Inelastic Deformation Research Articles

Correction to “Inelastic Deformation in Methylammonium Lead Iodide Perovskite and Mitigation by Additives during Thermal Cycling”

Correction to “Inelastic Deformation in Methylammonium Lead Iodide Perovskite and Mitigation by Additives during Thermal Cycling”

Theoretical nonlinear force-displacement constitutive model of triangular-plate steel damper

Utilizing the inelastic deformation of a steel damper to dissipate seismic energy and control structural damage is a prevalent design strategy in a passive control field. Such a design strategy requires an explicit force-displacement constitutive model of the steel damper in both the elastic and plastic deformation phases. Currently, the nonlinear force-displacement relationship of the steel damper is mainly determined by quasi-static tests or numerical simulations which are generally time-consuming, and there is a lack of a theoretical and straightforward approach to determine the nonlinear force-displacement constitutive model of the steel damper. This study thus theoretically derives the nonlinear force-displacement constitutive model for a commonly used triangular-plate steel damper. The theoretical formula is derived based on the equal curvature assumption commonly applied to the triangular plate and is further modified based on the curvature shape function proposed in this study for the first time. After that, the force-displacement curves obtained from the theoretical formula are compared with those obtained from a large number of numerical simulations and several sets of quasi-static tests. The result shows that the theoretical formula derived based on the curvature shape function can better predict the nonlinear force-displacement curve of the triangular-plate steel damper, which significantly outperforms the theoretical formula derived based on the equal curvature assumption especially as the triangular-plate steel damper has a large plastic deformation. Furthermore, the influence factors of the strain-hardening phenomenon existing in the force-displacement curve of the triangular-plate steel damper are analyzed based on the modified theoretical formula. The result implies that the thickness-to-height ratio of the plate is the most significant factor for the strain-hardening behavior of the triangular-plate steel damper.

Damped rigid substructure system for seismic protection of structures

Building codes commonly accept inelastic deformations that inevitably occur due to seismic excursions in structures. To control the damage, limits on the inelastic deformations have been established. Standard passive energy dissipation systems have been used to reduce the damage, generally with some effectiveness. The damped rigid substructure (DRS) passive damping system, proposed in this article, geometrically amplifies the damper displacements and exerts a re-centering force, leading to effective discharge of the seismic energy to the extent that structural damage can be prevented. This is achieved using common damped and undamped diagonals arranged per implementation and design principles introduced in this article. The DRS system can considerably reduce material consumption and construction costs, leading to more sustainable structures when seismic forces govern the design. It can also benefit from the usage of high-strength materials to enhance its re-centering mechanism. The system is adaptable to the architectural needs and can be used for all categories of importance and height variation, made of steel or concrete.

A finite strain micromechanical-based constitutive model: Application to porous polycrystal

A finite strain micromechanical-based constitutive model is developed for multi-phase polycrystal to characterize the interplay among strain hardening, texture evolution, and stress-strain relation. The phases are regarded as ellipsoidal inhomogeneities within the polycrystalline matrix, which can be considered as an aggregation of different orientated grains. At the grain level, the crystal plasticity model is applied to physically describe the inelastic deformation results from crystallographic slipping. At the polycrystalline level, an algorithmic finite strain self-consistent model is proposed to associate the strain and rotation rate at the grain level with the corresponding terms of the polycrystalline matrix rigorously. At the representative volume element level, the phases with different properties are investigated by extending the Mori–Tanaka model at finite strain. The algorithmic self-consistent model is validated by comparing the calculated normalized stress-strain curves and textures with those obtained by the model adopting extended Taylor hypothesis and the experimental data of stainless steel. Moreover, the grain and polycrystalline level behaviors calculated by the algorithmic self-consistent model are compared to those derived from the full-field model. The effects of void and elastic particles on overall mechanical behavior are analyzed by the extended Mori–Tanaka model, which is then verified by predicting the mechanical behavior of sintered nano-silver stub columns under stress-controlled compression loads.

