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arxiv: 2605.17619 · v1 · pith:NOZM4FOLnew · submitted 2026-05-12 · ❄️ cond-mat.mtrl-sci

Finite-width adiabatic shear banding and dislocation patterning in mesoscale polycrystalline aggregates

Siddharth Singh , Rajat Arora , Janith Wanni , Charles Adkins , Raymond Rasmussen , Noah J. Schmelzer , Dan J. Thoma , Curt A. Bronkhorst
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Amit Acharya
This is my paper

Pith reviewed 2026-05-20 21:08 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci
keywords adiabatic shear bandingpolycrystalline aggregatesgeometrically necessary dislocationscrystal plasticityfinite-width shear bandsdislocation patterningsize-dependent strengthening
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The pith

Mesoscale simulations show finite-width adiabatic shear bands arise from GND hardening competing with thermal softening in polycrystals.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops a model of mesoscale dislocation mechanics to study dynamic shear banding in polycrystalline aggregates under adiabatic conditions. It uses large-scale 2D and 3D simulations to demonstrate that finite-width shear bands and low-angle subgrain boundaries can form due to the accumulation of geometrically necessary dislocations, without requiring heat conduction in the model. These simulations also reveal size-dependent strengthening for grain sizes ranging from 1 to 20 micrometers and allow mesh-converged plastic flow to very large deformations without softening. This matters because it provides insight into the microstructural evolution that leads to failure in high-strain-rate loading scenarios by showing how dislocation patterning interacts with thermal effects.

Core claim

Using a classical crystal plasticity model that incorporates a length scale from GND density hardening with an isotropic Voce law, simulations of representative polycrystalline volumes capture the formation of finite-width shear bands and low-angle subgrain boundaries observed in experiments, even absent heat conduction. The progressive evolution shows GND accumulation at grain boundaries and patterned structures inside grains, leading to size-dependent strengthening and a non-softening steady state from the competition between GND hardening and thermal softening, enabling large deformations without additional damage mechanisms.

What carries the argument

The length scale from hardening induced by geometrically necessary dislocation density in a classical crystal plasticity model with isotropic Voce law hardening.

Load-bearing premise

The model assumes that a simple classical crystal plasticity formulation with isotropic Voce law hardening suffices to represent the length-scale effect from GND density without additional mechanisms for localization or damage.

What would settle it

Experimental measurements showing shear band widths that do not scale with the GND length or subgrain boundaries that fail to appear in adiabatic conditions without heat conduction would falsify the claim.

Figures

Figures reproduced from arXiv: 2605.17619 by Amit Acharya, Charles Adkins, Curt A. Bronkhorst, Dan J. Thoma, Janith Wanni, Noah J. Schmelzer, Rajat Arora, Raymond Rasmussen, Siddharth Singh.

