{"id":"147b03b4-7730-4de3-9797-a59a788f5296","arxiv_id":"1908.07826","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"Explicit finite element simulations show that finite-size boundaries make velocity-weakening friction unstable at long times, while velocity-weakening-strengthening friction reaches a steady sliding state.","lead":"This computational paper uses explicit finite element simulations to study rate-and-state friction between two elastic blocks, comparing velocity-weakening and velocity-weakening-strengthening laws. It shows that boundary reflections destroy the early fracture-like stress drop and that only the strengthening law reaches a stable long-term sliding state.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The VW long-time instability is asserted without a time-step/mesh convergence study, so the central claim that pure velocity-weakening friction lacks physical validity for finite systems is not yet separated from numerical noise.","rationale":"The reader's weakest assumption is exactly the load-bearing concern: Section 5.2's VW conclusion rests on a single simulation without the time-step/mesh convergence checks that Section 4.2 shows are necessary for this numerical method. Section 4.2 demonstrates that the same explicit scheme produces non-physical interfacial oscillations for alpha >= 0.05, with onset time scaling linearly with element size and attributed to internal-node noise. The finite-size VW run is described as following the same numerical procedure at alpha = 0.02, but no verification shows that the runaway after reflection is not the same internal-node mechanism excited by reflected waves. A VW law with a < b is classically unstable under load control, so the physical conclusion is plausible; however, the paper overreaches by declaring the law 'lacks physical validity' based on numerical evidence not separated from discretization artifacts. The proposed alpha/h refinement test would settle this. I do not see a different, more severe flaw: the early-time FEM/BIM agreement in Section 5.1.1 provides independent support for the method, so the concern is limited to the long-time VW conclusion. Thus the verdict remains conditional pending that test.","tokens_in":30835,"tokens_out":4841,"duration_ms":48667,"concrete_test":"Repeat the finite-H VW simulation of Section 5.2 with alpha = 0.02, 0.01, 0.005, 0.0025 and with interface meshes of 125, 250, 500, and 1000 elements, keeping H and L fixed. Record the onset time and peak slip velocity of the post-reflection acceleration. If the runaway time and peak velocity converge to nonzero limits as alpha -> 0 and h -> 0, the VW instability is physical. If the onset shifts monotonically with alpha/h or disappears below a threshold, it is numerical and the central claim fails.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim (Section 5.2) is that pure VW friction becomes unstable after boundary reflections and therefore \"lacks physical validity when the long term behavior of frictional interfaces... is investigated.\" The only evidence offered is that \"the calculations become unstable as soon as the reflected waves reach back the frictional interface,\" with no convergence analysis. This is precisely the regime in which Section 4.2 shows that explicit-FEM rate-and-state friction develops numerical instabilities from internal-node noise: for alpha >= 0.05, steady sliding breaks into non-physical oscillations, with instability onset scaling linearly with element size. The finite-size VW simulation uses the same procedure as the VWS case (alpha = 0.02, 250 interface elements, per Section 5.1.1), but no alpha- or h-refinement study is reported for the VW run. If the runaway is triggered by discretization noise rather than by the (a-b)<0 constitutive response, then the conclusion that VW is physically invalid and only VWS reaches steady state collapses. The physical expectation—that VW under fixed shear traction is classically unstable—is not in dispute, but the paper's evidence does not establish that the observed finite-size instability is physical rather than numerical.