Thermomechanical Numerical Model Research Articles

3D modelling of rifting through a pre-existing stack of nappes in the Gulf of Corinth (Greece): a mixed analogue/numerical approach

Abstract The Gulf of Corinth is a young (1 Ma) active rift currently extending N00, which displays significant contrasts in structural style along strike. A possible explanation for these variations is the presence of the Phyllades nappe in the basement of the western part of the Gulf. Previous 2D thermo-mechanical models have shown that a strong strength contrast between this metamorphic unit and the rest of the basement can explain the kinematics and the spacing of the faults in the western part. The rift, however, displays a wide variety of 3D features (e.g., en echelon faulting, N30 transverse normal faults) that cannot be taken into account using 2D modelling. To obtain 3D insights into the role of an inherited dipping weakness zone, analogue (sand and PDMS) experiments based on the results of the 2D numerical thermo-mechanical model have been performed. The analogue models show that a 30° discrepancy between the dipping direction of the weak nappe and the direction of extension leads to the formation of en echelon and N30 striking normal faults as observed in the Gulf of Corinth. However, fault spacing and graben width completely misfit both the data and the results of the thermo-mechanical models on which the analogue experiments were based. In order to understand those differences, numerical mechanical benchmarks of the analogue experiments have been run to test different factors (3D lateral displacements, values of the elastic parameters and bottom boundary conditions) that could have affected the dynamics of the analogue model. This approach highlights, for our case study, that the misfits are mostly related to the lack of isostatic compensation at the base of the analogue experiments.

What drives orogeny in the Andes?

Abstract The Andes, the world's second highest orogenic belt, were generated by the Cenozoic tectonic shortening of the South American plate margin overriding the subducting Nazca plate. We use a coupled thermomechanical numerical modeling technique to identify factors controlling the intensity of the tectonic shortening. From the modeling, we infer that the most important factor was accelerated westward drift of the South American plate; changes in the subduction rate were less important. Other important factors are crustal structure of the overriding plate and shear coupling at the plates' interface. The model with a thick (40–45 km at 30 Ma) South American crust and relatively high friction coefficient (0.05) at the Nazca–South American interface generates >300 km of tectonic shortening during 30–35 m.y. and replicates the crustal structure and evolution of the high central Andes. The model with an initially thinner (<40 km) continental crust and lower friction coefficient (<0.015) results in <40 km of South American plate shortening, replicating the situation in the southern Andes. Our modeling also demonstrates the important role of the processes leading to mechanical weakening of the overriding plate during tectonic shortening, such as lithospheric delamination, triggered by the gabbro-eclogite transformation in the thickened continental lower crust, and mechanical failure of the sediment cover at the shield margin.

Correction to “Tectonic evolution of a continental collision zone: A thermomechanical numerical model”

Correction to “Tectonic evolution of a continental collision zone: A thermomechanical numerical model”

Basal and thermal control mechanisms of the Ragnhild glaciers, East Antarctica

AbstractThe Ragnhild glaciers are three enhanced-flow features situated between the Sør Rondane and Yamato Mountains in eastern Dronning Maud Land, Antarctica. We investigate the glaciological mechanisms controlling their existence and behavior, using a three-dimensional numerical thermomechanical ice-sheet model including higher-order stress gradients. This model is further extended with a steady-state model of subglacial water flow, based on the hydraulic potential gradient. Both static and dynamic simulations are capable of reproducing the enhanced ice-flow features. Although basal topography is responsible for the existence of the flow pattern, thermomechanical effects and basal sliding seem to locally soften and lubricate the ice in the main trunks. Lateral drag is a contributing factor in balancing the driving stress, as shear margins can be traced over a distance of hundreds of kilometers along west Ragnhild glacier. Different basal sliding scenarios show that central Ragnhild glacier stagnates as west Ragnhild glacier accelerates and progressively drains the whole catchment area by ice and water piracy.

What drives orogeny in the Andes?

