factors that control the angle of shear bands in geodynamic numerical models of brittle deformation abstract numerical models of brittle deformation on geological timescales typically use a pressure dependent mohr coulomb or drucker prager plastic flow law to simulate plastic failure despite its widespread usage in geodynamic models of lithospheric deformation however certain aspects of such plasticity models remain poorly understood one of the most prominent questions in this respect is what are the factors that control the angle of the resulting shear bands recent theoretical work suggest that both roscoe 45 coulomb angles 45 2 where is the angle of internal friction and arthur angles 45 4 where is the dilation angle as well as all intermediate angles are possible published numerical models however show a large range of shear band angles with some codes favoring arthur angles whereas others yield coulomb angles in order to understand what causes the differences between the various numerical models here i perform systematic numerical simulations of shear localization around an inclusion of given length scale both numerical element type geometrical and rheological viscoplastic versus viscoelastoplastic effects are studied results indicate that the main factor controlling shear band angle is the non dimensional ratio between the length scale of the heterogeneity d and the size of the numerical mesh x coulomb angles are observed only in cases where the inclusion is resolved well d x 5 10 and in which it is located sufficiently far from the boundary of the box in most other cases either arthur or roscoe orientations are observed if heterogeneities are one element in size coulomb angles are thus unlikely to develop irrespective of the employed numerical resolution whereas differences in element types and rheology do have consequences for the maximum obtainable strain rates inside the shear bands they only have a minor effect on shear band angles shear bands initiated from random noise or from interactions of shear bands with model boundaries or other shear bands result in stress heterogeneities with dimensionless length scales d x 1 2 such shear bands are thus expected to form roscoe or arthur orientations consistent with the findings in previous numerical models

making coulomb angle oriented shear bands in numerical tectonic models abstract localization of shear strain can be induced by strain weakening plasticity in continuum models and is often used to represent faults of various scales the orientation of the shear bands is thus required to be consistent with those observed from natural faults and with simple theories of brittle failure although the coulomb angle at which a shear band satisfies the coulomb failure criterion is widely used as an assumed fault orientation the currently available numerical techniques do not always produce shear bands oriented at this angle we demonstrate that under an associated plastic flow rule for which dilation and friction angles are equal the coulomb angle becomes a unique initial shear band orientation regardless of the numerical methods employed and model resolution the known problem of overly expanding shear bands in case of a constant dilation angle is preventable if dilation angle is reduced as shear strain along the shear band increases this treatment corresponds to natural processes reducing roughness of a fault plane

modes of faulting at mid ocean ridges abyssal hill bounding faults that pervade the oceanic crust are the most common tectonic feature on the surface of the earth the recognition that these faults form at plate spreading centres came with the plate tectonic revolution recent observations reveal a large range of fault sizes and orientations numerical models of plate separation dyke intrusion and faulting require at least two distinct mechanisms of fault formation at ridges to explain these observations plate unbending with distance from the top of an axial high reproduces the observed dip directions and offsets of faults formed at fast spreading centres conversely plate stretching with differing amounts of constant rate magmatic dyke intrusion can explain the great variety of fault offset seen at slow spreading ridges very large offset normal faults only form when about half the plate separation at a ridge is accommodated by dyke intrusion

a rheological model of a fractured solid abstract experiments to study the behavior of various materials point to the relation that exists between elastic properties and the type of stress the influence of the state of stress on the elasticity of a fractured material will be discussed for a physically non linear model of an elastic solid the strain dependent moduli model of material presented in this paper makes it possible to describe this feature of a solid it also permits to simulate a dilatancy of rocks a damage parameter introduced into the model using a thermodynamical approach allows to describe a rheological transition from the ductile regime to the brittle one and to simulate the rock s memory narrow fracture zone creation and strain rate localization additionally the model enables the investigation of the final geometry of fracture zones and also to simulate their creation process taking into account pre existing fracture zones the process of narrow fracture zone creation and strain rate localization was simulated numerically for single axis compression and shear flow

do faults trigger folding in the lithosphere a number of observations reveal large periodic undulations within the oceanic and continental lithospheres the question if these observations are the result of large scale compressive instabilities i e buckling remains open in this study we support the buckling hypothesis by direct numerical modeling we compare our results with the data on three most proeminent cases of the oceanic and continental folding like deformation indian ocean western gobi central asia and central australia we demonstrate that under reasonable tectonic stresses folds can develop from brittle faults cutting through the brittle parts of a lithosphere the predicted wavelengths and finite growth rates are in agreement with observations we also show that within a continental lithosphere with thermal age greater than 400 my either a bi harmonic mode two superimposed wavelengths crustal and mantle one or a coupled mode mono layer deformation of inelastic folding can develop depending on the strength and thickness of the lower crust