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper presents an explicit-dynamics finite element formulation for rate-and-state friction between finite elastic blocks, with node-to-node contact and central-difference time integration detailed in the appendices. The authors analyze the time-step constraint for steady sliding, attribute the need for very small time steps to noise from internal discretization nodes, and benchmark the early-time rupture response against a boundary integral method. They then study the effect of boundary reflections on long-term sliding for a velocity-weakening (VW) law and a velocity-weakening-strengthening (VWS) law. The main claims are that VWS reaches a global steady-state sliding configuration after multiple reflections, while VW accelerates and becomes unstable, so that pure VW \"lacks physical validity\" for long-term finite-domain studies.","tokens_in":31120,"tokens_out":6787,"duration_ms":68411,"significance":"If the long-term dichotomy is physical, the paper is a useful contribution to finite-size rate-and-state friction modeling: unlike boundary integral formulations, the FEM captures boundary interactions, and the paper documents a nontrivial numerical-stability requirement (time steps well below the CFL limit) in the studied configuration. The early-time FEM/BIM agreement in Figure 7b is a genuine validation, and the energy accounting and interface-averaged diagnostics in Figures 10-12 are informative. The paper also makes a falsifiable prediction: pure VW friction cannot settle into a steady sliding state after boundary reflections, whereas VWS can. The main weakness is that the key VW prediction is asserted from a single run with no convergence study, in a regime where the authors themselves show that numerical noise can trigger instability.","major_comments":[{"comment":"The central claim that pure VW friction lacks physical validity in finite systems is supported only by the statement that \"the calculations become unstable as soon as the reflected waves reach back the frictional interface.\" Section 4.2 demonstrates that this explicit FEM develops non-physical oscillations for time steps alpha >= 0.05 (Figure 4) and that the onset time of such oscillations scales linearly with element size (Figure 5b). The VW reflected-wave run uses alpha = 0.02 and 250 interface elements, but no alpha- or h-refinement study is reported for this case. A convergence study (for example alpha = 0.02, 0.01, 0.005 and at least two mesh refinements, reporting the instability onset time, slip-velocity growth rate, and final state) is required to separate a physical VW instability from the discretization noise characterized in Section 4.2; without it, the paper's main conclusion is not established.","section":"Section 5.2 (VW perturbation analysis)"},{"comment":"The statement that \"the pure VW friction cannot generate interface tractions that equilibrate the far field load\" is imprecise and, taken literally, incorrect: for the chosen parameters, Equation (4) gives fss = 0.36 at v0_ss = 2.93627e-4 m/s (the purple star in Figure 3b), so the VW law does possess an interface traction that equilibrates the applied shear. What the simulations indicate is that this equilibrium is not stable under perturbations and after boundary reflections. The wording should be changed to \"cannot stably maintain\" or \"does not converge to\", and the discussion should distinguish between existence and stability of the equilibrium.","section":"Section 5.2, final paragraph"},{"comment":"The FEM/BIM validation is reported only for the maximum slip velocity and only for one discretization (250 interface elements, alpha = 0.02). Since the paper's long-term conclusions are drawn from simulations with this same discretization, a mesh- and time-step-convergence test of the rupture solution, not just of steady sliding, is needed to establish that the VWS/VW differences are not resolution effects. At minimum, a second mesh refinement and a smaller alpha should be reported for the rupture simulations.","section":"Section 5.1.1 and Figure 7b"}],"minor_comments":[{"comment":"The manuscript contains numerous typos (e.g., \"purturbed\", \"corresonding\", \"seubsequent\", \"caluclated\", \"fricition\") and should be carefully proofread.","section":"Throughout"},{"comment":"There are clear remnants of an earlier draft: orphan headings such as \"3.1.2. Contact algorithm\", \"3.1.3. Frcition algorithm\", and \"3.2. Spectral element approach\" appear in the text, and some equations and figures are numbered inconsistently (Equations 6-10 versus 7-9; \"Figure ??\" in Section 4.1). These should be cleaned.","section":"Sections 3 and 4.1"},{"comment":"Figure 1 is duplicated and the captions/panels do not match the text: one copy shows stationary friction curves with a different caption from the other copy, and the panel labels are inconsistent. Please regenerate the figure and a single correct caption.","section":"Figure 1"},{"comment":"The interpretation of the stress drop and radiation damping draws on refs [25,26]; reference [26] is listed as \"To be submitted\" and reference [25] is an arXiv preprint. The relevant statements should either be demonstrated from equations in the present paper or refer to published/archived versions.","section":"Sections 5.1 and 5.2"},{"comment":"The claim that the instability originates from internal