Viscoelastic Finite Element Model Research Articles

Functionally graded bi-material interface for Porcelain Veneered Zirconia dental crowns: A study using viscoelastic finite element analysis

ObjectivesDuring the manufacturing of Porcelain Veneered Zirconia (PVZ) dental crowns, the veneer-core system undergoes high-temperature firing cycles and gets fused together which is then, under a controlled setting, cooled down to room temperature. During this cooling process, the mismatch in thermal properties between zirconia and porcelain leads to the development of transient and residual thermal stresses within the crown. These thermal stresses are inherent to the PVZ dental crown systems and render the crown structure weak, acting as a precursor to veneer chipping, fracture, and delamination. In this study, the introduction of an intermediate functionally graded material (FGM) layer at the bi-material interface is investigated as a potentially viable alternative for providing a smoother transition of properties between zirconia and porcelain in a PVZ crown system. MethodsAnatomically correct 3D crown models were developed for this study, with and without the FGM layer modeled at the bi-material interface. A viscoelastic finite element model was developed and validated for an anatomically correct bilayer PVZ crown system which was then used for predicting residual and transient stresses in the bilayer PVZ crown. Subsequently, the viscoelastic finite element model was further extended for the analysis of graded sublayers within the FGM layer, and this extended model was used for predicting the residual and transient stresses in the functionally graded PVZ crown, with an FGM layer at the bi-material interface. ResultsThe study showed that the introduction of an FGM layer at the bi-material interface has the potential to reduce the effects from transient and residual stresses within the PVZ crown system relative to a bilayer PVZ crown structure. Furthermore, the study revealed that the FGM layer causes stress redistribution to alleviate the stress concentration at the interfacial surface between porcelain and zirconia which can potentially enhance the durability of the PVZ crowns towards interfacial debonding or fracture. SignificanceThus, the use of an FGM layer at the bi-material interface shows a good prospect for enhancing the longevity of the PVZ dental crown restorations by alleviating the abrupt thermal property difference and relaxing thermal stresses.

Integrated Investigation on Heterogeneous Lower Crust Rheology in Kyushu and Afterslip Behavior Following the 2016 Mw7.1 Kumamoto Earthquake

AbstractThe viscoelastic lower crust beneath Kyushu Island, influenced by the volcanic arc, interplays with active crustal faults in this region and helps to shape local tectonics. In this study, we employed a three‐dimensional viscoelastic finite element model to gain insights into the lithospheric rheology and crustal faulting kinematics, through modeling the postseismic deformation processes of the 2016 Mw 7.1 Kumamoto earthquake. Our model reveals a viscosity of 2 × 1020 Pa s for the lower crust and 2 × 1019 Pa s for the upper mantle. A reduced lower crust viscosity of 2 × 1019 Pa s in the volcanic arc area is required for better reproducing the Global Positioning System data. The stress‐driven afterslip decays rapidly over time and is up to 0.3 m within 5 years after the earthquake. We propose additional normal‐component afterslip to better explain the complex postseismic deformation in the near field, which may be due to the interaction between the fault and volcano Aso.

The impact of non-monotonic relaxation on numerical accuracy and stability of viscoelastic finite elements

Analysis of sound and vibration in linear viscoelastic materials is based on a relaxation function that is the time-dependent stress resulting from a unit step in strain. It is well established that relaxation functions decrease monotonically in time. The most common constitutive relaxation functions, such as the Kelvin–Voigt or General Maxwell Model, produce curves that must be monotonic. However, recently, the authors have produced a methodology that allows the use of discrete data for the time-dependent relaxation function. One result of this approach is the possibility of non-monotonic relaxation function input. This non-monotonic data may be the result of test and measurement errors. Alternatively, this non-monotonicity may be an actual anomalous physical result, such as in rock salt (He et al. 2019). The authors use validated viscoelastic finite element models in the time domain to determine the instability caused by such non-monotonic datasets. The study uses randomized non-monotonic datasets that maintain the fundamental material trend to find unstable or inaccurate results. A mathematical review highlights the conditions causing numerical instability in modern stepwise time integration solvers. The results provide clarity for viscoelastic analysts considering low-precision viscoelastic measurements or unusual physical properties. [Work supported by ONR under Grant N00014-22-1-2785.]

