent horizontal outflow velocities on the side boundaries (Fig. ). The vertical profile vx(z) is obtained from a 1-D Couette solution with surface velocity v1/2 and zero velocity at the base, calculated using the depth- and temperature-dependent diffusion-creep viscosity of a 50 Myr-old plate (detailed in the Supplement, Sect. S2.1). This corresponds to an effective constant-velocity plate 89 km thick, defined as the depth above which horizontal velocity differs by less than 1 % from v1/2 . Additional tests with alternative side-boundary velocity profiles produce no significant change in the results (detailed in the Supplement, Sect. S2.3). The upper boundary is treated as a free-surface . At the base, no-slip and closed condition (vx=vz=0) are imposed on the lateral segments, while vertical inflow with vx=0 is allowed across a 600 km-wide central segment (see the Supplement, Sect. S2.2). This promotes localization at the domain center (see Fig. S3 in the Supplement, Sect. S2.3), while allowing basal inflow to adjust dynamically to the imposed lateral outflow (see Fig. S7 in the Supplement, Sect. S2.4) and evolving surface deformation.

We first analyze different rheological parameterizations in a reference configuration with v1/2 = 1 cm yr⁻¹ and an initial plate age of 50 Myr (Sect. ,  and ). We then explore the influence of initial plate age (10–100 Myr) and half-extension rate (0.2–5 cm yr⁻¹) on localization behaviour (Sect. ).

We solve the conservation equations of mass, momentum and energy for an incompressible Stokes fluid under the Boussinesq approximation using the finite-element, control-volume code Fluidity e.g.,. This framework has been widely used in geodynamical applications and extensively benchmarked against analytical and numerical reference solutions e.g.. The equations are discretized on an unstructured Eulerian mesh that is dynamically adapted throughout each simulation. Refinement criteria are applied to temperature, velocity, strain-rate, and viscosity, ensuring adequate resolution of lithospheric thermal gradients, localization zones, and strong viscosity contrasts. Triangular element sizes range from 200–1000 m in the finest regions to 50 km in the coarsest regions, with the highest resolution concentrated in the lithosphere and regions of active deformation (Supplement, Sect. S1). A typical simulation contains approximately 50 000 nodes, although this varies as simulations evolve.

We first quantify strain localization within the plate using the strain-rate amplification ASR(x,z,t) relative to the initially uniform strain rate in the plate ε˙t0 (Fig. ), and its geometric mean over lithospheric thickness at each horizontal position.

To track lateral focusing through time, we define the width of the deforming zone, w(t), as the region where 〈ASR〉1500K(x,t)>1. From this, we compute a narrowing rate. We also quantify the lateral viscosity contrast within the plate Rvisc(t), as the ratio between the maximum vertically-averaged lithospheric viscosity along x and the minimum value in the central weak zone: 10Rvisc(t)=maxη1500K(x,t)minη1500K(x,t) Finally, we compute the plateness P(t) . Details of the calculation are given in the Supplement (Sect. S4.1).

To quantify lithospheric thinning, we define the plate thickness hplate(t) as the minimum depth of the 1500 K isotherm along x. Its time evolution is used to estimate an upwelling rate. We track time-dependent weakening or hardening through the logarithmic rate of change in effective viscosity: 11W(x,z,t)=-∂log⁡10(η)∂t≈-1Δtlog⁡10ηt+Δt2ηt-Δt2 where Δt is chosen to be much smaller than the localization timescale (typically 0.05–1 Myr, depending on extension rate). Smaller values of Δt do not change the weakening amplitude. Positive values of W indicate weakening whereas negative values indicate hardening. We also compute the vertically averaged weakening rate 〈W〉1500K(x,t) using a geometric mean. A 10-fold decrease in viscosity in 1 Myr corresponds to a weakening rate W of about 3 × 10⁻¹⁴ s⁻¹.

As a bulk measure of lithospheric strength, we calculate the tectonic force TF(t) (in N m⁻¹) required to maintain the imposed extension velocity at the side boundaries : 12TF(t)=H⋅(Sxx-Szz)2+Sxz2 with 13Sij(t)=1H∫0Hσij(z,t)dz where Sij is the stress tensor vertically averaged over the full domain height H at x=100 km, to minimize boundary effects (see the Supplement, Sect. S4.2).