discretization nodes is an inference from the linear tcrit-versus-element-size scaling and the structured/unstructured mesh comparison (Figure 5). A direct test, such as comparing with an interface-only discretization or with nodal filtering, would make the noise-source attribution more conclusive.","section":"Section 4.2"},{"comment":"The axis labels in Figure 4c and the legend in Figure 10c are difficult to read; please enlarge the fonts and define the symbols (for example, the \"123\" marking in Figure 10b).","section":"Figures 4c and 10c"}],"recommendation":"major_revision","confidential_remarks":"The main technical issue is the missing convergence study for the VW reflected-wave simulation; the rest of the paper appears sound. I would not raise novelty concerns, but the reliance on companion manuscripts [25,26], one of which is \"To be submitted\", should be resolved before publication. The manuscript also has extensive copy-editing needs, including duplicated figure captions and orphan section headings, that are not appropriate for the final version."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Let me cut to the chase. This is a useful paper, but the central claim is one convergence study short of being established. The authors show that in a finite elastic domain, velocity-weakening-strengthening friction reaches a steady sliding state after boundary reflections while pure velocity-weakening friction runs away. That qualitative contrast is plausible and physically expected under load control, but the VW runaway is reported without any time-step or mesh refinement, in a method where they themselves show that explicit FEM with rate-and-state friction develops numerical instabilities from internal-node noise once alpha >= 0.05. So the simulation evidence does not yet separate a physical instability from a discretization artifact.\n\nWhat is genuinely new: the systematic explicit FE treatment of rate-and-state friction, the time-step and mesh-size analysis of numerical noise, and the finite-size boundary-reflection study. The early-time FEM/BIM benchmark is convincing, and the energy accounting is clean. The paper does a service by showing that the fracture-like stress drop is erased by boundary reflections and that a temporary steady state is not a global one. The noise-source analysis, with structured versus unstructured meshes and the linear scaling of instability onset with element size, is informative and worth citing.\n\nThe soft spots are concentrated in Section 5.2. The statement that pure VW friction \"lacks physical validity\" is too strong given the evidence presented. A referee should ask for alpha- and h-convergence runs for the VW case, and for the VWS case too if not already done. If the runaway persists with decreasing time step and mesh size, the conclusion stands; if it does not, the physical claim collapses to the well-known classical instability of VW under fixed traction, which is not the same as the finite-size numerical observation. Also minor: the interpretation leans on companion references [25,26], one of which is unpublished; that should be cleaned up before publication.\n\nWho is this for? Researchers doing numerical rupture with rate-and-state friction, especially those interpreting laboratory PMMA experiments or thinking about boundary effects in finite samples. I would send it to peer review, with the convergence request above, and I would bring it to a reading group to discuss the numerical-versus-physical instability question.","headline":"Useful explicit-FEM study of rate-and-state friction with a real finite-size effect, but the claim that pure velocity-weakening lacks physical validity goes beyond the convergence evidence.","tokens_in":31629,"tokens_out":2937,"would_cite":true,"duration_ms":36076,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Pure velocity-weakening friction cannot equilibrate a far-field load, so finite-size frictional sliding needs the strengthening-branch law.","keywords":["rate and state friction","finite element method","explicit dynamics","frictional rupture","velocity weakening","velocity weakening-strengthening","boundary reflections","stress drop"],"falsifier":"Run the velocity-weakening long-time case with successively refined interface meshes and time steps (for instance, α = 0.01 and element sizes below 1.4 mm): if the runaway acceleration disappears or a steady sliding velocity emerges as resolution improves, the claim that pure VW cannot equilibrate the far-field load would be refuted; if the runaway persists at every resolution, the claim survives.","tokens_in":30638,"feed_emoji":"⚡","tokens_out":7255,"duration_ms":67487,"temperature":0.7,"pith_summary":"This paper asks what happens to a rate-and-state