The Andes, the world’s second highest orogenic belt, were generated by the Cenozoic tectonic shortening of the South American plate margin overriding the subducting Nazca plate. We use a coupled thermomechanical numerical modeling technique to identify factors controlling the intensity of the tectonic shortening. From the modeling, we infer that the most important factor was accelerated westward drift of the South American plate; changes in the subduction rate were less important. Other important factors are crustal structure of the overriding plate and shear coupling at the plates’ interface. The model with a thick (40‐45 km at 30 Ma) South American crust and relatively high friction coefficient (0.05) at the Nazca‐South American interface generates ! 300 km of tectonic shortening during 30‐35 m.y. and replicates the crustal structure and evolution of the high central Andes. The model with an initially thinner ( 40 km) continental crust and lower friction coefficient ( 0.015) results in 40 km of South American plate shortening, replicating the situation in the southern Andes. Our modeling also demonstrates the important role of the processes leading to mechanical weakening of the overriding plate during tectonic shortening, such as lithospheric delamination, triggered by the gabbro-eclogite transformation in the thickened continental lower crust, and mechanical failure of the sediment cover at the shield margin.

Continental extension: From core complexes to rigid block faulting

Extension of overthickened continental crust is commonly characterized by an early core complex stage of extension followed by a later stage of crustal-scale rigid block faulting. These two stages are clearly recognized during the extensional destruction of the Alpine orogen in northeast Corsica, where rigid block faulting overprinting core complex formation eventually led to crustal separation and the formation of a new oceanic backarc basin (the Ligurian Sea). Here we investigate the geodynamic evolution of continental extension by using a novel, fully coupled thermomechanical numerical model of the continental crust. We consider that the dynamic evolution is governed by fault weakening, which is generated by the evolution of the natural-state variables (i.e., pressure, deviatoric stress, temperature, and strain rate) and their associated energy fluxes. Our results show the appearance of a detachment layer that controls the initial separation of the brittle crust on characteristic listric faults, and a core complex formation that is exhuming strongly deformed rocks of the detachment zone and relatively undeformed crustal cores. This process is followed by a transitional period, characterized by an apparent tectonic quiescence, in which deformation is not localized and energy stored in the upper crust is transferred downward and causes self-organized mobilization of the lower crust. Eventually, the entire crust ruptures on major crosscutting faults, shifting the tectonic regime from core complex formation to wholesale rigid block faulting.

Numerical thermomechanical modelling of shape memory alloy wires

The dynamic properties of straight shape memory alloy (SMA)-actuator wires are characterised by the rate of heating and cooling procedures. Based on an analysis of energy fluxes into and out of the actuator, a numerical model that simulates the time response of SMA-wires is presented. Cause variables that have an impact on the actuator behaviour (actuator geometry, provided load, arbitrary time variant heating current, environmental conditions) can easily be implemented in the model. Taking these changing boundary conditions into consideration, the model enables a simple design layout for technical solutions with straight SMA-wires.

Asymmetric lithosphere as the cause of rifting and magmatism in the Permo-Carboniferous Oslo Graben

Abstract Compared to other Permo-Carboniferous rift basins of NW Europe, the Oslo Graben has two distinct characteristics. First, it initiated inside cold and stable Precambrian lithosphere, whereas most Permo-Carboniferous basins developed in weaker Phanerozoic lithosphere, and second, it is characterized by large volumes of magmatic rocks despite relatively little extension. Seismic reflection surveys show that the crust thickens from southern Norway to southern Sweden, the most significant Moho deepening occurring from the Oslo Region eastwards. Deep seismic studies also suggest that the base of the lithosphere deepens markedly eastwards from the Oslo Region. Such a long-wavelength lithospheric geometry cannot be explained by the Permian or post-Permian evolution of the area, hence the Oslo Graben appears to have evolved at the transition between two lithospheric domains with contrasting thickness. Numerical thermo-mechanical modelling is applied to test if this transitional position can influence the dynamics of rifting. Different models with varying lithosphere thickness contrast are considered. Model results show that a crust and lithosphere thickness contrast comparable to the Oslo Region can explain rifting and focusing of magmatism in a narrow zone with minor thinning of the crust. Models also account for the major characteristics of the Oslo Graben in terms of location and strain distributions in the crust.