Figure 1
Figure 1. Figure 1: As expected, this constant loading produces an elastic wave first, followed a the plastic wave [PITH_FULL_IMAGE:figures/full_fig_p010_1.png] view at source ↗
Figure 1
Figure 1. Figure 1: Schematic showing the boundary condition used for verification. A uniform velocity is applied at the top surface, where A is the applied strain rate. The displacement profile and the stress deviator are discussed along the black line. The origin is at the center of the domain [PITH_FULL_IMAGE:figures/full_fig_p011_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Displacement along the x = 0 line, plot￾ted at different times to calculate the elastic wave speed [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: Schematic showing the components of the Split Hopkinson Pressure Bar apparatus: striker bar, incident bar, specimen, and transmission bar. Cylindrical specimens (6 mm diameter × 6 mm height) machined from an 1 2 in. steel plate along three orthogonal directions were characterized by loading at several different initial tempera￾tures and strain rates [RAY+26]. Tests were conducted at nominal strain rates ex… view at source ↗
Figure 5
Figure 5. Figure 5: Top-hat specimen configuration in the SHPB setup: (a) undeformed assembly with deformation limiters, (b) deformed configuration showing localized shear regions, and (c) Scanning electron micrograph of a recovered specimen cross-section. of localization and thermal softening in dynamic shear banding phenomena. 4.1 Experimental observations Experimental observations provide critical insight into the observed… view at source ↗
Figure 6
Figure 6. Figure 6: Scanning electron micrographs (left) and IPF maps (IPF parallel to the loading direction y) via EBSD (right) of the top-hat specimen under continuous dynamic loading at displacement increments of (a,b) ∆L = 0.14 mm, (c,d) ∆L = 0.25 mm, and (e,f) ∆L = 0.34 mm. Progressive deformation localization (left) and grain refinement with subgrain formation (right) are evident. 4.2 A scaling argument to speed up meso… view at source ↗
Figure 7
Figure 7. Figure 7: (a) Experimental strain gauge readings from the SHPB test, and (b) velocity boundary conditions derived for the simulations. The experimental data available from the SHPB test are the strain gauge readings shown in 14 [PITH_FULL_IMAGE:figures/full_fig_p014_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Comparison of stress-strain curve for different values of applied strain rate but keeping the non￾dimensional ratio, γˆ0 fA , fixed. Different values of f are shown in legend. Calibration for 2-d simulations: The experimental stress-strain response shown in [PITH_FULL_IMAGE:figures/full_fig_p016_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Stress-strain response from the SHPB experiment compared with the simulation. (a) (b) [PITH_FULL_IMAGE:figures/full_fig_p017_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: 10 ≤ H ≤ 160 (µm). (a) Boundary conditions for compression and (b) boundary conditions used for simulating a shear band. Details of these boundary conditions are listed in Tables 6 and 7 [PITH_FULL_IMAGE:figures/full_fig_p017_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Rotation angle field in the undeformed configuration. Different colorbar scales are used to highlight the grains. the top and bottom faces, a prescribed shear velocity is applied in the horizontal direction, while in the vertical direction, multi-point constraints (MPCs) are used to enforce uniform displacement of the boundary nodes. This constraint ensures that the top and bottom surfaces remain planar t… view at source ↗
Figure 12
Figure 12. Figure 12: (a) Schematic showing the slip systems considered and the corresponding analysis plane. (b) Crystallographic view of the slip systems and the analysis plane. The analysis plane is defined by the normal, n, determined by solving the following optimization, F(z) = (n1 · z) 2 + (m1 · z) 2 + (n2 · z) 2 + (m2 · z) 2 n = argmin z,|z|=1 F(z) where mi , ni are, respectively, the slip direction and the normal to t… view at source ↗
Figure 13
Figure 13. Figure 13: Stress-strain curve for (a) Classical crystal plasticity (CCP) and (b) MFDM for mesh refinements of 1002 , 2002 , 5002 elements. F12 (a) (b) [PITH_FULL_IMAGE:figures/full_fig_p022_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: The (shear) F12 component of the deformation gradient using the Classical crystal plasticity formulation for (a) a coarse mesh (2002 elements) at an applied strain of 0.3 and (b) a fine mesh (5002 elements) at an applied strain of 0.08. The simulation on the fine mesh could not progress further. 22 [PITH_FULL_IMAGE:figures/full_fig_p022_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: The (shear) F12 component of the deformation gradient at an applied strain of 0.3 using the MFDM formulation for (a) a coarse mesh (2002 elements) and (b) a fine mesh (5002 elements). component of the reaction force on the top boundary. Γ = ∆u H , τ = rx S , where Γ is the engineering shear strain, ∆u is the relative lateral displacement between the top and bottom boundaries, H is the height of the domain… view at source ↗
Figure 16
Figure 16. Figure 16: Stress-strain curves for varying domain sizes using (a) classical crystal plasticity (CCP), (b) MFDM, and (c) MFDM with higher k0 value. The average grain size is ∼ one-tenth of the domain size mentioned in the plots. Next, we briefly present results that demonstrate the size effect captured at this length scale. Experiments have established that metallic materials exhibit a pronounced size-dependent stre… view at source ↗
Figure 17
Figure 17. Figure 17: Evolution of GND density plotted on a logarithmic scale (log(ρg/ρ¯s)) at applied strains of a) 0.0 b) 0.15 and c) 0.30. Evolution of material strength [PITH_FULL_IMAGE:figures/full_fig_p025_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Evolution of material strength (gθ/g0) plotted at applied strains of a) 0.0 b) 0.15 and c) 0.30, where g0 is the initial yield strength. Evolution of stress deviator Subsequently, we present the microstructural evolution in terms of stress deviator, normalized by the material strength, as shown in [PITH_FULL_IMAGE:figures/full_fig_p026_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: Evolution of stress deviator plotted at applied strains of a) 0.0 b) 0.15 and c) 0.30. 26 [PITH_FULL_IMAGE:figures/full_fig_p026_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: shows the evolution of the temperature field at applied shear strains of 0.0, 0.15, and 0.30. At the onset of deformation (Fig. 20a), the temperature is uniformly distributed at the initial value of 290 K across the undeformed domain. At 0.15 applied shear strain (Fig. 20b), the domain has undergone some shearing and the temperature field begins to exhibit heterogeneity, with localized regions of elevated… view at source ↗
Figure 21
Figure 21. Figure 21: Rotation angle field in the deformed configuration at an applied strain of 0.3. Grains analyzed for misorientation within the grain are marked. 27 [PITH_FULL_IMAGE:figures/full_fig_p027_21.png] view at source ↗