benchmarking numerical models of brittle thrust wedges we report quantitative results from three brittle thrust wedge experiments comparing numerical results directly with each other and with corresponding analogue results we first test whether the participating codes reproduce predictions from analytical critical taper theory eleven codes pass the stable wedge test showing negligible internal deformation and maintaining the initial surface slope upon horizontal translation over a frictional interface eight codes participated in the unstable wedge test that examines the evolution of a wedge by thrust formation from a subcritical state to the critical taper geometry the critical taper is recovered but the models show two deformation modes characterised by either mainly forward dipping thrusts or a series of thrust pop ups we speculate that the two modes are caused by differences in effective basal boundary friction related to different algorithms for modelling boundary friction the third experiment examines stacking of forward thrusts that are translated upward along a backward thrust the results of the seven codes that run this experiment show variability in deformation style number of thrusts thrust dip angles and surface slope overall our experiments show that numerical models run with different numerical techniques can successfully simulate laboratory brittle thrust wedge models at the cm scale in more detail however we find that it is challenging to reproduce sandbox type setups numerically because of frictional boundary conditions and velocity discontinuities we recommend that future numerical analogue comparisons use simple boundary conditions and that the numerical earth science community defines a plasticity test to resolve the variability in model shear zones

robust characteristics method for modelling multiphase visco elasto plastic thermo mechanical problems abstract we have extended our previous 2d method gerya t v yuen d a 2003 characteristics based marker in cell method with conservative finite differences schemes for modeling geological flows with strongly variable transport properties phys earth planet interiors 140 295 320 which is a combination of conservative finite differences with marker in cell techniques to include the effects of visco elasto plastic rheology self gravitation and a self consistently derived evolving curvilinear planetary surface this code is called i2elvis and can solve a new class of computationally challenging problems in geodynamics such as shear localization with large strains crustal intrusion emplacement of magmas bending of realistic visco elasto plastic plates and core formation by vigorous shell tectonics activities related to a global rayleigh taylor instability of a metal layer formed around silicate rich lower density primordial core during planetary accretion we discuss in detail the computational strategy required the rheological constraints to be satisfied at each time step and spatial location we show analytical benchmarks and examples drawn from comparing between numerical and analogue experiments in structural geology subducting slab bending with a visco elasto plastic rheology and equilibrium spherical configurations from self gravitation we have also tested possibilities of future applications by addressing 3d geometries based on multigrid method and including inertial effects in the momentum equation with tracers in order to simulate meteoritic impact events and eventually earthquake instabilities

fracture and weakening of jammed subduction shear zones leading to the generation of slow slip events geodetic data have revealed that parts of subduction interfaces creep steadily or transiently transient slow slip events sses are typically interpreted as aseismic frictional sliding however sses may also occur via mixed visco brittle deformation as observed in shear zones containing mixtures melange of strong fractured clasts embedded in a weak visco brittle matrix we test the hypothesis that creep in a subduction melange occurs through distributed matrix deformation where flow is intermittently impeded by load bearing clast networks jamming our numerical models demonstrate that bulk melange rheology can be dominated by the strong clasts in the absence of fracturing while at high driving stresses or low frictional strength clast fracturing redistributes deformation into the matrix leading to high bulk strain rates because melange stress is heterogeneous fracturing of clasts occurs throughout jammed melange when the driving stresses are only 20 of the clast yield strength the effective rheology of jammed melange can be characterised by a logarithmic dependence of stress on strain rate which is used to explore strain rate transients caused by temporal variation in clast friction clasts must weaken significantly 75 in order to increase strain rate by 8 spring block slider models with a more idealized visco brittle rheology also demonstrate that strain rate transients can be generated when rate and state friction is incorporated we outline a model where high bulk strain rates are generated when pervasive fracturing occurs but further slip is limited by viscous processes incorporating such viscous damping into models may widen the conditions under which sses can occur while preventing development of seismic slip