Finite-element stress and strain analysis of tin–silver–copper solders exposed to isothermal ageing at 100°C

This research aims to investigate the influence of pre-isothermal aging on the mechanical behaviour of 98.5Sn–1.0Ag-0.5Cu (SAC105) and 96.5Sn–3.0Ag–0.5Cu (SAC305) interconnects using non-linear finite-element simulations. To accomplish this, reliable literature sources are used to gather the material properties (both elastic and inelastic) of the aged SAC solders, which are then appropriately incorporated into the simulation process. Various aging durations, ranging from 1 to 6 months, are analysed. The results of the numerical computations demonstrate that the mechanical response of pre-aged SAC solders, subjected to thermal cycling, is significantly influenced by the ageing process. Specifically, the non-aged SAC305 configuration exhibits lower inelastic deformations and strain energies compared to the SAC105 system, indicating potentially better thermal fatigue performance. However, SAC105 solders generally exhibit greater resistance to aging, leading to lower levels of inelastic strains and strain energies, particularly for shorter aging durations. In general, it is expected that pre-aged SAC105 solders will demonstrate improved thermal fatigue performance compared to aged SAC305 interconnects.

Efficient beam-based model for reinforced concrete walls considering shear-flexure interaction

This paper presents an efficient beam-based modelling scheme for the seismic analysis of reinforced concrete structural walls. The model combines a force-based beam element with a fibre section for flexural response and a zero-length element for shear response. The fibre-based element simulates the nonlinear flexural behaviour through uniaxial material laws that account for concrete cracking, concrete crushing, and yielding and rupture of reinforcing bars. The zero-length element represents the shear behaviour with a trilinear lateral force-displacement curve representing, in a phenomenological way, nonlinear deformations caused by diagonal cracking. The reduction of shear resistance caused by inelastic flexural deformations is accounted for in the model to reproduce failures due to shear-flexure interaction. The model has been validated using data from 52 tests on wall specimens exhibiting flexure, shear and mixed shear-flexure modes from experimental campaigns reported in the literature, showing good accuracy in predicting the effective stiffness, maximum strength and displacement capacities obtained in the tests. Model results for ultimate displacement capacity correlate better with experimental results than simplified code-oriented expressions in performance-based evaluation standards and recommendations. Considering its balanced accuracy and computational efficiency, it is concluded that the proposed modelling scheme can effectively be used for performance-based seismic design and assessment of RC wall buildings.

Tough and Ductile Architected Nacre‐Like Cementitious Composites

AbstractEnhancing fracture toughness and ductility of brittle materials such as concrete remains a challenge. Nature offers numerous mechanisms to enhance fracture toughness using purposeful designs of materials’ architecture. Natural nacre exhibits high fracture toughness by promoting inelastic deformation and hierarchical toughening mechanisms. Here, “nacre‐like‐separated” and “nacre‐like‐grooved” cementitious composites inspired by brick‐and‐mortar arrangement of mollusk shells are proposed. These nacre‐like composites are engineered by laser processing cement paste into individual tablets and grooved patterns (as intentional defects) and laminating them with limited amounts of suitable elastomeric (polyvinyl siloxane) interlayers. It is found that interlayer deformation, tortuous crack propagation guided by the defects, and crack bridging are the main toughening mechanisms in these composites that lead to rising resistance curves. The study hypothesizes tablet sliding as an additional toughening mechanism in “nacre‐like‐separated”, preventing tablet failure and leading to the postponed onset of bulk composite failure. These mechanisms significantly enhance both fracture toughness and ductility by 17.1 and 19 folds, compared to constituent hardened cement paste, respectively. By engineering laser‐induced defects into tabulated cementitious‐elastomeric material at meso‐scale, a class of tough and ductile cementitious composites is introduced, resulting in significantly high fracture toughness values (73.68 MPa.mm1/2), comparable to Ultra‐high‐performance‐concrete without sacrificing the strength.

A mixed nonlocal finite element model for thermo‐poro‐elasto‐plastic simulation of porous media with multiphase fluid flow

SummaryA new mixed nonlocal finite element framework is developed for nonlinear thermo‐poro‐elasto‐plastic simulation of porous media with multiphase pore fluid flow and thermal coupling. The solid‐fluid interaction is accounted for using the mixture theory of Biot based on the volume fractions concept. Different sources of nolinearities arising from the multiphase fluid flow effects, advective‐diffusive heat transfer, inelastic deformation, fluid flux injection induced mechanical tractions, solid skeleton deformation permeability dependence, and temperature dependent viscosity are included in developing a robust numerical solver for the targeted coupled multiphysics problem. To address the effect of microstructure in inelastic localized deformation behaviour with dilational softening, a nonlocal plasticity model is proposed based on a characteristic length scale which rectifies the non‐physical pathological mesh dependence problem encountered in conventional plasticity. The accuracy and strength of the developed model is shown with comparing the obtained numerical results of a benchmark bilateral compression test with existing published data in the literature. To show the versatility and robustness of the developed computational framework in modelling the geomechanics of real‐case engineering practices, large scale thermo‐hydro‐mechanical (THM) subsurface stimulation processes with applications in enhanced oil recovery (EOR) are effectively simulated and the targeted enhanced recovery and performances are demonstrated. The current formulation does not include phase transformation modelling capability, and therefore, the developed models may not be applicable for simulation of the engineering processes that involve phase change behaviour (e.g., steam injection).