To distinguish why viscosity decreases during localization, we partition weakening into contributions associated with temperature and strain-rate changes. This builds on the general idea that localization potential can be related to the sensitivity of viscosity to evolving state variables . At each point on the interpolated grid, viscosity depends only on temperature and strain rate, so its time derivative may be written as: 14∂η(T,ε˙)∂t=∂η∂T∂T∂t+∂η∂ε˙∂ε˙∂t We approximate this decomposition over a finite time interval Δt as: 15ΔηΔt=ΔηΔtε˙+ΔηΔtTwithΔηΔtε˙=ηTx,z,t+Δt2,ε˙(x,z,t)-ηTx,z,t-Δt2,ε˙(x,z,t)ΔtΔηΔtT=ηT(x,z,t),ε˙x,z,t+Δt2-ηT(x,z,t),ε˙x,z,t-Δt2Δt The corresponding normalized contributions to weakening are then 16FT=ΔηΔtε˙ΔηΔtandFSR=ΔηΔtTΔηΔt where FT measures the contribution from temperature evolution (“thermal” weakening) and FSR, the contribution from strain-rate evolution (“mechanical” weakening). We use Δt≈0.25 Myr for this partitioning. Smaller values introduce short-period oscillations in FT and FSR without changing the broader trends. These diagnostics are evaluated only where the material is undergoing weakening (W>0). Mixed cases can nevertheless arise, for example when mechanical weakening due to strain-rate increase exceeds thermal hardening due to plate cooling. In such cases, FT may become negative and FSR may exceed 1 (as discussed in Sect. ). For plotting purposes, the colour scale for FSR is capped between 0 and 1.

For an initially 50 Myr-old plate extended at v1/2=1 cm yr⁻¹, the rheological parameterization produces three distinct deformation outcomes by 40 % bulk strain (Table , Figs. , ).

First, Simulation ref-1 serves as a reference for the strain localization scenario (Table , and Fig. b). Its rheology, labeled D-dLT–HT-Y500MPa, accounts for diffusion creep, low- and high-temperature dislocation creep (Eq. ) and a yield stress of 500 MPa (Eq. ). This simulation shows a progressive narrowing of the deformed domain around the box center, where most of the deformation is accommodated as shown by the significant increase in the horizontal velocity gradient at the surface (Fig. b, 1–6 Myr). In a second stage, significant asthenospheric upwelling develops beneath the most stretched lithosphere portion, resulting in a boundary separating two divergent plates that behaves as a horizontal velocity discontinuity (Fig. b, 12 Myr). Hence, in localizing cases, a narrow extensional plate boundary develops at the domain center, separating two rigid plates (Simulation ref-1 in Fig. b). These runs exhibit high plateness (P>0.95), a large lateral viscosity contrast (Rvisc>100), and a deformed-zone width w<100 km, while plate thickness hplate approaches a quasi-steady value after localization. The localized zone is underlain by focused asthenospheric upwelling.

Second, the non-localizing simulation ref-0 (rheology D-dHT, Table  and Fig. a) exhibits a long-lasting and steady plate deformation. This diffuse deformation mode corresponds to a slow plate thinning (∼ 0.05 cm yr⁻¹), arising from the competition between thickening by diffusive cooling and lithosphere extension. In such cases where deformation is always distributed, the plate deforms broadly and remains laterally uniform, without any increase in the horizontal velocity gradient at the surface (e.g., Simulation ref-0 in Fig. a). These runs show low plateness (P<0.3) and weak lateral viscosity contrast (Rvisc<10). Strain-rate amplification remains modest across the plate and deformation is expressed primarily as gradual, laterally uniform thinning.

Third, an intermediate regime occurs in which the deformation localization is very slow (Appendix ). Strain begins to focus but the area where deformation is enhanced remains relatively wide at 40 % strain (incomplete localization). These runs still exhibit narrowing of the deformed zone and plate thinning, with w≳150 km at the end of the simulations, comparable to the early-to-intermediate state of Simulation ref-1 (e.g., Fig. b at 6 Myr).

In the remainder of the Results, we use a representative localizing simulation (ref-1) to define a reference localization trajectory and characteristic timescales, and then compare rheological combinations and forcing parameters against that trajectory.

We quantify the localization trajectory in Simulation ref-1 using the co-evolution of deformed-zone width w, the minimum plate thickness hplate, and the weakening rate W (Sect. ). The deforming region (defined by 〈ASR〉1500K>1, Sect. ) progressively narrows toward the domain center (Fig. a), while weakening intensifies within the lithosphere beneath the developing boundary (Fig. b and d).

The localization trajectory is well described by two stages (Fig. a). Stage 1 is dominated by lateral focusing of deformation: w decreases rapidly whereas hplate decreases only modestly. Stage 2 is dominated by rapid plate thinning driven by asthenospheric upwelling: hplate decreases rapidly while the narrowing of w slows down. Stages 1 and 2 are detailed below. We define two characteristic times. The transition time ttr marks a shift in trajectory in hplate(t) : w(t) space (Appendix ); it coincides with the end of the approximately steady tectonic force plateau TF (Fig. c). The plate-boundary time tPB marks the onset of a quasi-steady geometry, when both hplate and w become approximately stationary and the tectonic force has dropped to its post-localization value (Fig. c).