Geodetic signature of a weak Lithosphere-Asthenosphere Boundary in postseismic deformation of large subduction earthquakes

The rheology of the seismically imaged Lithosphere-Asthenosphere Boundary (LAB) is an important new question in plate tectonics. If the LAB is associated with ponding of partial melts as inferred from many seismic studies, it should have a low viscosity that minimizes resistance to plate motion and subduction. Here, we propose that recently observed postseismic enhanced landward motion (ELM) in coastal areas outside the rupture zone of large subduction earthquakes provides the first geodetic evidence for a low-viscosity LAB beneath subducting oceanic lithosphere. Using three-dimensional viscoelastic finite element models, we demonstrate that a low-viscosity LAB readily leads to postseismic ELM over broad coastal areas far beyond the rupture zone. If the LAB thickness is assumed to be 10 km, key spatiotemporal characteristics of the observed ELM can be well explained by an LAB viscosity of 5 × 1016 Pa s, orders of magnitude lower than typical asthenospheric viscosities. A thicker LAB such as 20 km with a higher viscosity may also explain the postseismic ELM but is incompatible with existing, albeit limited, near-field vertical deformation observations. The small thickness and the low viscosity of the model LAB are consistent with inferences from seismological observations and support the notion of ponding melts. Our preliminary weak-LAB models also predict diagnostic deformation features that can be tested by future onshore and offshore geodetic observations. Whether a weak LAB is ubiquitously present before and after plate subduction and how its presence and spatial heterogeneity impact postseismic and plate-scale deformation are important research targets for future investigations.

Seismic potential in the southeastern margin of Bayanhar block after 2017 Jiuzhaigou earthquake, China – insight from stress evolution and earthquake probability estimation

The southeastern margin of the Bayanhar block (BHB) is located at the junction of the Bayanhar block and the southern China block (SCB). Strong earthquakes occurred frequently in this region because of the intensive tectonic movement. The stress changes caused by strong earthquakes and the observed background seismicity can be used to forecast strong earthquake probability in this region. Therefore, we construct a 3D (three Dimension) viscoelastic finite element model that includes the complex fault system, inhomogeneous medium, tectonic stress, and gravity to simulate the evolutionary stress field when using the observed Global Positioning System (GPS) vectors as the boundary conditions. In addition, we calculate the strong earthquake probability based on the calculated stress and a Poisson probability distribution. The stress evolution result shows the Xianshuihe fault (XSHF), the Huya fault (HYF) and the southern segment except for the Yaan County of Longmenshan fault (LMSF) are located in the stress enhancement area indicating high seismic potential. However, the Minjiang fault (MJF) is located in the stress shadow area. After the Lushan and Jiuzhaigou earthquakes, there is still a high possibility of strong earthquakes in the MJF, HYF, and LMSF zone, according to the strong earthquake probability result.

Identification of the periodontal ligament material parameters using response surface method

The orthodontic treatment can be guided by the finite element (FE) simulation of periodontal ligament (PDL) mechanical properties, and the biomimetic degree of FE simulation can be primarily affected by the material properties of the PDL. According to the principle of parameter inverse, a method: response surface (RS) method and FE inverse method were proposed to identify the material parameters of PDL. The Prony series viscoelastic FE model was established based on the relaxation experiment. With root mean square error of simulation results and experimental results as the objective function, the optimal parameter combination was obtained by RS method, and the FE simulation result were compared with the experimental result. The result showed that the optimal parameters of the PDL were elastic modulus: 3.791 MPa, Poisson's ratio: 0.42, temperature: 29.294°C separately, and the simulation result of optimal combination maintained consistency with experiment with the correlation coefficient of 0.97258, indicating that the method proposed in this paper could well identify of PDL material parameters. The parameter identification method used in this paper can significantly improve the calculation efficiency, and reduce the parameter identification error compared with the simple FE inverse method, which has scientific significance and theoretical value.