A multiscale constitutive model of magnesium-shape memory alloy composite

In this work, a multiscale constitutive model is established to describe the deformation behaviors of magnesium-shape memory alloy (Mg-SMA) composite in a wide temperature range and reveal the strengthening mechanism of SMA reinforcement on Mg. The model is established at the grain scale firstly and gradually transited to the macroscopic scale by employing a newly developed three-level scale transition rule. At the grain scale, the thermodynamic-consistent constitutive models of Mg and SMA are, respectively, constructed by addressing different inelastic deformation mechanisms. The basal, prismatic, pyramidal, slip systems and extension twinning system are considered for the Mg phase, and the martensite transformation (MT) and austenitic plasticity are addressed for SMA reinforcement. Thermodynamic driving forces of each inelastic deformation mechanism are derived from the dissipative inequality and the constructed Gibbs free energies. At the polycrystalline scale, to evaluate the interactions among the grains and pores, and obtain the whole responses of the polycrystalline Mg and SMA, a thermo-mechanically coupled self-consistent homogenization scheme is employed. At the mesoscopic scale, a modified thermo-mechanically coupled Mori-Tanaka's homogenization scheme is adopted to evaluate the interaction between the Mg phase and SMA phase, and predict the whole responses for the representative volume element (RVE) of the composite. According to the geometrical features and mechanical loadings applied on the specimen, a hypothesis of homogeneous stress and strain fields at the macroscopic scale is adopted to achieve the scale transition from the RVE of the composite to the whole specimen. The capacity of the multiscale model is verified by comparing the predictions with the existing experimental data (Aydogmus, 2015). Moreover, the influences of characteristic information for the microstructures at different spatial scales on the deformation behaviors of the composite are predicted and discussed.

On elastoplastic behavior of porous enamel–An indentation and numerical study

The micro/nano pores in natural mineralized tissues can, to a certain extent, affect their responses to mechanical loading but are generally ignored in existing indentation analysis. In this study, we first examined the void volume fraction of sound and caries lesion enamels through micro-computed tomography (micro-CT). A Berkovich indentation study was then carried out to characterize the effect of porous microstructure on the mechanical behavior of the human enamels. The indentation tests were also modeled using the nonlinear finite element analysis technique to simulate indentation load-displacement curves, which showed reasonable agreement with the experimental measurements. From the simulation results, the extent of densification in the plastic zone was identified and the corresponding stress and contact pressure evolutions were quantified. Further, a conventional elastic-perfectly plastic material model without considering micropores was also developed to investigate the compaction effect of the porous structure. The simulation results reveal that conventional elastic perfect-plastic constitutive models become less reliable to model the mechanical behavior of carious lesion enamel with increasing loss of mineral content as it underestimates the yield stress and plastic energy dissipation. This study divulges the importance of compaction of porous enamel structure beneath the indented area. Note that understanding the effect of porous microstructures on plastic behavior is vital as the involved inelastic deformation mechanism associated with irreversible processes, such as wear and localized microcracking, has a significant bearing on wear and fatigue behavior of enamel. Statement of significanceBased on micro-CT and nano-indentation characterization, a numerical model was developed aiming to precisely describe the deformation behavior of naturally porous enamel. Inelastic properties and energy dissipation characteristics of porous enamel were investigated in detail. This work demonstrated that the existence of micro-pores in White Spot Lesions (WSLs) contributes to mechanical stability, which can mitigate the reduction in Young's modulus and fracture toughness resulting from loss of mineral components. The knowledge gained from this study can be used to explain the mechanisms related to irreversible processes, such as contact induced cracking and wear, and strengthen understanding of the mechanical behavior of porous mineralized tissues.