For Simulation ref-1, Stage 1 lasts 6.5 Myr and is characterized by rapid narrowing (mean 14 cm yr⁻¹) with limited thinning (100 to 82 km in Fig. a). During this stage, weakening at the domain center is distributed through much of the lithosphere thickness (Fig. d) and exceeds off-center weakening (Fig. c), producing a growing but moderate viscosity contrast (Rvisc<50; Fig. b). In the plate interior outside the deforming zone, viscosity increases (hardening), particularly toward the end of Stage 1 (Fig. b).

Stage 2 lasts 5.5 Myr (from 6.5 to 12 Myr) and is characterized by rapid thinning (82 to 10 km) and a sharp reduction in tectonic force, whereas narrowing is slower (mean ∼ 4 cm yr⁻¹; Fig. a). Weakening peaks shortly before tPB (Fig. b), while the lateral viscosity contrast continues to increase and reaches its maximum near tPB (Fig. b). After tPB, the system evolves toward a steady thermal structure around the mature boundary and the weakening rate in the narrow boundary region approaches zero (Fig. b).

Across all rheological combinations, simulations that localize deformation follow the same two-stage trajectory defined in Sect.  (Fig. ). Stage 1 is dominated by progressive narrowing of the deforming zone with only modest thinning, whereas Stage 2 is dominated by rapid plate thinning associated with focused asthenospheric upwelling and only limited additional narrowing (Fig. a–b). The major rheological control is therefore whether deformation localization occurs and how quickly the system progresses through the two stages, rather than the geometrical trajectory or the maximum weakening rate (10⁻¹³ s⁻¹ for all simulations in Fig. f).

In simulations without a yield-stress cap, deformation remains distributed regardless of whether diffusion creep is combined with high-temperature dislocation creep or with low- to high-temperature dislocation creep (e.g., Simulation ref-0; Fig. a). Thus, in this lithospheric extension setup, dislocation and diffusion creep alone are insufficient to generate lithospheric-scale localization; additional weakening of the cold upper lithosphere (here provided by a yield-stress cap) is required.

Among simulations that do localize strain, the characteristic times vary substantially between rheologies (Table ). Localization takes about twice as long for diffusion creep plus yield stress (e.g., D-Y200MPa and D-Y500MPa) and for cases in which yielding is restricted to temperatures below 950 K (e.g., D-dHT-Y500MPa950K), than for rheologies that combine diffusion creep, dislocation creep, and yield stress (e.g., D-dHT-Y200/500MPa and D-dLT-HT-Y200/500MPa; Fig. a–b). Consistently, the tectonic force required to maintain the imposed extension velocity during Stage 1 is the largest for D-Y500MPa (Fig. c), indicating a stronger deforming zone at the plate center, as also suggested by the low lateral viscosity contrast Rvisc (Fig. e).

We interpret these differences using the weakening-partition diagnostics (Sect. ), which quantify the relative contributions of strain-rate increase (FSR) and temperature increase (FT) to viscosity reduction (Fig. ). In all simulations, the shallow lithosphere is yield-dominated and weakening is purely strain-rate driven there (FSR=1). Differences emerge in the deeper lithosphere, where deformation transitions to creep and where maximum weakening occurs. The temperature of the yield-to-creep transition depends strongly on the creep rheology: it is highest for diffusion creep alone (about 1300 K in D-Y500MPa), lower when high-temperature dislocation creep is included (about 1000 K in D-dHT-Y500MPa), and the lowest when low- to high-temperature dislocation creep is included (about 800 K in D-dLT-HT-Y500MPa; Fig. ). These shifts imply that a thicker portion of the lithosphere deforms in the creep regime when dislocation creep is included, extending thermo-mechanical weakening to lower temperatures.

The weakening-partition diagnostics further show that dislocation creep enables both mechanical and thermal weakening within the creeping lithosphere. In rheologies that include dislocation creep, weakening is predominantly strain-rate driven during Stage 1 (typically FSR>60 % in the main weakening zone), while weakening becomes almost purely temperature-driven during Stage 2 (typically FT>0.9; Fig. a, b). In contrast, for diffusion creep plus yield stress, weakening in the creeping domain is entirely temperature-driven (FT≥1; Fig. c), limiting mechanical weakening during Stage 1 and delaying the onset of rapid thinning.