indentation as an extrusion mechanism of lower crustal rocks insight from analogue and numerical modelling application to the eastern bohemian massif abstract recent petrological structural and geochronological studies of the eastern margin of the bohemian massif czech republic suggest a conceptual geodynamical model to explain exhumation of lower crustal 20 kbar 800 c felsic rocks the model involves indentation of a weak orogenic lower crust by an adjacent rigid mantle lithosphere resulting in crustal scale buckling of the weak orogenic lower middle crust interface followed by extrusion of a ductile nappe over the rigid promontory the hypothesis has been investigated using both analogue and numerical models analogue experiments using a three layer sand silicone setup were carried out in rennes laboratory france results show that the most important features of the conceptual model can be reproduced extrusion of lowermost silicone over the indenter and flow of horizontal viscous channel underneath a rigid lid above the actively progressing promontory furthermore experimental results show that a plateau develops above the channelling lower crust two sets of sandbox scale numerical simulations were performed the first set of experiments is designed to study the influence of viscosity stratification within the crust on the extrusion process a second set of experiments were performed in order to quantify the influence of the viscosity and the geometry of the indentor non dimensional scaling laws were derived to predict the maximum extrusion rates associated with the indentation mechanism such laws enable the computation vertical extrusion rates that are in good agreement with natural exhumation rates inferred from petrological data finally we discuss the potential positive feedback of rayleigh taylor instability on vertical extrusion for the case of eastern bohemian massif

lacode a lagrangian two dimensional thermo mechanical code for large strain compressible visco elastic geodynamical modeling abstract we present lacode lagrangian compressible deformation a matlab solver for the stokes equations for compressible non newtonian visco elastic flow in two dimensions based on a lagrangian formulation of the finite element method the incompressible boussinesq approximation is a widespread assumption in numerical models of lithospheric deformation thus potentially masking a significant contribution of mechanisms linked to volumetric changes that occur in the asthenospheric mantle and the lithosphere lacode employs a compressible formulation of the stokes equations designed to address such volume changing processes first we provide a description of the equations governing the deformation of earth rocks and detailed overview of the algorithm its numerical implementation treatment of the non linearities rising from the compressible formulation and ineleastic deformation and the remeshing algorithm that tracks and transfers the physical fields from a highly distorted mesh to a high quality one lacode is then benchmarked by comparing numerical results to analytical solutions for the bending of a thin elastic beam under a constant uniform load flow around a rigid inclusion rayleigh taylor instability stress build up in a visco elastic maxwell body and couette flow with viscous heating the rayleigh taylor instability test is further used to demonstrate the accuracy of the remeshing algorithm the importance of including volumetric strain for geodynamic processes is illustrated by two numerical experiments i volumetric strain inducing phase changes in amagmatic slow spreading ridges and ii subducting slabs

computational approaches to studying non linear dynamics of the crust and mantle we outline a mathematical formulation for mantle convection which can deal with the viscoelastic plastic rheology of the cool parts of the lithosphere this formulation is then analyzed to expose the numerical challenges inherent in the equations and a suitable solution strategy is outlined with this strategy in place we discuss a parallel implementation explaining how we maintain computational efficiency in a tiered and modular software environment we show two examples from geodynamics which demonstrate the capability of the numerical method and its implementation c 2007 elsevier b v all rights reserved

initiation of salt diapirs with frictional overburdens numerical experiments we have studied the initiation of salt diapirs with frictional overburdens under lateral compression and extension the overburden is assumed to be elasto plastic with mohr coulomb yield criterion and non associated flow rule plastic flow localizes into narrow shear bands which may represent faults the geometry and the evolution of these shear zones are simulated for various rheological parameters the dilational and frictional properties of frictional overburdens are found to be important controls on the types of shear zones formed in lateral compression and extension the friction and dilation angles influence the angle of shear and the width dip spacing and development history of conjugate zones of shear plus dilation fault zones that define wedges and grabens

the benefits of using a consistent tangent operator for viscoelastoplastic computations in geodynamics strain localization is ubiquitous in geodynamics and occurs at all scales within the lithosphere how the lithosphere accommodates deformation controls for example the structure of orogenic belts and the architecture of rifted margins understanding and predicting strain localization is therefore of major importance in geodynamics while the deeper parts of the lithosphere effectively deform in a viscous manner shallower levels are characterized by an elastoplastic rheological behavior herein we propose a fast and accurate way of solving problems that involve elastoplastic deformations based on the consistent linearization of the time discretized elastoplastic relation and the finite difference method the models currently account for the pressure insensitive von mises and the pressure dependent drucker prager yield criteria consistent linearization allows for resolving strain localization at kilometer scale while providing optimal that is quadratic convergence of the force residual we have validated our approach by a qualitative and quantitative comparison with results obtained using an independent code based on the finite element method we also provide a consistent linearization for a viscoelastoplastic framework and we demonstrate its ability to deliver exact partitioning between the viscous the elastic and the plastic strain components the results of the study are fully reproducible and the codes are available as a subset of m2di matlab routines