Numerical simulation of fault deformation and seismic activity in the southern Qinghai–Tibet Plateau

The moderate-strong (M ≥ 5, since 1976; or M ≥ 6.5, overall) earthquakes of the north to south trending (NS-trending) faults and their vicinity in the southern Qinghai–Tibet Plateau exhibit prominent spatial concentration distribution characteristics. However, research on the southern Tibet faults is limited. Hence, this study used a two-dimensional viscoelastic finite element model to simulate crustal movement in southern Tibet based on 1991–2015 GPS velocity data. The current deformation field, tectonic stress field, fault slip, and stress accumulation rates distribution were obtained to analyze the relationship between fault activity and earthquake distribution. The results revealed that the simultaneous effected by of the NE-trending compression and uneven EW-trending tension on the study area. Crustal deformation exhibited simultaneous NS-trending compression and EW-trending stretching. The EW- and NWW-trending faults and the NS-trending faults differed in their mechanical properties and movement modes. The NS faults were primarily subjected to extensional stress with normal motion. The remarkable heterogeneity of the fault segments influenced the distribution of moderate-strong earthquakes and types of earthquake ruptures. The concentrated distribution of moderate-strong earthquakes on the NS-trending normal fault and its vicinity depended largely on the high slip rate, strong tensile stress, and geometric strike of the fault segment. This study aids in understanding the heterogeneity in normal fault activity in southern Tibet and is the basis for seismic hazard assessment.

Cure-induced stress build-up in adhesives: model building and parameter studies

ABSTRACT Prediction of stresses in adhesively bonded joints requires high effort in determination of relevant material properties, which change during cure. In addition, the computational effort using complex viscoelastic finite element (FE) models impends efficient prediction of stress build-up. Rotational and oscillatory rheometry can help to reduce the experimental effort by measuring of modulus of elasticity (MoE) and axial shrinkage along curing. In this publication, shrinkage, development of MoE and Poisson’s ratio of a curing adhesive were numerically modelled between two parallel rheometer plates in order to calculate cure-induced stresses using finite element analysis (FEA). To identify effects of different material properties on stress distribution, a parameter study was carried out and the reciprocal influence of the varied parameters was investigated. Consequently, resulting stresses within the adhesive layer and occurring deformations were investigated with respect to curing time as well as their location. The results showed that final shrinkage and MoE need to be considered not only in final values but also in terms of course of shrinkage and reaction. Stress build-up led to deformation of the rheometer plates, which has to be considered when using rheometry for determination of cure shrinkage.

Effect of various interface bonding conditions on critical response characteristics for cracking potential of asphalt pavements

Interface bonding conditions are important to ensure the desired performance of multi-layered asphalt pavements. Most previous studies only investigated the sole effect of the interface at a specific location, although the most extreme case is when poor bonding occurred at multiple locations simultaneously. Also, the sensitivity of bonding effects to structural parameters is unclear. Therefore, this study investigated the effects of multiple bonding scenarios and structural parameters on critical responses, the 3-D viscoelastic finite element model. The results indicated that critical locations for cracking potential depend on bonding scenarios. Interface bonding between asphalt and aggregate base layers mainly contributed to bottom-up cracking, while the interface between asphalt layers was more associated with top-down and near-surface cracking. In addition, the use of a thicker asphalt layer was more effective than the use of a strong base layer to mitigate the negative effects of poor bonding conditions.

Modelling transcranial ultrasound neuromodulation: an energy-based multiscale framework

Several animal and human studies have now established the potential of low intensity, low frequency transcranial ultrasound (TUS) for non-invasive neuromodulation. Paradoxically, the underlying mechanisms through which TUS neuromodulation operates are still unclear, and a consensus on the identification of optimal sonication parameters still remains elusive. One emerging hypothesis based on thermodynamical considerations attributes the acoustic-induced nerve activity alterations to the mechanical energy and/or entropy conversions occurring during TUS action. Here, we propose a multiscale modelling framework to examine the energy states of neuromodulation under TUS. First, macroscopic tissue-level acoustic simulations of the sonication of a whole monkey brain are conducted under different sonication protocols. For each one of them, mechanical loading conditions of the received waves in the anterior cingulate cortex region are recorded and exported into a microscopic cell-level 3D viscoelastic finite element model of a neuronal axon embedded in extracellular medium. Pulse-averaged elastically stored and viscously dissipated energy rate densities during axon deformation are finally computed under different sonication incident angles and are mapped against distinct combinations of sonication parameters of the TUS. The proposed multiscale framework allows for the analysis of vibrational patterns of the axons and its comparison against the spectrograms of stimulating ultrasound. The results are in agreement with literature data on neuromodulation, demonstrating the potential of this framework to identify optimised acoustic parameters in TUS neuromodulation. The proposed approach is finally discussed in the context of multiphysics energetic considerations, argued here to be a promising avenue towards a scalable framework for TUS in silico predictions. Statement of significanceLow-intensity transcranial ultrasound (TUS) is poised to become a leading neuromodulation technique for the treatment of neurological disorders. Paradoxically, how it operates at the cellular scale remains unknown, hampering progress in personalised treatment. To this end, models of the multiphysics of neurons able to upscale results to the organ scale are required. We propose here to achieve this by considering an axon submitted to an ultrasound wave extracted from a simulation at the organ scale. Doing so, information pertaining to both stored and dissipated axonal energies can be extracted for a given head/brain morphology. This two-scale multiphysics energetic approach is a promising scalable framework for in silico predictions in the context of personalised TUS treatment.