Thermomechanical response and stress analysis of copper interconnects

This study is devoted to thermomechanical response and modeling of copper thin films and interconnects. The constitutive behavior of encapsulated copper film is first studied by fitting the experimentally measured stress-temperature curves during thermal cycling. Significant strain hardening is found to exist. Within the continuum plasticity framework, the measured stress-temperature response can only be described with a kinematic hardening model. The constitutive model is subsequently used for numerical thermomechanical modeling of Cu interconnect structures using the finite element method. The numerical analysis uses the generalized plane strain model for simulating long metal lines embedded within the dielectric above a silicon substrate. Various combinations of oxide and polymer-based low-k dielectric schemes, with and without thin barrier layers surrounding the Cu line, are considered. Attention is devoted to the thermal stress and strain fields and their dependency on material properties, geometry, and modeling details. Salient features are compared with those in traditional aluminum interconnects. Practical implications in the reliability issues for modern copper/low-k dielectric interconnect systems are discussed.

Time-dependent surface topography in a coupled crust-mantle convection model

SUMMARY Recent geodynamic research has shown that convective flow in the mantle may have an important role in the development of long-wavelength surface topography. This flow-induced ‘dynamic topography’ is usually derived from mantle convection models by computing the vertical component of hydrodynamic stress at the top of the model and assuming the stress is compensated by deflection of the surface. However, these models have generally ignored the presence of an overlying buoyant crust and its deformational response to the mantle flow. We consider the effects of horizontal convective forcing on the crust and investigate how this crust/lithosphere deformation interacts with the vertical component of mantle flow-induced subsidence/uplift at the surface. In particular, we test the response of various rheologies of the crust and mantle lithosphere to an episode of mantle downwelling. The evolution of crustal thickness and topography is tracked using thermomechanical numerical models of the crust‐ mantle system with a free surface upper boundary. A strong crust (ηc = 2.5 × 10 25 Pa s) does not experience significant internal deformation and subsides above a mantle downwelling. For a weaker crust (ηc < =10 23 Pa s), descending mantle flow initially induces subsidence, but there is an inversion to surface uplift as crustal thickening induced by convergent mantle flow overcomes the dynamic subsidence. The presence of a strong mantle lithosphere, however, may effectively shield a weak crust from deformation imposed by the underlying horizontal mantle convective stresses. With temperature-dependent rheologies in the model, the interplay of the vertical/horizontal mantle forcings with the thermal evolution of the crust results in a highly time-dependent signal of topography. Subsequent to crustal thickening and uplift, the system may undergo rapid topographic subsidence and crustal thinning by localized channel flow in the hot and weak lower crust. These results suggest an alternative interpretation for the development of mantle-flow induced topography in certain tectonic environments.

Cold fingers in a hot magma: Numerical modeling of country-rock diapirs in the Bushveld Complex, South Africa

Partially molten diapirs and domes in Earth9s continental crust can be an effective means of transporting heat from lower to higher levels, often producing pronounced prograde metamorphic aureoles. Our numerical thermomechanical models show that this classical thermal scenario is violated by the diapirs of partially molten metasedimentary rocks to 8 km in diameter that penetrate the Bushveld Complex, the world9s largest layered intrusion. Here, diapirism was triggered by the emplacement of an 8-km-thick, hot, and dense mafic magma over a cold and less dense sedimentary succession. These diapirs promoted cooling of the giant magma chamber, bringing cooler material into higher crustal levels. Comparison between numerical results and geological observations indicates that diapir nucleation is crucially dependent on the presence of initial topographic disturbances between 800 and 1000 m in height in the floor of the magma chamber, and also allows critical parameters of initial geometry and temperature distribution of the Bushveld event to be outlined.

Rifting in heterogeneous lithosphere: Inferences from numerical modeling of the northern North Sea and the Oslo Graben