the seismic cycle at subduction thrusts 2 dynamic implications of geodynamic simulations validated with laboratory models 1 the physics governing the seismic cycle at seismically active subduction zones remains poorly understood due to restricted direct observations in time and space to investigate subduction zone dynamics and associated interplate seismicity we validate a continuum visco elasto plastic numerical model with a new laboratory approach paper 1 the analogous laboratory setup includes a visco elastic gelatin wedge underthrusted by a rigid plate with defined velocity weakening and strengthening regions our geodynamic simulation approach includes velocity weakening friction to spontaneously generate a series of fast frictional instabilities that correspond to analog earthquakes a match between numerical and laboratory source parameters is obtained when velocity strengthening is applied in the aseismic regions to stabilize the rupture spontaneous evolution of absolute stresses leads to nucleation by coalescence of neighboring patches mainly occurring at evolving asperities near the seismogenic zone limits consequently a crack or occasionally even pulse like rupture propagates toward the opposite side of the seismogenic zone by increasing stresses ahead of its rupture front until it arrests on a barrier the resulting surface displacements qualitatively agree with geodetic observations and show landward and from near the downdip limit upward interseismic motions these are rebound and reversed coseismically this slip increases adjacent stresses which are relaxed postseismically by afterslip and thereby produce persistent seaward motions the wide range of observed physical phenomena including back propagation and repeated slip and the agreement with laboratory results demonstrate that visco elasto plastic geodynamic models with rate dependent friction form a new tool that can greatly contribute to our understanding of the seismic cycle at subduction zones

palaeokarst in the ordovician of the southern great basin usa implications for sea level history abundant and regionally unique dolostone lithoclast breccias occur throughout the shallow marine lower to middle ordovician pogonip group in the nopah range and adjacent ranges in eastern california and southern nevada breccia bodies display sharply cross cutting relationships with host dolostone bedrock stratigraphy they also show stratigraphic variability in size shape and dolostone clast composition but similarity in breccia matrix composition and framework texture and fabric these characteristics are consistent with a palaeokarst origin upsection changes in breccia clast lithology as well as multiple occurrences of associated quartz sand filled grikes solution widened fissures indicate multiple episodes of carbonate platform exposure and karstification repeated karstification is also indicated by stratiform bodies of quartz sand and thin terra rossa palaeosols that locally truncate breccias and grike systems thus bracketing karstified exposure surfaces facies successions and stacking patterns between recognized exposure surfaces are developed as transgressive regressive cycles and thus show depositional sequence architecture hence these breccias and other associated palaeokarst features are related to a succession of disconformities that provide a sequence stratigraphic framework for assessing ordovician relative sea level history of the south western cordilleran margin of laurentia

generation of earth s early continents from a relatively cool archean mantle this research has been supported by dfg grant spp 1833 building a habitable earth and magma consolidator grant erc project 71143

thermomechanical modeling of slab eduction 1 plate eduction is a geodynamic process characterized by normal sense coherent motion of previously subducted continental plate this mechanism may occur after slab detachment has separated the negatively buoyant oceanic plate from the positively buoyant orogenic root eduction may therefore be partly responsible for exhumation of high pressure rocks and late orogenic extension we used two dimensional thermomechanical modeling to investigate the main features of the plate eduction model the results show that eduction can lead to the quasi adiabatic decompression of the subducted crust 2 gpa in a timespan of 5 my large localized extensional strain in the former subduction channel flattening of the slab and a topographic uplift associated with extension of the orogen in order to further investigate the forces involved in the eduction process we ran systematic parametric simulations and compared them to analytic plate velocity estimations these experiments showed that eduction is a plausible mechanism as long as the viscosity of the asthenospheric mantle is lower than 1022 pa s while subduction channel viscosity does not exceed 1021 pa s we suggest that eduction can be a viable geodynamic mechanism and discuss its potential role during the orogenic evolution of the norwegian caledonides

comment on focal mechanism and locations of earthquakes in the vicinity of the 1975 kalapana earthquake aftershock zone 1970 1979 implications for tectonics of the south flank of kilauea volcano island of hawaii by r s crosson and e t endo