Constrained shape optimization of free-form shells considering material creep

Shape optimization is an effective tool for designing free-form structures for a variety of design objectives. Aiming at long-term structural performance, a computational framework is presented for performing shape optimization of free-form shells while considering material creep. The material creep model is incorporated into a gradient-based optimization algorithm using a viscoelastic finite element model. Non-uniform rational B-spline (NURBS) is employed to parameterize the free-form geometric shapes of shells. Optimization is conducted for minimizing the shell volume subject to constraints of specified maximum displacement. The results demonstrate that it is necessary to consider creep when designing shells made of viscoelastic materials for long-term performance.

Lateral variation in slab window viscosity inferred from global navigation satellite system (GNSS)–observed uplift due to recent mass loss at Patagonia ice fields

AbstractThe geographic coincidence of the Chile Ridge slab window and the Patagonia ice fields offers a unique opportunity for assessing the effects of slab window rheology on glacial isostatic adjustment (GIA). Mass loss of these ice fields since the Little Ice Age causes rapid but variable crustal uplift, 12–24 mm/yr around the North Patagonia ice field, increasing to a maximum of 41 mm/yr around the South Patagonia ice field, as determined from newly collected or processed geodetic data. We used these observational constraints in a three-dimensional Maxwell viscoelastic finite element model of GIA response above both the subducting slab and slab window in which the upper-mantle viscosity was parameterized to be uniform with depth. We found that the viscosity of the northern part of the slab window, ~2 × 1018 Pa·s, is lower than that of the southern part by approximately an order of magnitude. We propose that this along-strike viscosity contrast is due to late Cenozoic ridge subduction beneath the northern part of the slab window, which increases asthenospheric temperature and reduces viscosity.

Influences of the heterogeneity of viscoelastic medium on postseismic deformation of the 2008 MW7.9 Wenchuan earthquake

The study of postseismic deformation is important for constraining the viscoelastic properties of the Earth and inverting the post-earthquake process. The levelling survey revealed that the area near Beichuan elevated 5.3 cm about two years after the MW7.9 Wenchuan earthquake (05/12/2008), during which the area underwent significant downward movement. The GPS horizontal displacements showed a non-monotonic variation after the Wenchuan earthquake. In this study, a 3-D viscoelastic finite element model is employed to simulate the coseismic and postseismic deformation of the Wenchuan earthquake. The numerical simulations show that the lateral heterogeneity across the Longmenshan fault plays an important role in the postseismic displacements. The results reveal that the coseismic deformation is not sensitive to the horizontal heterogeneity, but the postseismic deformation is sensitive to it. The postseismic deformation of the horizontally heterogeneous model is generally consistent with the observations of all geodetic surveys, such as GPS, InSAR and levelling, but not for the horizontally homogenous model. We also find that the non-monotonous variation of the postseismic deformation of the Wenchuan earthquake could be explained by a viscoelastic relaxation model with lateral heterogeneous medium across the Longmenshan fault.

Finite element simulation of stress change for the MS7.4 Madoi earthquake and implications for regional seismic hazards

On May 22, 2021, the MS 7.4 earthquake occurred in Madoi County, Qinghai Province; it was another strong event that occurred within the Bayan Har block after the Dari MS 7.7 earthquake in 1947. An earthquake is bound to cast stress to the surrounding faults, thus affecting the regional seismic hazard. To understand these issues, a three-dimensional viscoelastic finite element model of the eastern Bayan Har block and its adjacent areas was constructed. Based on the co-seismic rupture model of the Madoi earthquake, we analyzed the co- and post-seismic Coulomb stress change caused by the Madoi earthquake on the surrounding major faults. The results show that the Madoi earthquake caused significant co-seismic stress increases in the Tuosuo Lake and Maqin-Maqu segments of the East Kunlun fault (>10 ​kPa), which exceeded the proposed threshold of stress triggering. By integrating the accumulation rate of the inter-seismic tectonic stress, we conclude that the Madoi earthquake caused future strong earthquakes in the Tuosuo Lake and Maqin-Maqu segments of the East Kunlun fault to advance by 55.6-623 and 24.7-123 ​a, respectively. Combined with the influence of the Madoi earthquake and the elapsed time of the last strong earthquake, these two segments have approached or even exceeded the recurrence interval of the fault prescribed by previous research. In the future, it is necessary to focus greater attention on the seismic hazard of the Maqin-Maqu and Tuosuo Lake segments. This study provides a mechanical reference to understand the seismic hazard of the East Kunlun fault in the future, particularly to determine the seismic potential region.