frictional interface when the sliding bodies are finite, so elastic waves bounce off the domain boundaries and return to the interface. Using an explicit finite element method with node-to-node contact, it shows that before those reflected waves arrive, both a pure velocity-weakening (VW) law and a velocity-weakening-strengthening (VWS) law reach a temporary steady sliding state with a well-defined stress drop behind the rupture front, matching the fracture analogy. After repeated reflections, the VWS law converges to a global steady state in which interface friction balances the applied far-field shear stress, while the VW law makes the blocks accelerate and never reaches equilibrium. The paper concludes that pure VW friction cannot produce interface tractions that balance the far-field load, and therefore lacks physical validity for long-term frictional sliding in finite systems. This matters because most rate-and-state simulations use infinite-domain boundary integral methods, which cannot see the boundary-reflection effects that decide whether a sliding state is stable.","feed_headline":"Pure velocity-weakening friction never reaches steady sliding","feed_subtitle":"Once boundary waves return, the interface accelerates without bound; only the strengthening law reaches equilibrium.","key_machinery":"The central object is the rate-and-state friction law, in which the friction coefficient $f$ depends on the slip velocity $v$ and a state variable $\\varphi$ (the average lifetime of load-carrying contact asperities) through $f=f_0+a\\ln(v/v_*)+b\\ln(\\varphi/\\varphi_*)$ and $\\dot\\varphi=1-v\\varphi/D$, together with a revised law that adds a velocity-strengthening branch at high slip velocity. The numerical machinery is an explicit finite element solver with central-difference time integration and node-to-node contact, which is needed to include finite domain boundaries that boundary integral methods cannot represent. The physical mechanism that carries the argument is the return of reflected elastic waves to the interface: each reflection changes the average slip velocity and shear traction, and the paper shows that these successive changes drive VWS friction to the equilibrium point on its steady-state friction curve while driving VW friction away from any equilibrium. The paper also identifies the finite element internal-node noise that requires time steps far below the CFL stability limit for accurate rate-and-state solutions.","core_discovery":"The central claim is that the physically relevant distinction between the two families of rate-and-state friction laws only appears once finite boundaries are included. In an infinite-domain setting, both the pure velocity-weakening law and the velocity-weakening-strengthening law generate rupture fronts with a temporary steady state and a sharp shear-stress drop, so the fracture-mechanics analogy holds. When the blocks have finite height, the waves reflected from the top and bottom boundaries come back to the interface and repeatedly change the slip velocity and shear traction. For the VWS law these repeated impacts push the interface toward the intersection of the steady-state friction curve with the far-field loading line, so the blocks slide uniformly and the stress drop decays to zero. For the pure VW law, the same reflected waves accelerate the interface: the friction coefficient drops as velocity increases, so the interface can never produce enough traction to balance the applied shear stress, and the numerical simulation becomes unstable once reflections arrive. The paper therefore asserts that pure VW friction is not physically valid for the long-term behavior of frictional interfaces in interaction with domain boundaries, whereas VWS friction is.","pith_inferences":["If the VW runaway is physical, then long-term earthquake and laboratory sliding models on finite faults that use pure VW friction may need a high-velocity strengthening cutoff or additional regularization to avoid unbounded acceleration—a modification the paper does not explore.","A direct numerical test of the paper's central claim would be to refine the mesh and reduce the time step for the VW long-time case; the runaway should persist at every resolution if it is physical, and disappear if it is an artifact of internal-node noise.","The near-linear relation the paper observes between the average stress drop and the velocity jumps at each reflection suggests a quantitative finite-size radiation-damping law could be derived, extending infinite-domain crack theory to finite blocks.","Laboratory interfaces that exhibit long-term stable sliding may be those whose friction has a strengthening branch, implying that the VWS form, rather than pure VW, is the safer default