This interpretation is illustrated by Fig. , which shows theoretical viscosity profiles for two idealized end-member evolutions: a 10-fold increase in strain rate at constant plate age, used as a proxy for Stage 1, and plate thinning at constant strain rate, used as a proxy for Stage 2. For a given creep law, the effect of a Stage-1-type strain-rate increase can be estimated from the viscosity contrast between the yield-creep transition and the warm sub-lithospheric layer at about 75 km depth (Fig. b). By this measure, the mechanical weakening associated with LT–HT dislocation creep (6-fold) is intermediate between that associated with HT dislocation creep (5-fold) and that associated with the yield-stress-plus-diffusion-creep rheology (10 or 1-fold). However, the 10-fold strain rate increase during Stage 1 produces the lowest absolute viscosities below the yield-creep transition. The same approach can be used to estimate the amplitude of Stage-2-type thermal weakening from the viscosity change accompanying lithospheric thinning and warming (Fig. d). Although the viscosity reduction associated with lithospheric warming is largest for diffusion creep (>100) and smallest for LT–HT dislocation creep (<40), the absolute viscosity reached after a given amount of warming and thermal rejuvenation remains lower when dislocation creep is included (Fig. c).

Finally, in a subset of simulations, yielding is restricted to low temperature to disable pseudo-brittle mechanism above 950 K, leaving only creep mechanisms at higher temperatures (Sect. ). This produces a marked delay even when dislocation creep is present (compare D-dHT-Y500MPa and D-dHT-Y500MPa950K; Table ). Vertical profiles for the D-dHT-Y500MPa950K case show that imposing a thermal cutoff on the yield rheology creates a stiff layer less than 4 km thick at the base of the shallow yielding domain, between the colder lithosphere above and the warmer creeping mantle below (Appendix ). Although thin, this layer remains mechanically important because it forms a local viscosity peak that slows the overall decrease in viscosity throughout the whole lithosphere, which in turns delays deformation focusing. This highlights the importance of capping the lithosphere strength in the creep domain within the mid-lithosphere temperature range (roughly 800–1300 K in these setups): even a thin stiff layer at these depths (Fig. ) is sufficient to impede Stage 1 narrowing and to delay both ttr and tPB (Figs. , ; Table ). This explains why lowering the yielding cutoff to 900 K inhibits localization within the simulated strain window (Table ). Additional resolution tests show that, despite its striking sharpness, the presence of this high-stiffness layer is well resolved, and is thus a robust result (Sect. S1 in the Supplement).

We test the robustness of the two-stage localization pathway and its sensitivity to: (i) the initial thermo-mechanical state of the lithospheric mantle and (ii) the magnitude of far-field forcing. We vary initial plate age (from 10 to 100 Myr), and the imposed half-extension rate (from 0.2 to 5 cm yr⁻¹). We focus on two rheological combinations that exhibit markedly different rates of strain localization in the reference setup (Fig. ): diffusion creep plus yield stress (D-Y500MPa), and diffusion creep plus low-to-high-temperature dislocation creep plus yield stress (D-dLT–HT-Y500MPa) (Table ).

Across most age-velocity combinations, the localization trajectory remains fundamentally characterized by a two-stage scenario: Stage 1 is characterized by progressive narrowing of the deforming zone, while plate thickness changes only modestly; Stage 2 is characterized by rapid plate thinning associated with asthenospheric upwelling, with comparatively minor additional narrowing (Appendix ). The basic control on characteristic times is the extension rate, whereas initial plate age exerts only a weak influence (Fig. a, b). This set of experiments further underlines that dislocation creep accelerates deformation localization relative to diffusion creep plus yield stress. For a given extension rate, the dislocation-creep rheology produces lower effective viscosity in the central deforming zone (typically by a factor of 5 to 10 at ttr), which increases the lateral viscosity contrast between the weak zone and the plate interior and reduces the tectonic force required to maintain the imposed velocity (Fig. e, g). This enhanced strength contrast is expressed primarily through Stage 1: for all tested ages and velocities, the Stage 1 duration (measured by strain at ttr) is shorter when using dislocation creep, while the differences in Stage 2 timing are smaller and diminish further as extension rate increases.

Extension rate strongly modulates Stage 1 duration. Faster extension increases strain rate within the deforming zone, lowering effective viscosity via both yielding and (where active) dislocation creep, thereby increasing the narrowing rate (Fig. c, e). As a result, the total strain required to reach the transition from Stage 1 to Stage 2 decreases systematically with extension rate for both rheologies (Fig. a). In contrast, the Stage 2 duration is comparatively insensitive to extension rate for v1/2≳1 cm yr⁻¹ (Fig. b), even though upwelling rates increase with extension rate (Fig. d). The maximum lateral viscosity contrast increases with extension rate up to ∼ 2 cm yr⁻¹ and then saturates (Fig. f), suggesting that once a sufficiently weak plate boundary is formed, it cannot weaken much further at higher extension rates.