Seismic retrofit of structures using steel frames with viscoelastic hinges

In this paper a new seismic retrofit system composed of a steel frame with viscoelastic hinges is proposed and its applicability and efficiency are evaluated in a theoretical framework. First, the mechanical behavior of viscoelastic hinges and the system are studied and the related formulas are derived. The analytical model of the proposed seismic damper is established first, and the damper is subjected to cyclic loads to compare its hysteretic behavior with the one from the formulation. In order to further evaluate the efficiency of this system, the validated analytical model is used in seismic retrofit of a case study structure to reach the collapse prevention performance under the maximum considered earthquake hazard level. The seismic performance of the analysis model is compared before and after retrofit in terms of maximum interstory drift ratio, residual displacement, and energy dissipation of structural members and dampers. The results show that the proposed damper can be used to reach the stipulated drift limit state. Furthermore, the inelastic energy dissipated by the structural members is reduced drastically and the structure can be effectively protected against irreversible damages due to inelastic deformations.

Self-centering of steel braced frames equipped with Fe-SMA TADAS dampers

This study proposes a novel triangular added damping and stiffness (TADAS) damper that uses the shape memory effect of iron-based shape memory alloy (Fe-SMA) to provide a self-centering system to recover the initial shape of a structure after significant inelastic deformation induced by nonlinear response of fused elements, without the need for difficult and expensive replacement procedures of conventional TADAS systems. Unlike most studies which consider simplified uniaxial behavior of Fe-SMAs, the present non-linear finite element simulations cover the full 3D material non-linearity of Fe-SMA component based on the SMA constitutive law to capture both flexural and shear behavior in various coupled thermomechanical loadings, including the mechanical loading/unloading, the heating, and the final cooling (as the recovering process). Simulations performed on a one-bay steel frame for different drift ratios reveal that although the dissipation energy of the new device is at most 10% less than the ordinary one, it enjoys the self-centering property to recover the initial shape of the frame before loading, showing that the proposed damper is an effective alternative to ordinary TADAS yielding dampers to achieve the self-centering characteristics.

Constitutive modelling of glassy polymers considering shear plasticity and craze yielding

The inelastic behaviour of thermoplastic polymers below the glass transition temperature can involve shear plasticity or crazing, depending on the strain rate and temperature. Shear plasticity is driven by local shear stresses and is essentially volume preserving. In contrast, crazing is a failure phenomenon occurring under tension and causes significant volume change. In some cases, crazing can also result in large inelastic deformations at macroscopic scale, referred to as craze yielding. The aim of this study is to propose a thermodynamically-consistent constitutive framework that accounts for both shear plasticity and craze yielding in glassy polymers. The main assumption is that shear plasticity and craze yielding occur exclusively from each other, depending on the local stress state. Both are modelled as thermally-activated processes with different activation stresses and flow rules. The theory is validated against experimental data for polylactic acid (PLA). Our model is capable of reproducing the stress–strain response including yielding, softening, and drawing under both shear plasticity and craze yielding, and also accurately predicts the volumetric deformation under tension. In particular, our simulations well capture the interesting phenomenon that craze yielding stabilises localised deformations and prevents necking. Our model can also simulate complex scenarios where both mechanisms occur simultaneously at different locations of the specimen.

Stress-Strain State of Steel Fiber-Reinforced Concrete under Compression Taking into Account Unloading from Inelastic Region

The purpose of the study is to examine the physical and mechanical characteristics of steel fiber-reinforced concrete under compression, including: modulus of elasticity, Poisson ratio, values of ultimate strains under compression, values of compressive strength with different percentages of dispersed reinforcement. An experimental investigation program, which included the production of cube samples measuring 100×100×100 mm, as well as a compression test under static loading, taking into account unloading from the region of inelastic deformations, was developed and carried out. Two types of steel fiber were chosen as dispersed reinforcement: hooked end and wave shape. The volume content of steel fiber in the cube samples was 0.5, 1.0, 1.5 and 2.0 %. As a result of the investigation, the strength and deformation characteristics of steel fiber reinforced concrete under compression were obtained. Based on the experimental data, actual strain diagrams of steel fiber reinforced concrete were constructed, taking into account the type of reinforcing fibers and the percentage of reinforcing fiber. Based on the obtained diagrams, a law of deformation of steel fiber reinforced concrete is proposed, which can be described by a polynomial function of the fourth order with constant coefficients that determine the shape of the stress-strain curve. The presented research results can be used in developing a methodology for physically nonlinear analysis of steel fiber reinforced concrete elements with a percentage of dispersed reinforcement from 0.5 to 2.0 %.