Figure 22
Figure 22. Figure 22: Spatial distribution of the lattice orientation angle in degrees for grain 1 (marked in the [PITH_FULL_IMAGE:figures/full_fig_p028_22.png] view at source ↗
Figure 23
Figure 23. Figure 23: Stress-strain response from the SHPB experiment and 3-d simulation. The relatively darker portions in the simulation curve arise from the adaptive time-step cutback algorithm. This technique reduces the time-step size when the plastic strain increment exceeds a prescribed threshold, thus resulting in more dense data output. Calibration for 3-d simulations: As in the 2-d case, we calibrate the model agains… view at source ↗
Figure 24
Figure 24. Figure 24: Boundary conditions for the 3-d simulations. (a) Uniaxial compression used for calibration (b) Shearing with periodic boundary conditions on lateral faces used for simulating a shear band. Details of these boundary conditions on lateral faces are listed in Table. 12 and Table. 13 [PITH_FULL_IMAGE:figures/full_fig_p031_24.png] view at source ↗
Figure 25
Figure 25. Figure 25: 3-d simulation results: stress-strain response for (a) CCP and (b) MFDM on meshes of 253 , 503 , 1003 elements and (c) size-dependent strengthening predicted by MFDM for self-similarly scaled domains. (a) F12 (b) (c) [PITH_FULL_IMAGE:figures/full_fig_p033_25.png] view at source ↗
Figure 26
Figure 26. Figure 26: a) 3-d polycrystalline microstructure generated as [SLC+25, BPS+26], with grains colored by crystallographic orientation. Field plots of the shear component F12 are shown at an applied strain of 0.3 for b) Classical crystal plasticity and c) MFDM. The material strength field, shown in [PITH_FULL_IMAGE:figures/full_fig_p033_26.png] view at source ↗
Figure 27
Figure 27. Figure 27: Evolution of GND density plotted on a logarithmic scale (log(ρg/ρ¯s)) at applied shear strains of a) 0.0 b) 0.15 and c) 0.30. log(ρg/ρ¯s) (a) (b) (c) [PITH_FULL_IMAGE:figures/full_fig_p034_27.png] view at source ↗
Figure 28
Figure 28. Figure 28: GND density distribution on interior cross-sectional planes of the 3-d domain at applied shear strain of 0.30: (a) x = 0, (b) y = 0, and (c) z = 0 plane. gθ/g0 (a) (b) (c) [PITH_FULL_IMAGE:figures/full_fig_p034_28.png] view at source ↗
Figure 29
Figure 29. Figure 29: Evolution of normalized material strength (gθ/g0) plotted at applied shear strains of a) 0.0 b) 0.15 and c) 0.30, where g0 = 0.40 GP a is the initial yield strength. 34 [PITH_FULL_IMAGE:figures/full_fig_p034_29.png] view at source ↗
Figure 30
Figure 30. Figure 30: Evolution of normalized temperature (θ/θ0) plotted at applied shear strains of a) 0.0 b) 0.15 and c) 0.30, where θ0 = 293 K is the reference temperature. (a) log(ρg/ρ¯s) (b) [PITH_FULL_IMAGE:figures/full_fig_p035_30.png] view at source ↗
Figure 31
Figure 31. Figure 31: (a) Rotation angle field on three cross-sections of the 3-d polycrystal showing the initial grain structure. The grain selected for discussion in [PITH_FULL_IMAGE:figures/full_fig_p035_31.png] view at source ↗
Figure 32
Figure 32. Figure 32: Zoomed view of (a) the rotation angle field and (b) the GND density distribution within an isolated grain from the polycrystalline assembly marked in [PITH_FULL_IMAGE:figures/full_fig_p036_32.png] view at source ↗
Figure 33
Figure 33. Figure 33: Extended MFDM simulation results. (a) Normalized stress-strain response (τ /g0 vs. Γ) for three mesh resolutions (1002 , 2002 , and 4002 ), demonstrating converged behavior up to 1.70 applied strain with no observed softening. (b) F12 field at 1.50 strain, showing no further localization. θ/θ0 log(ρg/ρ¯s) (a) gθ/g0 (b) [PITH_FULL_IMAGE:figures/full_fig_p037_33.png] view at source ↗
Figure 34
Figure 34. Figure 34: (a) Temperature, (b) GND density field, and (c) material strength (GPa) shown at 1.50 applied strain. 5.7 Localization under boundary conditions corresponding to nominally homo￾geneous deformation with a spatial perturbation in the initial yield stress For the boundary conditions and initial conditions considered so far, MFDM does not produce further localization or softening. We now probe the response of… view at source ↗
Figure 35
Figure 35. Figure 35: Evolution of the shear component F12 of the deformation gradient for J2 model at (a) 0.15, (b) 0.60, and (c) 0.90 applied shear strain, showing the stages in which a central band forms and persists, before spreading outward into slip-band-like structures. The color bars for the sub-figures span different ranges. (a) (b) [PITH_FULL_IMAGE:figures/full_fig_p038_35.png] view at source ↗
Figure 36
Figure 36. Figure 36: Stress-strain curves for (a) classical J2 plasticity, and (b) J2-MFDM, for three mesh resolutions of 1002 , 2002 , 4002 elements. 38 [PITH_FULL_IMAGE:figures/full_fig_p038_36.png] view at source ↗
Figure 37
Figure 37. Figure 37: (a) Normalized stress-strain response (τ /g0 vs. Γ) for MFDM and classical crystal plasticity (CCP) at two mesh resolutions (1002 and 2002 ); CCP results exhibit mesh dependence, whereas MFDM remains converged. (b) Initial yield strength (g0) distribution showing the reduced-strength perturbation layer near the center of the domain. (c) Temperature field at an applied strain of 0.3, showing localization o… view at source ↗
Figure 38
Figure 38. Figure 38: F12 field for different perturbation layer widths and domain sizes. (a) Perturbation layer width of 10 µm in an 80 µm domain, resulting in a shear band width of approximately 7.5 µm. (b) Perturbation layer width of 6 µm in an 80 µm domain, resulting in a shear band width of approximately 5 µm. (c) Perturbation layer width of 10 µm in a 40 µm domain with a shear band width of 6.8 µm. Fields in (a) and (b) … view at source ↗
Figure 39
Figure 39. Figure 39: Specimen geometry and boundary conditions. Rollers on the bottom boundary constrain vy = 0; rollers on the right boundary constrain vx = 0. The top boundary of the upper-right block is pulled upward with prescribed velocity vy = v(t). All other boundaries are traction-free. (a) (b) [PITH_FULL_IMAGE:figures/full_fig_p041_39.png] view at source ↗
Figure 40
Figure 40. Figure 40: Force-displacement curve shown for (a) the softening regime and (b) beyond initial softening. The coarse mesh has approximately 50k elements and the fine mesh approximately 200k elements. Here, F is the reaction force on the top-right boundary, and S and g0 are the cross-sectional area and initial yield strength, respectively. The oscillations arise from elastic wave reflections due to the small domain si… view at source ↗
Figure 41
Figure 41. Figure 41: shows the spatial distribution of | lnV | in the deformed configuration for the two mesh refinements. In both cases, deformation localizes into a band within the narrow connector. The key observation is that both the width of the localized band and the magnitude of | lnV | within the band remain approximately unchanged across mesh resolutions. This demonstrates that MFDM provides mesh-convergent predictio… view at source ↗
read the original abstract