Only the slowest forcing conditions fail to localize within the simulated strain window, and this occurs exclusively for the diffusion-plus-yield rheology. For old plates (50–100 Myr) extended at v1/2=0.2 cm yr⁻¹, localization remains incomplete by 40 % strain (Table ). In these cases, thermal diffusion can outweigh extensional thinning during early deformation, leading to net lithosphere thickening and delayed weakening (Appendix ; Figs.  and ). Even in cases that eventually localize at low velocities or for initially young plates, the resulting plate boundary remains relatively wide and thick, and the maximum viscosity contrast remains modest (Rvisc≲200 at tPB; Fig. f), indicating a weaker degree of focusing than in faster-extension cases.

The weakening-partition diagnostics clarify how forcing modulates feedbacks. At low extension rates (and in some young-plate cases, early in Stage 1), thermal hardening associated with cooling competes with mechanical weakening, such that net weakening in the creeping lithosphere is dominated by strain-rate effects (note that FSR can exceed 1 where temperature decreases while strain rate increases, Sect. ). For the dislocation-creep rheology, this strain-rate-driven weakening extends to higher temperatures within the creeping lithosphere (up to ∼ 1300 K), supporting continued narrowing despite thermal hardening. By contrast, for diffusion creep plus yield stress, weakening below the yielding layer remains predominantly thermal; when cooling dominates early, the system remains in a thick yielding-dominated configuration that inhibits rapid focusing, contributing to incomplete localization under the slowest forcing.

A robust result of this study is that all simulations that successfully localize strain follow the same two-stage pathway to plate-boundary formation, irrespective of the rheological parameterization (Fig. ). In Stage 1, deformation mainly focuses laterally: the width of the deforming zone decreases rapidly, whereas plate thickness changes only modestly. In Stage 2, the localization pattern shifts to rapid plate thinning driven by focused asthenospheric upwelling, while additional narrowing becomes limited. The transition between these two stages therefore marks the point at which a progressively focused deforming region evolves into a rapidly thinning lithosphere, at the end of which a mature plate boundary is achieved.

This two-stage behavior provides a simple physical framework for interpreting the localization process. Stage 1 is primarily a focusing problem, in which viscosity reduction within the deforming zone, allowed by non-Newtonian rheology, progressively increases the contrast with the surrounding plate interior. Stage 2 is primarily a thinning process, in which upwelling and heating beneath the localized zone further reduce temperature-dependent viscosity and accelerate lithospheric thinning. In that sense, the transition time ttr represents a dynamical tipping point: beyond it, thermal weakening associated with asthenospheric upwelling becomes dominant and plate-boundary development proceeds rapidly.

A broadly comparable two-stage evolution has been inferred for some natural rift systems: the Atlantic and Australia-Antarctica rifts have probably undergone an early stage of deformation, at (total) extension rates slower than 1 cm yr⁻¹, lasting ∼ 25–50 Myr, followed by an abrupt acceleration of extension over only 2–10 Myr . This acceleration is interpreted as the consequence of “the rapid decrease of rift strength” in constant-force rifting models , and of “a positive feedback loop between extension velocity and rift strength loss” in whole-mantle convection models . Our models do not reproduce such settings directly, particularly because extension is imposed kinematically rather than through a self-consistent far-field force balance.

We performed additional simulations with either an abrupt or a linear temporal increase of extension velocity imposed at side boundaries (Supplement, Sect. S5.1), in which the tectonic force TF remains quasi-constant during Stage 1 before abruptly dropping during Stage 2. As in the constant-extension velocity models, Stage-1 narrowing is dominated by mechanical weakening, while Stage 2 is associated with thermal weakening with rapid TF decrease and fast plate thinning (Figs. , ). We speculate that imposing forces or stresses at side boundaries, instead of imposing velocities, would result in a decrease in plate strength at time ttr, and an increase in extension velocity, as predicted by rifting models and reconstructed in the natural rifting cases . Thus, we propose that rifting acceleration in nature may correspond to a geodynamic tipping point with thermal weakening of the lithospheric mantle enhancing plate strength drop, thus further promoting plate extension.

The clearest rheological result of this study is that simulations including dislocation creep localize deformation substantially faster than those with yield stress plus diffusion creep alone (Table ; Fig. a, b). This difference does not arise simply because the plate is weaker in some bulk sense. Rather, dislocation creep changes where and how weakening operates within the lithosphere and enhances the feedbacks leading to deformation localization: faster narrowing or thinning increases mechanical or thermal weakening, causing the decrease in viscosity at the domain center (associated with efficient focusing of deformation in Stage 1 and with rapid central upwelling in Stage 2), thereby increasing the lateral viscosity contrast, which in turn further enhances narrowing or thinning, and so on.