Permian rifting and magmatism are widely documented across NW Europe. The different Permian basins often display contrasting structural styles and evolved in lithospheric domains with contrasting past evolution and contrasting thermotectonic ages. In particular, the Oslo Graben and the northern North Sea rift initiated in close areas of northern Europe. The Oslo Graben evolved in the cold and stable Precambrian lithosphere of Fennoscandia, whereas the northern North Sea rift took birth in freshly reworked Caledonian lithosphere. Huge volumes of magmatic rocks characterize the relatively narrow Oslo Graben. In contrast, little magmatism is documented for the wide northern North Sea rift. Differences in timing between both rifts are inferred but still debated. We present numerical thermomechanical models along a lithospheric E‐W section that involves both the Oslo Graben and the northern North Sea area. Because the modeled section crosses the boundary between Caledonian and Proterozoic provinces, thermal and compositional heterogeneities are considered. As is suggested by various geophysical data sets, we also consider lithospheric thickness heterogeneities in the Precambrian lithosphere. Modeling results suggest that the northern North Sea was on top of “weak” lithosphere very sensitive to far‐field stresses. Consequently, we suggest that rifting in the northern North Sea began as early as regional extension was effective (i.e., Late Carboniferous–Early Permian) and does not postdate the Oslo Graben as it is commonly assumed. Rifting in the “strong” Precambrian lithosphere is unexpected. Modeling results suggest that a pre‐existing lithospheric thickness contrast within the Fennoscandian lithosphere favored rifting in the Oslo Graben.

A thermomechanical model of exhumation of high pressure (HP) and ultra-high pressure (UHP) metamorphic rocks in Alpine-type collision belts

Using a fully coupled numerical thermomechanical model handling strain localization, surface processes and ultra-high viscosity contrasts (11 orders of magnitude) we test a number of possible mechanisms of High Pressure (HP)–Low Temperature (LT)/High Temperature (HT) exhumation in continental collision zones. The model considers two end-member cases, low or high buoyancy of the downgoing crust. The first model case predicts three levels of exhumation in the same collisional context: the “classical” corner flow LP–LT (Low Pressure–Low Temperature) exhumation in the accretionary prism; deeper (70 km) HP–HT exhumation for the thickened subducting crustal–sedimentary wedge, and ultra HP–HT exhumation from the “lower” crustal chamber, forming at the depth of 100–120 km and separated from the upper one by a narrow crustal channel. The width of this channel can oscillate in the process of shortening, thus controlling the quantity of the crustal material exchanged between the crustal wedge and the lower crustal chamber. Although both zones of crustal accumulation and the narrow channel between them resemble a vortex-shaped nozzle, this “nozzle” appears to be too soft to produce any significant overpressures. From the upper crustal wedge, the material is exhumed following the ascending shear flow created by the overriding plate assisted by positive buoyancy of the heated crustal material. From the lower crustal chamber, the material is transported upward to the upper crustal wedge by a flow induced by the asthenospheric traction and a small-scale convective instability forming in the lower crustal chamber due to its heating by the overriding asthenosphere. In the second modelled case of high buoyancy, the latter mechanisms become dominant resulting in hyper fast exhumation of the crust to the surface, accelerated or slowed subduction in case of full or partial crustal decoupling, respectively, and upper plate extension.

Thermomechanical behavior of large ash flow calderas

The fundamental thermal and mechanical processes that occur within the “ash flow caldera‐magma chamber” systems remain largely enigmatic. To date, the only models of caldera collapse are simple, mostly elastic or viscoelastic mechanical models that can predict some of the conditions preceding the collapse. They cannot, however, predict the collapse itself because they are incapable either of reproducing the formation of faults or of accounting for the brittle‐ductile transitions and fault‐related thermal anomalies. We have constructed analytical and numerical thermomechanical models that account for both elastic‐plastic‐ductile rheology and physical properties of the caldera rocks. The overpressured magma is evacuated through a central vent and transforms into ash flow units deposited within the forming caldera. Brittle deformation, faulting, and subsequent collapse of the structure are reproduced. The results show that in the absence of a regional stress field the collapse on both sides will occur only for aspect ratios (i.e., caldera diameter to the depth of the magma chamber) exceeding 5 and that internal embedded faults may also appear when the aspect ratio exceeds 10. Thermal conductivity contrasts in ash flow calderas give rise to strong heat refraction that localizes deep seated thermal anomalies to the outer sides of the faults. In the presence of regional extension the border faulting can be attenuated or disappear, and the faults tend to localize around the central part of the chamber roof. Coupled thermomechanical modeling suggests that the outer sides of the border faults have high trapping capabilities for hydrothermal fluids. The geometry of the brittle‐ductile transition largely controls that of the fractured zones within and around the chamber roof, thus justifying a new “mechanical definition” of magma chamber geometry.