thermomechanical implications of sediment transport for the architecture and evolution of continental rifts and margins erosion and deposition redistribute mass as a continental rift evolves which modifies crustal loads and influences subsequent deformation surface processes therefore impact both the architecture and the evolution of passive margins here we use coupled numerical models to explore the interactions between the surface crust and lithosphere this interaction is primarily sensitive to the efficiency of the surface processes in transporting mass from source to sink if transport is efficient there are two possible outcomes 1 faulting within the zone of extension is longer lived and has larger offsets this implies a reduction of the number of faults and the width of the proximal domain 2 efficient transport of sediment leads to significant deposition and hence thermal blanketing this will induce a switch from brittle to ductile deformation of the upper crust in the distal domains the feedbacks between these two outcomes depend on the extension history the underlying lithospheric rheology and the influence of submarine deposition on sediment transport high erosion sedimentation during early faulting leads to abrupt crustal necking while intermediate syntectonic sedimentation rates over distal deep submarine hotter crust leads to unstructured wide distal domains in models where rheological conditions favor the formation of asymmetric conjugate margins only subaerial transport of sediments into the distal domains can increase conjugate symmetry by plastic localization these models suggest that passive margin architecture can be strongly shaped by the solid earth structure sea level and climatic conditions during breakup

insights into the effects of oblique extension on continental rift interaction from 3d analogue and numerical models abstract continental rifts often develop from linkage of distinct rift segments under varying degrees of extension obliquity these rift segments arise from rift initiation at non aligned crustal heterogeneities and need to interact to develop a full scale rift system here we test the effects of 1 oblique extension and 2 initial heterogeneity seed offset on continental rift interaction with the use of an improved analogue model set up x ray computer tomography ct techniques are used to analyse the 3d models through time and the results are compared with additional numerical models and natural examples the experimental results reveal that increasing extension obliquity strongly changes rift segment structures from wide rifts in orthogonal settings to narrower rifts with oblique internal structures under oblique extension conditions to narrow strike slip dominated systems towards the strike slip domain we also find that both decreasing seed offset and increasing extension obliquity promote hard linkage of rift segments through the formation of continuous rift boundary faults at the surface initial soft linkage through the formation of relay ramps is more likely when seed offset increases or extension is more orthogonal rather than linking at depth the rift boundary faults curve around each other at depth and merge towards the surface to form a continuous trough orthogonal extension promotes the formation of intra rift horsts which may provide hydrocarbon traps in nature

how ductile are ductile shear zones three premises of ductile deformation in the middle and lower crust are widely accepted 1 rocks flow with power law viscous rheology 2 localization in ductile shear zones involves strain softening and 3 fluid flows into and is channelized within ductile shear zones ductile viscous shear zones should therefore initially develop along planes of maximum shear stress strain soften and rotate as material planes into the field of progressive extension however the mean stress or pressure within a weak elongate viscous band being stretched is higher than the surrounding matrix and this is difficult to reconcile with premise 3 in contrast mohr coulomb brittle faults always have lower pressure within the fault zone flow of fluid and melt into high temperature shear zones therefore implies that ductile shear zones are not perfectly viscous but have a pressure dependent viscoplastic rheology the continued pressure dependence may reflect significant microcracking on the grain scale even when localized deformation does not produce larger scale discrete fractures

modeling megathrust earthquakes across scales one way coupling from geodynamics and seismic cycles to dynamic rupture abstract taking the full complexity of subduction zones into account is important for realistic modelling and hazard assessment of subduction zone seismicity and associated tsunamis studying seismicity requires numerical methods that span a large range of spatial and temporal scales we present the first coupled framework that resolves subduction dynamics over millions of years and earthquake dynamics down to fractions of a second using a two dimensional geodynamic seismic cycle sc method we model 4 million years of subduction followed by cycles of spontaneous megathrust events at the initiation of one such sc event we export the self consistent fault and surface geometry fault stress and strength and heterogeneous material properties to a dynamic rupture dr model coupling leads to spontaneous dynamic rupture nucleation propagation and arrest with the same spatial characteristics as in the sc model it also results in a similar material dependent stress drop although dynamic slip is significantly larger the dr event shows a high degree of complexity featuring various rupture styles and speeds precursory phases and fault reactivation compared to a coupled model with homogeneous material properties accounting for realistic lithological contrasts doubles the amount of maximum slip introduces local pulse like rupture episodes and relocates the peak slip from near the downdip limit of the seismogenic zone to the updip limit when an sc splay fault is included in the dr model the rupture prefers the splay over the shallow megathrust although wave reflections do activate the megathrust afterwards