Metal-ceramic and porcelain-veneered lithium disilicate crowns: a stress profile comparison using a viscoelastic finite element model

Metal-ceramics (MC) are one of the oldest dental restorative systems, which are considered to be the gold standard for full crown restoration. Porcelain-veneered lithium disilicate (PVLD), on the other hand, are newer material systems that have shown high survival rate in clinical follow-ups but needs to be studied more. This study compares the stresses developed in the single crowns made from newer PVLD system against those with MC configuration. For this comparison, influence of the layer thickness and cooling rates is also taken into consideration. An experimentally validated viscoelastic finite element model (VFEM) has been developed to predict the stress profile in these systems. Three-dimensional rotationally symmetric crowns were analyzed using this validated model for both material systems, three veneer to core thickness ratios (2:1, 1:1, 1:2), and two cooling rates: slow cooling at 1.74E-5 W/mm2 (∼30 K/min) and fast cooling at 1.74E-4 W/mm2 (∼300 K/min). PVLD showed lower values of transient and residual stresses than MC. The maximum tensile residual stresses in MC systems were observed in the cusp area, whereas those in PVLD were located in the central fossa. With the reduction in veneer layer, there was reduction in residual stress in MC; however, the veneer thickness had little to no effect in PVLD. The effect of cooling rate was also evident as slow cooling resulted in lower residual and tensile stresses for both material systems.

Inter-episodes earthquake migration in the Bohai-Zhangjiakou Fault Zone, North China: Insights from numerical modeling.

In this paper, we focus on why intraplate seismic initiation and migration occurs, which has widely been considered to be caused by static stress triggering caused by earthquakes, as well as post-seismic slips. To illustrate the mechanism underlying large earthquakes, in particular the migration caused by two key episodes that occurred after 1500 in the Bohai-Zhangjiakou Fault Zone (BZFZ) of North China, we developed a high-resolution three-dimensional viscoelastic finite element model that includes the active faults with vertical segmentation, their periodical locking, and the lithosphere heterogeneity. We used the birth and death of element groups to simulate stress intensity changes during the two episodes (named Episode I and II), with our results showing that the Tangshan earthquake was primarily triggered by the Sanhe-Pinggu M8.0 earthquake in 1679, whereas the Zhangbei M6.2 earthquake in 1998 was not triggered by earthquakes in Episode I. According to our work, the calculated stress changes in the different segments of the fault zone correspond to the magnitude of the triggered earthquakes. Further, the largest stress decrease was near the Sanhe-Pinggu fault and occurred the largest earthquake in Episode I, whereas the largest stress increase was near the Tangshan fault and occurred during the largest earthquake in Episode II. Given the above, we propose a model for seismic migration to describe the dynamic mechanisms of earthquake migration within the BZFZ and North China, in which the factors affecting both the seismic migration path and intensity primarily include the distance between the triggered active fault and the original fault, the coupling of the active faults, the location and scale of the low-velocity anomaly, its distance from the active fault, and the location and scale of the crustal thinning.

Numerical modelling of porphyroclast rotation in the brittle-viscous transition zone

Porphyroclasts have been widely used to determine the shear sense, vorticity and other kinematic parameters of shear zones. Previous studies have revealed that several factors affect the rotation angle of porphyroclasts. These studies mostly regard porphyroclasts as rigid objects or viscous deformable objects to simulate porphyroclast rotation in the upper or lower crust. However, research on how these porphyroclasts behave in the brittle-viscous transition zone is still limited.In this study, a two-dimensional viscoelastic finite element model is presented to simulate the rotation and deformation of an elastic porphyroclast embedded in a viscoelastic matrix with various mechanical parameters (Young's modulus, Poisson's ratio and viscosity coefficient) and different boundary conditions (load magnitude and load time). The modelling results demonstrate that the rotation angle of the porphyroclast is strongly influenced by the Young's modulus, Poisson's ratio and viscosity coefficient of the matrix and boundary conditions. The modelling results have a level of consistency with the natural examples of porphyroclast-matrix systems of the Taili and Tianhuang ductile shear zones of the North China Craton. These results are helpful to further explain the rotation and deformation mechanism of porphyroclasts in the brittle-viscous transition zone.