Feasibility of using superelastic shape memory alloy in plastic hinge regions of steel bridge columns for seismic applications

AbstractThis paper contributes to the further development of seismic resilient infrastructure by introducing a novel prototype bridge which integrates tubular steel piers with superelastic shape memory alloy (SMA). The proposed bridge pier is composed of a circular steel tube which is bonded to a superelastic SMA tube in regions of high stress. The pier is distinguished by its ability to minimize residual drifts following inelastic deformations induced by cyclic loading. Three‐dimensional continuum finite element (FE) models are utilized to examine its lateral behavior. Experimental data is used to demonstrate the effectiveness of the continuum FE procedure in replicating the cyclic response and capturing both global and localized behaviors. A novel composite material model is proposed to represent the degradation of strength and accumulation of irreversible strains in the cyclic response of superelastic SMAs. An iterative procedure for the calibration of this material is presented. Investigations, employing the calibrated FE procedure, focus on the quasi‐static cyclic response of steel piers with superelastic SMA in the plastic hinge zone, aiming to identify the optimal length of the SMA tube for achieving a self‐centering response with reduced residual deformation. The study is then further expanded to examine the seismic response of a bridge structure incorporating such piers. Development of the FE model for the prototype bridge includes the modelling of the piers using continuum elements, while the superstructure, bearing units, abutment walls, and backfill material are modelled using discrete elements. Nonlinear time history analyses are undertaken to investigate the effects of column wall thickness and materials used in the plastic hinge zones of the piers. Dynamic FE study results indicate that bridges employing such piers are capable of returning to their original position, provided the SMA tube is of adequate length.

New source model for the 1771 Meiwa tsunami along the southern Ryukyu Trench inferred from high-resolution tsunami calculation

The 1771 Meiwa tsunami which struck the southern Ryukyu Islands (Sakishima Islands) had greater than 22 m run-up height, leaving about 12,000 casualties in its wake. At many places, the tsunami inundation or lack of inundation is well recorded in historical documents. Several tsunami source models have been proposed for this event using historical records as constraints of tsunami calculations. Nevertheless, the source model remains under discussion. This study re-evaluated the tsunami wave source model of the 1771 Meiwa tsunami using high-resolution (10 m mesh) bathymetric and topographical data for tsunami calculation, the latest historical record dataset, and seismological knowledge. Results demonstrated that a tsunami earthquake along the southern Ryukyu Trench was the likely cause of the 1771 event. However, it is noteworthy that assumption of a large slip with 30 m is necessary for a shallow and narrow region (fault depth = 5 km, fault width = 30 km, Mw = 8.49) of the plate boundary in the Ryukyu Trench, which is far larger than previously thought. This requirement of very large initial water level change at the source might involve not only the fault rupture along the plate boundary but also deformation by splay faults, inelastic deformation of unconsolidated sediments near the trench axis, and/or giant submarine landslides. Results also show that the effects of fault parameters on the run-up were quite different depending on the offshore coral reef width. This phenomenon strongly constrained the fault width to 30 km. Our tsunami ray tracing analysis further revealed the effects of bathymetry on tsunami propagation. It is noteworthy that meter-long huge tsunami boulders tend to be distributed along the specific coasts at which the tsunami was concentrated by bathymetric effects. This finding suggests that past tsunamis, including the 1771 event, might have affected the specific coral reefs on Sakishima Islands repeatedly, which is crucially important for understanding the heterogeneous distribution of tsunami boulders. This feature might also be useful to elucidate the effects of large tsunamis on the corals and reefs because a direct comparison of coral reefs that are damaged and not damaged by tsunami waves is testable in narrow areas in the case of the Sakishima Islands.