Contrasting styles of rifting: Models and examples from the Eastern Canadian Margin

We present the results of a dynamical model of lithospheric rifting and rupture which show that a wide range of crustal thinning patterns across rifted passive margins can be produced by varying the steady state geotherm, lithospheric composition (dry versus wet materials), and strain rate. The basic mechanism of continental rupture is assumed to be passive rifting and necking. We use a numerical thermomechanical model of lithosphere extension based on a finite element approach. When plasticity is significant (i.e., at lower temperatures or for “harder” materials) deformation is unstable and thinning takes place abruptly, over a narrow area. Conversely, a progressive thinning across the margin is observed when creep is dominant (i.e., in warm or ductile conditions). Cooling and associated hardening of the thinned area can occur during extension and cause the locus of extension to migrate laterally. In these circumstances, rupture is likely to take place asymmetrically along one edge of the thinned area, producing a narrow margin and a very wide conjugate. The eastern margins of Canada and their conjugates across the North Atlantic provide examples which cover this range of theoretical profiles. The crustal thinning patterns, inferred from deep seismic data, and the duration of rifting compare well with model results. We discuss also the constraints that these geodynamical models provide on such current issues as the seismic reflectivity of the lower crust, or the location of the ocean‐continent boundary in wide areas supposedly underlain by 5‐km thin continental crust.

Factors controlling the style of continental rifting: insights from numerical modelling

Passive continental margins, similarly formed by lithospheric stretching and rifting, can differ significantly in terms of width, ranging from 50 to 400 km, or subsidence history. Our interest lies in determining what properties of the lithosphere and what stress and strain boundary conditions control this regional variability and the siting of rupture. Continental breakup occurs probably as the result of a stretching instability which develops in a zone of material or geometrical heterogeneity. To analyze the factors controlling these instabilities, we use a numerical thermo-mechanical model of lithosphere extension based on a finite-element program. The particular program was chosen because it combines constitutive models appropriate to our knowledge of lithosphere rheology (elasticity, plasticity and nonlinear, temperature-dependent creep) with a kinematic formulation for large inelastic strain. We choose to weaken the plate by locally increasing the crustal thickness by a very small amount and examine how this “defect” or “perturbation” acts to localize the deformation. We compare the geometry and timing of necking for relatively “wet” versus “dry” rheology, “cold” versus “warm” geotherm and “fast” versus “slow” strain-rate. We examine as well how the width and amplitude of the perturbation itself affects the deformation history. Since a velocity boundary condition is applied, the required extensional forces are evaluated and compared to estimates of plate driving forces. Conditions that favor deformation by plasticity rather than creep (“cold” geotherms, “dry” rheologies) lead to a more localized extension and rapid rupture but the forces involved ( > 10 13 N/m) are larger than typical plate driving forces. Increasing the amplitude of the defect, i.e. crustal thickness contrasts, accelerates necking as well. Cooling of the thinned area becomes significant at low extension rates. Depending on the initial rheology, cooling simply delays the moment when deformation becomes unstable or, conversely, inhibits necking.

Thermomechanical models of active rifting

Geological and geophysical evidence (in particular thermal and gravity anomalies) suggests the presence of hot mantle material below the zones of continental rifting. Using a thermomechanical numerical model we quantify the lithospheric thinning caused by such a deep thermal anomaly. The mantle is assumed to be an incompressible non‐Newtonian fluid with temperature‐ and pressure‐dependent viscosity. The index power law is 3 in the mantle and 7 in the crust. This yields a viscosity minimum at the base of the lithosphere and therefore favors rapid convective thinning. The corresponding mass displacements disturb the lithosphere. The stresses at the bottom of the crust are used to quantify the vertical movements and the tectonic regime within the continental crust. The heat flow anomalies are also computed. The present work indicates that these deep geodynamic processes can induce well‐localized extensive tectonic stresses and the thinning of the lithosphere on a short time scale. This analysis also suggests that the subsidence in the rift valley is mainly due to crustal thinning while the uplift of the shoulders of the rift is a consequence of the advection of hot material from the asthenospheric channel. A regional extensional stress enhances the convective phenomena and favors the crustal thinning but is not necessary. A decrease in this far‐field force drastically increases the uplift of the shoulders and reduces the width of the rift valley. This case may be representative of the African rift.