the interior structure of ceres as revealed by surface topography abstract ceres the largest body in the asteroid belt 940 km diameter provides a unique opportunity to study the interior structure of a volatile rich dwarf planet variations in a planetary body s subsurface rheology and density affect the rate of topographic relaxation preferential attenuation of long wavelength topography 150 km on ceres suggests that the viscosity of its crust decreases with increasing depth we present finite element fe geodynamical simulations of ceres to identify the internal structures and compositions that best reproduce its topography as observed by the nasa dawn mission we infer that ceres has a mechanically strong crust with maximum effective viscosity 10 25 pa s combined with density constraints this rheology suggests a crustal composition of carbonates or phyllosilicates water ice and at least 30 volume percent vol low density high strength phases most consistent with salt and or clathrate hydrates the inference of these crustal materials supports the past existence of a global ocean consistent with the observed surface composition meanwhile we infer that the uppermost 60 km of the silicate rich mantle is mechanically weak with viscosity 21 pa s suggesting the presence of liquid pore fluids in this region and a low temperature history that avoided igneous differentiation due to late accretion or efficient heat loss through hydrothermal processes

an arbitrary lagrangian eulerian formulation for creeping flows and its application in tectonic models summary this paper presents and analyses numerical techniques developed to investigate viscoplastic stokes flows within a model of lithospheric deformation in particular the techniques are related to a subduction model of compressional orogens the driving mechanism in the model corresponds to the near rigid convergence and subduction of one mantle lithosphere beneath another in plane strain and this boundary condition forces flow in an overlying viscoplastic model crust the numerical techniques use the arbitrary eulerian lagrangian formulation in which flows with free surfaces and large deformation are computed on an evolving eulerian finite element grid that conforms to the material domain a regridding algorithm allows the associated lagrangian motion and fields to be followed and in addition coupled back to the eulerian calculation of the flow mass flux boundary conditions are used so that the effects of erosion and deposition by surface processes and mass loss by subduction can be included in the model calculation the evolving model crustal layer is flexurally compensated using a general elastic beam formulation the applicability of the numerical techniques to problems ranging from accretionary wedges to crustal and lithospheric scale deformation is discussed simple flows a linear viscous subduction model a whirl flow and a quasi convection model are used to show that the mass conservation regridding and surface tracking errors are small the broader applicability of the modelling techniques is reviewed

toward 4d modeling of orogenic belts example from the transpressive zagros fold belt abstract latest developments in computer power and computational solutions open new ways to envision complex natural systems advances in high resolution 3d geodynamic modeling in particular allow investigating tectonic processes such as transpression which involve normal and tangential kinematics with respect to the bulk orogenic trends we demonstrate that implementing the 4 dimensions space and time provides and constrains new answers to long lasting discussions as case study we have chosen the zagros simply folded belt in iran which exhibits spatial variations of structural patterns from the homogeneously shortened wide fold belt in the fars to the narrower higher elevated area in the izeh high resolution 4d numerical modeling shows how a low viscosity decollement becoming frictional toward the dezful embayment influences the exposed fold patterns results also emphasize the importance of an oblique backstop to produce en echelon arranged folds where convergence related and backstop controlled folds are mingled in the transpressional orogen

finite thickness of shear bands in frictional viscoplasticity and implications for lithosphere dynamics permanent deformations in the lithosphere can occur in the brittle as well as in the ductile domain for this reason the inclusion of viscous creep and frictional plastic deformation is essential for geodynamic models however most currently available models of frictional plasticity are rate independent and therefore do not incorporate an internal length scale which is an indispensible element for imposing a finite width of localized shear zones therefore in computations of localization either analytical or numerical a width of the shear zone is obtained which tends to zero in numerical computations this manifests itself in a severe mesh sensitivity moreover convergence of the global iterative procedure to solve the non linear processes is adversely affected which negatively affects the reliability and the quality of predictions the viscosity which is inherent in deformation processes in the lithosphere can in principle remedy this mesh sensitivity however elasto visco plastic models which are commonly used in geodynamics assume a series arrangement of rheological elements maxwell type approach which does not introduce an internal length scale here we confirm that a different rheological arrangement which put a damper in parallel to the plastic slider kelvin type approach introduces an internal length scale as a result pressure and strain and strain rate profiles across the shear bands converge to finite values upon decreasing the grid spacing we demonstrate that this holds for non associated plasticity with constant frictional properties and with material softening with respect to cohesion finally the introduction of kelvin type viscoplasticity also significantly improves the global convergence of non linear solvers