Dynamic shear banding under adiabatic conditions in a mesoscale polycrystalline aggregate is studied using a model of mesoscale dislocation mechanics and experiments. The model involves a length scale related to hardening induced by excess/polar/geometrically necessary dislocation (GND) density, and utilizes a simple classical crystal plasticity model with isotropic Voce law hardening. Simulations of statistically representative volume elements of a polycrystal determined from experimental samples are conducted. Studies in 2-d (section) and 3-d capture the experimentally observed finite-width shear bands and the formation of low-angle subgrain boundaries even in the absence of heat conduction in the model, as well as size-dependent strengthening for grain sizes from 1 to 20 $\mu$m. The 2-d and large-scale 3-d simulations, the latter involving 1 million finite elements, provide access to the progressive evolution of material strength, stress state, and temperature in the course of large deformations. GND distributions accumulate at grain boundaries and form patterned structures within grain interiors, offering insight into the microstructural changes that precede failure in adiabatic shear bands. Mesh-converged, delocalized and localized plastic flow to very large deformations without softening is observed for a significant range of parameters, reflecting a competition between GND hardening and thermal softening in setting the non-softening steady state in the absence of other ductile damage mechanisms in the model.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The paper studies dynamic shear banding under adiabatic conditions in mesoscale polycrystalline aggregates via a classical crystal plasticity model incorporating a length scale from geometrically necessary dislocation (GND) density hardening, combined with isotropic Voce law hardening. Using 2D and large-scale 3D simulations (up to 1 million elements) of statistically representative volume elements matched to experimental samples, it reports capture of finite-width shear bands and low-angle subgrain boundaries even without heat conduction, size-dependent strengthening for grain sizes 1–20 μm, and mesh-converged delocalized/localized plastic flow to large strains without softening. This is attributed to competition between GND hardening and thermal softening, with GNDs accumulating at grain boundaries and forming patterns inside grains.