for interpreting finite-size experiments."],"forward_implications":["In finite-size rate-and-state models, pure velocity-weakening friction is only usable for times shorter than the wave-return time; after that it predicts runaway acceleration rather than steady sliding.","The fracture-mechanics analogy for frictional rupture—a stress drop behind the front—is a finite-time effect that disappears once boundary reflections homogenize the interface.","Long-term numerical models of frictional interfaces in finite domains should adopt velocity-weakening-strengthening friction if they aim to reproduce steady sliding under constant far-field load.","Explicit finite element simulation of rate-and-state friction requires time steps orders of magnitude smaller than the CFL limit, and the instability seeded by internal-node noise must be controlled before long-time physics can be extracted.","The agreement with boundary integral results in the pre-reflection phase establishes finite element simulations as a valid tool for capturing finite-size effects that infinite-domain methods cannot address."],"supporting_citations":[{"why":"Supplies the experimental rate-and-state constitutive law with the state variable the simulations use.","marker":"[39]"},{"why":"Provides the state-variable evolution framework adopted in the simulations.","marker":"[40]"},{"why":"Introduces the revised rate-and-state form whose steady-state curve has the velocity-strengthening branch.","marker":"[42, 43]"},{"why":"Supplies the spectral boundary integral method used as the infinite-domain comparison baseline.","marker":"[27]"},{"why":"Provides the theoretical relation between stress drops and slip velocity that underpins the fracture analogy.","marker":"[25]"},{"why":"Provides the boundary integral solution the finite element results are validated against in the pre-reflection phase.","marker":"[47]"},{"why":"Supplies the finite element formulation and notation for the explicit dynamic solver.","marker":"[30]"}],"fun_headline_variants":["Finite boundaries doom velocity-weakening friction","Wave reflections destabilize velocity-weakening friction","Why velocity-weakening friction is unstable in finite solids","Boundaries decide: velocity-weakening fails, strengthening survives"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The conclusion that pure velocity-weakening friction is physically invalid for long-term sliding rests on the assumption that the runaway acceleration seen in the simulations is a real physical instability and not an artifact of the numerical noise that the paper itself shows can destabilize explicit finite element solutions.","fun_headline_variants_meta":{"raw":{"variants":["Finite boundaries doom velocity-weakening friction","Wave reflections destabilize velocity-weakening friction","Why velocity-weakening friction is unstable in finite solids","Boundaries decide: velocity-weakening fails, strengthening survives"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000187,"raw_usage":{"total_tokens":1372,"prompt_tokens":1030,"completion_tokens":342,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":646,"completion_tokens_details":{"reasoning_tokens":282}},"tokens_in":646,"tokens_out":342,"duration_ms":4228,"temperature":1.0,"reasoning_tokens":282,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T15:20:03.219982+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the velocity-weakening long-time case with successively refined interface meshes and time steps (for instance, α = 0.01 and element sizes below 1.4 mm): if the runaway acceleration disappears or a steady sliding velocity emerges as resolution improves, the claim that pure VW cannot equilibrate the far-field load would be refuted; if the runaway persists at every resolution, the claim survives.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the experimental rate-and-state constitutive law with the state variable the simulations use."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the state-variable evolution framework adopted in the simulations."},{"cited_title":"Geubelle and J","cited_arxiv_id":null,"evidence_quote":"Supplies the spectral boundary integral method used as the infinite-domain comparison baseline."},{"cited_title":"Barras, M","cited_arxiv_id":null,"evidence_quote":"Provides the theoretical relation between stress drops and slip velocity that underpins the fracture analogy."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the boundary integral solution the finite element results are validated against in the pre-reflection phase."},{"cited_title":"Belytschko, W","cited_arxiv_id":null,"evidence_quote":"Supplies the finite element formulation and notation for the explicit dynamic solver."}],"review_version":1}