Influence of crustal rheology and heterogeneity on tectonic stress accumulation characteristics of North China constrained by GNSS observations

Abstract North China is characterized by significant lithosphere heterogeneity and numerous faults, with the occurrence of many historical and ongoing devastating earthquakes. To extend our understanding of the mechanisms of seismicity initiation and fault activity due to lithospheric rheology and lateral difference, we first established a three-dimensional viscoelastic finite element model based on the lithospheric lateral heterogeneity of physical properties across the north–south gravitational lineament (NSGL), spatial distribution of faults, and interseismic global navigation satellite system (GNSS) velocities (1999–2018). We then analyzed the stress accumulation characteristics across the NSGL and its relationship with seismicity. Finally, we explored the temporal and spatial variations of stress along major faults and further analyzed potential relationships between the stress components and rupture mechanisms of typical faults. The results showed that high maximum shear stress, mainly distributed in eastern North China (ENC) and western North China (WNC), corresponding to the focal depth, which suggests that the different brittle crustal thicknesses across the NSGL may be one of the major factors that dominates earthquake depth in North China. Significant maximum shear stress is mainly accommodated on faults around the Ordos Block in WNC and northern faults in ENC, which is consistent with frequent seismic activity in these regions. The relationship between the calculated stress components and rupture mechanisms of typical faults imply that the differential tectonic loading from neighboring blocks may be one of the major dynamic factors for seismogenic processes in North China.

Optimizing a Viscoelastic Finite Element Model to Represent the Dry, Natural, and Moist Human Finger Pressing on Glass.

When a fingerpad presses into a hard surface, the development of the contact area depends on the pressing force and speed. Importantly, it also varies with the finger's moisture, presumably because hydration changes the tissue's material properties. Therefore, we collected data from one finger repeatedly pressing a glass plate under three moisture conditions, and we constructed a finite element model that we optimized to simulate the same three scenarios. We controlled the moisture of the subject's finger to be dry, natural, or moist and recorded 15 pressing trials in each condition. The measurements include normal force over time plus finger-contact images that are processed to yield gross contact area. We defined the axially symmetric 3D model's lumped parameters to include an SLS-Kelvin model (spring in series with parallel spring and damper) for the bulk tissue, plus an elastic epidermal layer. Particle swarm optimization was used to find the parameter values that cause the simulation to best match the trials recorded in each moisture condition. The results show that the softness of the bulk tissue reduces as the finger becomes more hydrated. The epidermis of the moist finger model is softest, while the natural finger model has the highest viscosity.

Current-Dependent Dynamics of Bidirectional Self-Folding for Multi-Layer Polymers Using Local Resistive Heating

Abstract The purpose of this paper is to characterize the dynamics and direction of self-folding of pre-strained polystyrene (PSPS) and non-pre-strained styrene (NPS), which results from local shrinkage using a new process of directed self-folding of polymer sheets based on a resistively heated ribbon that is in contact with the sheets. A temperature gradient across the thickness of this shape memory polymer (SMP) sheet induces folding along the line of contact with the heating ribbon. Varying the electric current changes the degree of folding and the extent of local material flow. This method can be used to create practical three-dimensional (3D) structures. Sheets of PSPS and NPS were cut to 10 × 20 mm samples, and their folding angles were plotted with respect to time, as obtained from in situ videography. In addition, the use of polyimide tape (Kapton) was investigated for controlling the direction of self-folding. Results show that folding happens on the opposite side of the sample with respect to the tape, regardless of which side the heating ribbon is on, or whether gravity is opposing the folding direction. The results are quantitatively explained using a viscoelastic finite element model capable of describing bidirectional folds arising from the interplay between viscoelastic relaxation and strain mismatch between polystyrene and polyimide. Given the tunability of fold times and the extent of local material flow, resistive-heat-assisted folding is a promising approach for manufacturing complex 3D lightweight structures by origami engineering.