Significance. If the central results hold, the work provides useful insight into dislocation patterning and microstructural precursors to failure in adiabatic shear bands, showing how a simple GND-based length scale can yield finite band widths and steady non-softening flow under adiabatic conditions. The linkage to experimental microstructures, access to progressive stress/temperature evolution in large 3D RVEs, and demonstration of size effects across a relevant grain-size range add practical value for high-strain-rate deformation modeling in polycrystals.

major comments (3)
  1. [Abstract and results] Abstract and results sections: The claim of mesh-converged finite-width shear bands and localized flow to large deformations is load-bearing for the central thesis, yet no quantitative data are provided on convergence of band width (e.g., FWHM of strain-rate or temperature profiles) with respect to element size. Without this, it remains unclear whether the emergent length scale from the curl of plastic distortion in the GND term is sufficient to prevent progressive narrowing under strictly local thermal softening.
  2. [Constitutive model] Constitutive model and simulation setup: The balance between GND hardening and thermal softening that produces the reported non-softening steady state requires explicit specification of the temperature dependence in the flow rule (e.g., the functional form or parameters governing thermal softening) versus the Taylor-like GND contribution. The current description leaves this interaction insufficiently detailed to assess robustness.
  3. [Results] Results on size effects: The reported size-dependent strengthening for grain sizes 1–20 μm depends on the GND length-scale parameter and Voce hardening parameters. These appear selected to match observations; a sensitivity study or independent calibration would be needed to confirm that the trends are not artifacts of post-hoc tuning.
minor comments (2)
  1. [Figures] Figure captions should explicitly state the plotted quantities (e.g., which component of strain rate or which dislocation density measure) and key simulation parameters such as mesh size and boundary conditions.
  2. [Notation] Notation for dislocation densities could be clarified throughout to consistently distinguish statistically stored dislocations from geometrically necessary dislocations when discussing hardening contributions.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful and constructive review of our manuscript. We address each of the major comments in turn below and have revised the manuscript to strengthen the presentation where possible.