Elastic and Elastoplastic Contact Mechanics of Concentrated Coated Contacts

Machines operate under increasingly harsher contact conditions, causing significant wear and contact fatigue. Sub-surface stresses are responsible for the premature contact fatigue of rolling element bearings, meshing gears, and cam–follower pairs. Surface protection measures include hard, wear-resistant coatings. Traditionally, contact integrity has been predicted using classical Hertzian contact mechanics. However, the theory is only applicable when the contact between a pair of ellipsoidal solids of revolution may be considered as a rigid indenter penetrating a semi-infinite elastic half-space. Many coatings act as thin bonded elastic layers that undergo considerably higher pressures than those predicted by the classical theory. Furthermore, inelastic deformation of bonded solids can cause plastic flow, work-hardening, and elastoplastic behaviour. This paper presents a comprehensive, integrated contact mechanics analysis that includes induced sub-surface stresses in concentrated counterformal finite line contacts for all the aforementioned cases. Generated pressures and deformation are predicted for hard coated surfaces, for which there is a dearth of relevant analysis. The contact characteristics, which are of particular practical significance, of many hard, wear-resistant advanced coatings are also studied. The paper clearly demonstrates the importance of using efficient semi-analytical, detailed holistic contact mechanics rather than the classical idealised methods or empirical numerical ones such as FEA. The novel approach presented for the finite line contact of thin-layered bonded solids has not hitherto been reported in the open literature.

Evaluation of New Seismic provisions for special concentrically braced frames in AISC 341-22

The seismic provisions for special concentrically braced frame (SCBF) had expected the properly detailed braces to provide inelastic cyclic deformation of 10 - 20 ductility without fracture during the design earthquake ground motions over 30 years prior to 2022. The new seismic provisions for SCBF in AISC 341–22 eliminates the clear and quantifiable statements on the expected capacity and demand of the braces, and indicates that the diagonal braces can sustain large inelastic cyclic deformations without experiencing premature failures if they are properly detailed for ductility as prescribed in the provisions. The appearance of such word as “large inelastic deformation” and “premature failure” causes a concern about the uncertainty. One might wonder why a range of amount of inelastic cyclic deformation capacity for a properly detailed brace cannot be defined after more than 40 years of extensive research on SCBF. This paper presents a study using available data accumulated over more than 40 years to investigate how much inelastic cyclic deformations are needed for braces to avoid fracture under the design earthquake, and concludes that the SCBFs with properly detailed square HSS have insufficient inelastic cyclic deformations to avoid experiencing premature failures that lead to structural collapse under the design earthquake.

Numerical study of time-dependent stresses in the floor of the stope with powered support

When sections of the powered support are clamped in the stope, one of the ways to move them is to explode the rock under them. In the case when there is outburst-prone sandstone in the seam floor, blasting operations becomes dangerous and it is necessary to study the stress field in the host rocks. In this work, a numerical study of the time-dependent stress field in the floor of the stope with powered support is performed. Distributions of values of geomechanical parameters characterizing the stress field and zones of inelastic deformations at different time steps are given. Graphs of changes in these parameters in the floor of the stope are plotted. The minimum time for unloading sandstone at the place of drilling the hole for explosive charge is calculated. It is shown that in front of the mine face plane, the sandstone in the seam floor is in a uniform compressed state; all components of the stress field are close to unity. However, they start to decrease already 2.5 m before the mine face plane. At the hole drilling site, the maximum stress is 0.77γH, the minimum stress is 0.35γH at a depth of 1 m for given conditions.

The evolution of stresses and shear resistance on rough faults at large slip

The deviation of natural faults from planarity results in geometric asperities and a heterogeneous stress field, affecting the shear resistance and slip behavior. This study numerically examines the effects of macro-scale roughness, local friction, and wear on the evolution of the fault stresses and shear resistance with fault slip. In contrast to previous analytical and numerical studies, our quasistatic simulations allow for slip at the scale of roughness wavelengths, large roughness levels, and fault opening. The simulations indicate that analytical solutions, which predict a linear increase in shear resistance with slip, significantly overestimate the additional shear resistance from roughness, i.e., the roughness drag, at slips larger than several percent of the minimum roughness wavelength. Starting with mated fault surfaces, the average shear resistance on the fault initially rises rapidly, but the rate of increase diminishes significantly as slip increases and the faults open. While initially showing a larger increase in shear resistance than self-similar faults, at large slip, self-affine faults exhibit significantly smaller shear resistance, and the background stresses are bounded without the need for off-fault inelastic deformation. Although smaller than predicted by analytical solutions, the simulation results show that the additional resistance from macro-scale geometrical irregularities is important, enabling rough faults to operate under shear resistance significantly larger than that from local friction only. The impact of macro-scale roughness increases with the roughness amplitude and the friction coefficient, while wear reduces fault stresses and average shear resistance. The combined effect of local friction and roughness is nonlinear, involving a direct contribution to shear resistance from roughness, as observed in prior studies, and an additional contribution from the increasing average normal stress with slip, which amplifies the resistance from friction and becomes more pronounced at large slip.