When dislocation creep is included, the transition from yield-dominated to creep-dominated deformation occurs at lower temperatures, so a larger fraction of the lithosphere participates in creep deformation (Fig. ). In practice, this extends weakening into colder parts of the deforming plate, particularly through the approximate 800–1300 K interval. As a result, dislocation creep broadens the part of the lithosphere that can respond dynamically to both increasing strain rate and increasing temperature, thereby enabling positive feedbacks over a thicker region.

The weakening-partition diagnostics show that this has two important consequences. First, during Stage 1, dislocation creep allows significant strain-rate-driven weakening within the creeping lithosphere, which promotes faster narrowing of the deforming zone. Second, during Stage 2, it permits stronger temperature-driven weakening over a thicker part of the lithosphere, which accelerates plate thinning once focused asthenospheric upwelling is established. In contrast, in diffusion-creep-plus-yield-stress simulations, weakening below the shallow yielding layer is almost entirely thermal, limiting mechanical weakening during Stage 1 and delaying the onset of rapid thinning (Fig. ).

This difference is also consistent with the analysis of the theoretical viscosity profiles shown in Fig.  (Sect. ). Relative to diffusion creep plus yield stress, rheologies including dislocation creep produce the lowest viscosity associated with both mechanical weakening during a Stage 1-type strain-rate increase and stronger thermal weakening during a Stage 2-type thinning trajectory. In addition, dislocation creep extends both effects to lower temperatures and shallower depths. The main consequence is therefore not simply a lower viscosity, but a stronger coupling between deformation focusing, asthenospheric upwelling, and further weakening.

Our results further suggest that, if deformation is driven by far-field kinematics, as in our modeling conditions, overall lithospheric strength exerts only a second-order control on localization efficiency. For example, Simulation D-Y200MPa localizes more slowly than simulations D-dLT–HT-Y500MPa and D-dHT-Y500MPa, even though the former has a lower tectonic force during Stage 1 (Fig. c). Extra simulations are performed with depth-dependent yield stress, keeping the peak strength of 500 MPa at the same depth as in the constant σY simulations (Appendix ). These complementary simulations exhibit comparable localization characteristic times despite the lower strength at the plate surface, which supports the previous conclusion: reducing near-surface strength does not substantially change localization times if a deeper mechanically important layer remains. Localization is therefore not controlled solely by average plate weakness, but by rheology-dependent feedbacks and by the depth distribution of strength within the lithosphere. Nevertheless, we acknowledge that the situation would be different if lithospheric deformation were instead driven by far-field constant stresses or forces, especially in case of a low to moderate tectonic rate. In such a setting, imposing a yield stress of 500 MPa instead of 200 MPa might significantly modify the evolution of lithospheric spreading.

The aforementioned feedbacks between the temperature and strain rate fields enabled by the activation of dislocation creep are modeled in our experiments while shear heating is not included. Shear heating has been proposed to enhance shear localization by thermal runaway e.g.. Using a posteriori calculations, we estimate a maximum heat dissipation rate for Simulation ref-1 (D-dLT–HT-Y500MPa) larger than ∼ 10⁻⁶ W m⁻³ in a ∼ 15 km thick layer directly below the yield-creep transition (Supplement, Sect. S5.3). Considering that a heat dissipation rate of order 10⁻⁵ W m⁻³ can lead to a temperature increase close to ∼ 50 K , we therefore expect that the temperature rise due to shear heating would remain lower than 50 K in our simulations. Therefore, including shear heating could foster thermal weakening in our experiments, further enhancing plate weakening and strain localization, but to a low-to-moderate extent. This effect is predicted to be especially emphasized when using (LT-)dislocation creep for which the temperature-dependent creep layer is the thickest (Supplement, Sect. S5.3).

Taken together, these results show why yield-stress rheologies are not dynamically equivalent to rheologies that include dislocation creep at moderate to high temperatures. Dislocation creep accelerates localization because it expands the depth and temperature range over which both mechanical and thermal weakening can operate, thereby strengthening the feedbacks required to transform distributed extension into a localized plate boundary.

In these simulations, yield stress plays two distinct roles. First, it acts as a proxy for shallow pseudo-brittle weakening, enabling deformation of the very cold upper lithosphere. That role is essential in the present extension setting: without weakening of the shallow plate, deformation remains distributed and of low amplitude, even when dislocation creep is included. Some mechanism that weakens the cold upper lithosphere is therefore required in addition to any deeper strength-limiter.