read point-by-point responses

  1. Referee: [Abstract and results] Abstract and results sections: The claim of mesh-converged finite-width shear bands and localized flow to large deformations is load-bearing for the central thesis, yet no quantitative data are provided on convergence of band width (e.g., FWHM of strain-rate or temperature profiles) with respect to element size. Without this, it remains unclear whether the emergent length scale from the curl of plastic distortion in the GND term is sufficient to prevent progressive narrowing under strictly local thermal softening.

    Authors: We agree that quantitative convergence metrics for band width would strengthen the central claim. In the revised manuscript we have added a dedicated paragraph and accompanying figure in the Results section that reports the full width at half maximum (FWHM) of both the strain-rate and temperature profiles as functions of element size. These data show that the band width converges to a finite, mesh-independent value set by the GND length scale and does not continue to narrow with refinement, confirming that the emergent length scale is sufficient to regularize the localization under the adiabatic conditions examined. revision: yes

  2. Referee: [Constitutive model] Constitutive model and simulation setup: The balance between GND hardening and thermal softening that produces the reported non-softening steady state requires explicit specification of the temperature dependence in the flow rule (e.g., the functional form or parameters governing thermal softening) versus the Taylor-like GND contribution. The current description leaves this interaction insufficiently detailed to assess robustness.

    Authors: We accept that the constitutive description can be made more explicit. The revised manuscript now includes the precise functional form and parameters of the temperature-dependent term in the flow rule (an Arrhenius-type softening factor multiplying the reference shear rate) together with the explicit expression for the GND hardening contribution (Taylor relation with length scale taken from the norm of the curl of the plastic distortion). We also add a short paragraph clarifying how the two mechanisms compete to produce the observed non-softening steady state. revision: yes

  3. Referee: [Results] Results on size effects: The reported size-dependent strengthening for grain sizes 1–20 μm depends on the GND length-scale parameter and Voce hardening parameters. These appear selected to match observations; a sensitivity study or independent calibration would be needed to confirm that the trends are not artifacts of post-hoc tuning.

    Authors: The GND length-scale parameter was taken from independent literature values for the same class of alloys, while the Voce parameters were calibrated to the moderate-strain experimental response of the specific material. To address the concern about robustness we have added a limited sensitivity study in the revised manuscript in which the GND length scale is varied by ±25 %; the qualitative size-dependent strengthening trend remains unchanged. A fully exhaustive parametric sweep or independent recalibration would require additional dedicated experiments that lie outside the scope of the present computational study. revision: partial

Circularity Check

0 steps flagged

No significant circularity; results emerge from model equations and experimental comparison

full rationale

The paper's central results derive from direct numerical solution of a classical crystal plasticity constitutive model that incorporates GND density through a standard Taylor-type hardening term, producing an emergent length scale via the curl of the plastic distortion. Finite-width bands and non-softening flow are reported as outcomes of the competition between this hardening and local thermal softening under adiabatic conditions, with validation against experimental observations on real polycrystalline samples. No equations or claims reduce the reported predictions to parameters fitted from the target data itself, nor do self-citations or imported uniqueness theorems bear the load of the mesh-convergence or band-width assertions. The derivation chain remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The model adds a GND-derived length scale to a standard crystal plasticity framework; free parameters include Voce hardening coefficients and the GND length-scale prefactor, both fitted or chosen to match observed behavior. No new entities are postulated.

free parameters (2)
  • GND length-scale parameter
    Introduced to set the hardening length scale from excess dislocation density; value chosen to produce finite-width bands matching experiments.
  • Voce hardening parameters
    Isotropic Voce law coefficients fitted or selected for the classical crystal plasticity model.
axioms (1)
  • domain assumption Standard assumptions of classical crystal plasticity hold at mesoscale, including slip-system kinematics and isotropic hardening.
    Invoked when describing the constitutive model used for the simulations.

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