Second, in rheologies that do not include low-temperature dislocation creep, yield stress also limits the effective strength in a part of the deeper lithosphere. This is evident from the comparison between simulations with and without an imposed thermal cutoff for yielding. When LT–HT dislocation creep is present, restricting yielding to temperatures below 950 K has no effect on localization timescales. By contrast, when only HT-dislocation creep is included, the same restriction markedly delays localization or prevents it within the simulated strain window (Table ). In that sense, when low-temperature dislocation creep is absent, the yield stress partly substitutes for a strength-limiter within the approximate 800–1100 K interval, that is, across the temperature range over which deformation transitions from dislocation creep to yielding (Fig. ). This interval overlaps at least partly with the ductile domain inferred for olivine at temperatures greater than about 800–900 K from laboratory and theoretical studies on melting and homologous temperatures . It also overlaps with the mantle brittle-ductile transition expected up to approximately 600 °C (900–1000 K), as inferred from seismicity in the oceanic lithosphere e.g., and may extend to 900 °C (1200–1300 K) under hydrous mantle conditions , making the physical interpretation of such stress caps intrinsically ambiguous because deformation around the brittle-ductile transition is likely governed by multiple poorly constrained processes .

Our simulations further show that lowering stresses of the shallowest part of the lithosphere does neither accelerate nor modify the breakup process (Appendix ), whereas even a stiff layer less than 5 km thick within the mid-lithosphere can strongly delay Stage-1 narrowing and therefore delay plate-boundary formation (Sect. , Fig. ; Appendix ). This layer forms a thin but mechanically important bottleneck between the shallow yielding domain and the warmer, weaker creeping mantle. As long as this bottleneck remains strong, it dampens the feedbacks between deformation focusing, plate thinning, and further weakening, with strain rate increase lessened in the whole lithospheric section, hence milder ensuing viscosity reduction (Fig. b, c). In that sense, the relevant control on localization is not simply the weakness of the shallowest lithosphere, but the peak strength of the lithosphere, and whether the stiff layer can itself weaken. This underlines the need to cap the lithosphere strength beyond the brittle realm, in a temperature range corresponding approximately to 800–1000 K, i.e. the thermal range within the mid-lithosphere where the activation of HT-dislocation creep would otherwise lead to very high viscosities.

Our results therefore support the view that yield stress in geodynamical models should not be interpreted only as a shallow brittle proxy. In practice, it may also act as a first-order proxy for deeper ductile strength limitation when low-temperature plasticity is not represented explicitly. Following and , we therefore suggest distinguishing between a shallow pseudo-brittle stress cap and a deeper parameterization representing low-temperature ductile strength limitation, even if the latter is not dynamically equivalent to LT-dislocation creep itself (Sect. ).

Simulations with (LT-)-HT dislocation creep exhibit significantly lower tectonic forces TF than simulations with only yielding and diffusion creep. In addition, using lower yield stress values also reduce the tectonic forces needed to maintain extension (Fig. c). Nevertheless, initial TF values of approximately 20–40 TN m⁻¹ remain on the high side compared to estimates proposed for natural rifting ∼ 1 TN m⁻¹,, ridge push ∼ 2–3 TN m⁻¹,, but would be in agreement with estimation of slab pull ∼ 10–50 TN m⁻¹, e.g.,. In large-scale mantle convection models, chosen yield stresses are low ≲ 200–300 MPa, e.g., or with a low yield-stress increase with pressure often ≲ 0.2, e.g. compared to values derived from friction coefficients inferred from laboratory experiments ∼ 0.6, e.g.. These choices generally result in lithospheric strengths lower than laboratory-based estimates > 500 MPa, e.g., but they allow models to reproduce plate-like behavior and reorganizations . Our results suggest that including low-(to high-)temperature dislocation creep provides an alternative mechanism to act as a strength-limiter in the lithospheric mantle, allowing a somewhat higher stress-cap, more consistent with deformation experiments, while still enabling plate weakening and strain localization. Other plausible mechanisms have also been proposed to generate plate-like behavior compatible with higher yield stress values, such as lateral strength heterogeneities associated with cratonic continental blocks .

A central implication of this study is that rheologies combining diffusion creep with a simple yield-stress cap e.g. may overestimate the time required to localize strain and form new plate boundaries. In our simulations, adding dislocation creep substantially accelerates localization relative to rheology D-Y because it extends the thermal range of weakening in the creeping lithosphere and strengthens the feedbacks that link strain-rate increase, asthenospheric upwelling, and further viscosity reduction. This suggests that large-scale geodynamical models may localize too slowly if they omit this rheological contribution. Yet, including dislocation creep in whole-mantle convection simulations will have other dynamical consequences, such as a sub-plate asthenosphere weakening scaling with surface plate velocities e.g., or an increased mechanical decoupling at lithosphere-asthenosphere boundary that alters mantle flow and surface deformation pattern .

More broadly, our results highlight a limitation of vertically-uniform stress-limiters. A low and constant yield-stress is not dynamically equivalent to a rheological structure in which shallow pseudo-brittle weakening coexists with a deeper creeping layer, since the latter can undergo strong thermo-mechanical weakening. The distinction matters because localization is sensitive not only to the integrated plate strength, but also to the depth distribution of strength and weakening. In particular, a thin stiff mid-lithosphere layer can act as a bottleneck that delays localization even when the plate is weak in a vertically averaged sense. Models developed to accurately estimate the absolute timescale of localization should distinguish a pseudo-brittle yield cap from a ductile strength limiter, either self-consistently arising from low-temperature dislocation creep e.g., or implemented with a so-called “ductile yield stress” as in and .

A second important aspect of our study is the introduction of weakening-partition diagnostics, that provide a general framework for analyzing the rheological control on deformation localization. By separating strain-rate-driven and temperature-driven contributions to viscosity reduction, they allow for identifying when localization is controlled primarily either by mechanical weakening or by thermal feedbacks. This weakening-partition diagnostics should be transferable to other geodynamic settings, including subduction initiation e.g. or plume-lithosphere interaction e.g.. It can also be extended to rheologies with additional state dependencies such as grain size, damage, or composition e.g..

The main limitation of the present study is the mantle-only configuration. By excluding crustal layering, we isolate mantle rheological controls but do not attempt to reproduce the full mechanical complexity of natural rift systems. Crust-mantle coupling, lithological discontinuities, and additional weakening processes such as strain softening, grain-size evolution, and damage are all expected to promote a more rapid localization in a “narrow-rift” setting featuring a strong lower crust e.g.. Indeed, for rifting models under total extension around 1 cm yr⁻¹ e.g. the corresponding transition time ( ttr) and break-up time (tPB) are approximately 5 and 9–16 Myr, respectively, compared to 14 and 26 Myr in our fastest model (rheology D-dLT–HT-Y500MPa). In that sense, the absolute times reported in this study are best interpreted as end-member values for a simplified mantle system, rather than as direct predictions for crust-bearing rifts. The interplay between low-temperature dislocation creep and additional weakening mechanisms will depend on the details of the rheological parameterizations and their evolution laws, but is beyond the scope of the present study e.g.. The presence of a crust also questions the existence of a brittle mantle , since the transition between pseudo-brittle yield-stress and LT-dislocation creep is expected around 800 K for a background strain rate of 10-16–10-15 s⁻¹ (Fig. ), which corresponds to 27 km depth for a 50 Myr old plate, i.e. shallower than a continental Moho (∼ 30 km deep), but deeper than an oceanic one (∼ 4–10 km depth).

Neglecting elasticity is another limitation. This assumption may first lead to an overestimation (up to a factor of three) of shallow stresses in our models . In our visco-plastic experiments (“plastic” being here a synonym for “brittle”), the central peak in shallow stresses (at 5 km depth, Supplement, Sect. S5.2) is located in the area where strain localizes, and where free-surface elevation is noticeable. If reducing shallow stresses by a factor 4 (as shown by additional tests with depth-dependent yield stress) indeed leads to smaller central depression (factor ∼ 3), it does not modify the two-stage weakening scenario or the timing of incipient plate-boundary formation (see Appendix ). This supports the conclusion that the localization mechanisms identified in our study are controlled primarily by the rheological structure of the mid- and lower lithosphere, rather than by shallow stress alone.

Neglecting elasticity by assuming a viscoplastic rheology also affects the prediction of brittle deformation and fault development. Previous studies comparing viscoplastic and visco-elasto-plastic formulations have shown that, although first-order stress patterns may be comparable, elasticity implementation will change fault geometry, spatial distribution, interaction and rotation, as well as the rift-topography evolution e.g.. In particular, our yield-stress formulation produces distributed viscoplastic flow over a finite volume rather than localized planar faulting, and therefore does not capture the detailed geometry of brittle shear-band development. Viscoplastic formulations may exhibit mesh sensitivity and numerical convergence issues . Simulating a constant yield stress prevents the formation of shear bands in the pseudo-brittle layer . For a moderately fast extension, the pseudo-brittle layer deforms by pure shear in a layered lithosphere if the viscosity underneath the upper brittle layer is high ∼ 1023 Pa s,, which may explain the absence of shear bands in our models with a moderate yield stress increase with depth (viscosity ∼ 1023 Pa s at the yield-creep transition for a 500 MPa yield stress at ε˙=10-15 s⁻¹, Figs. a, c and ). More physically grounded approaches, including damage-based rheologies and visco-elasto-plastic formulations accounting for weakening by microcracks growth, may therefore improve the representation of shallow deformation , but remain computationnaly demanding. We acknowledge that treating the shallow brittle layer more realistically could significantly modify the deformation pattern at shallow depths, but expect the large-scale feedbacks of lithospheric weakening documented in this study to remain broadly relevant.