Inverse Numerical Modeling Research Articles

Plasticity and ductile fracture behaviour of four armour steels

Under ballistic impact or blast loading, the strength and fracture behaviour of armour steels is key to their response, however a comprehensive understanding and modelling of material behaviour for multiple grades of high strength armour steels has not been presented in literature. This experimental and numerical investigation comprehensively characterises the plasticity and ductile fracture behaviour of four high strength armour steels: rolled homogenous armour (RHA); improved rolled homogenous armour (IRHA); high hardness armour (HHA); high strength abrasive resistant steel (ARS) with a TRIP strengthening mechanism. Thirteen specimen types are used to investigate a range of stress states from uniaxial tension to high stress triaxiality plane strain as well as elevated temperatures and strain rates. A modified Johnson-Cook strength model with combined Voce-Ludwik strain hardening and a J3-dependant yield function was calibrated and used. A new calibration approach for the ductile fracture model is presented that incorporates the time-dependence of the stress state taken from inverse numerical modelling of each experiment. The modelling is shown to accurately capture material response up to fracture across all specimens. High strain rate experiments identified dislocation drag effects at 2700s−1, which were captured by the modelling approach. The experimental results provide a characterisation of armour steels to an extent not previously seen in literature, particularly considering comparison of four materials across identical test conditions.

Development of a Semiglobal Reaction Mechanism for the Thermal Decomposition of a Polymer Containing Reactive Flame Retardants: Application to Glass-Fiber-Reinforced Polybutylene Terephthalate Blended with Aluminum Diethyl Phosphinate and Melamine Polyphosphate.

This work details a methodology for parameterization of the kinetics and thermodynamics of the thermal decomposition of polymers blended with reactive additives. This methodology employs Thermogravimetric Analysis, Differential Scanning Calorimetry, Microscale Combustion Calorimetry, and inverse numerical modeling of these experiments. Blends of glass-fiber-reinforced polybutylene terephthalate (PBT) with aluminum diethyl phosphinate and melamine polyphosphate were used to demonstrate this methodology. These additives represent a potent solution for imparting flame retardancy to PBT. The resulting lumped-species reaction model consisted of a set of first- and second-order (two-component) reactions that defined the rate of gaseous pyrolyzate production. The heats of reaction, heat capacities of the condensed-phase reactants and products, and heats of combustion of the gaseous products were also determined. The model was shown to reproduce all aforementioned experiments with a high degree of detail. The model also captured changes in the material behavior with changes in the additive concentrations. Second-order reactions between the material constituents were found to be necessary to reproduce these changes successfully. The development of such models is an essential milestone toward the intelligent design of flame retardant materials and solid fuels.

Simulation of less‐mobile porosity dynamics in contrasting sediment water interface porous media

AbstractConsidering heterogeneity in porous media pore size and connectivity is essential to predicting reactive solute transport across interfaces. However, exchange with less‐mobile porosity is rarely considered in surface water/groundwater recharge studies. Previous research indicates that a combination of pore‐fluid sampling and geoelectrical measurements can be used to quantify less‐mobile porosity exchange dynamics using the time‐varying relation between fluid and bulk electrical conductivity. For this study, we use macro‐scale (10 s of cm) advection–dispersion solute transport models linked with electrical conduction in COMSOL Multiphysics to explore less‐mobile porosity dynamics in two different types of observed sediment water interface porous media. Modeled sediment textures contrast from strongly layered streambed deposits to poorly sorted lakebed sands and cobbles. During simulated ionic tracer perturbations, a lag between fluid and bulk electrical conductivity, and the resultant hysteresis, is observed for all simulations indicating differential loading of pore spaces with tracer. Less‐mobile exchange parameters are determined graphically from these tracer time series data without the need for inverse numerical model simulation. In both sediment types, effective less‐mobile porosity exchange parameters are variable in response to changes in flow direction and fluid flux. These observed flow‐dependent effects directly impact local less‐mobile residence times and associated contact time for biogeochemical reaction. The simulations indicate that for the sediment textures explored here, less‐mobile porosity exchange is dominated by variable rates of advection through the domain, rather than diffusion of solute, for typical low‐to‐moderate rate (approximately 3–40 cm/day) hyporheic fluid fluxes. Overall, our model‐based results show that less‐mobile porosity may be expected in a range of natural hyporheic sediments and that changes in flowpath orientation and magnitude will impact less‐mobile exchange parameters. These temporal dynamics can be assessed with the geoelectrical experimental tracer method applied at laboratory and field scales.

Development of a semi-global reaction mechanism for thermal decomposition of a polymer containing reactive flame retardant

To enable intelligent design of fire resistant polymeric materials, it is highly important to have a quantitative understanding of the relation between the composition of these materials and chemical and physical properties that control the process of fire growth. This paper presents a methodology that provides a capability to determine the core subset of these properties including the kinetics and thermodynamics of the thermal decomposition of the condensed-phase constituents and enthalpy of combustion of gaseous pyrolyzates. This methodology is based on three experimental techniques – Thermogravimetric Analysis, Differential Scanning Calorimetry and Microscale Combustion Calorimetry – and inverse numerical modeling of the results of these tests. The material system analyzed in this study is polyamide 66 reinforced with chopped glass fiber and flame retarded with red phosphorous. This system shows a complex decomposition behavior that is highly dependent on the phosphorus concentration. First, a semi-global thermal decomposition mechanism consisting of a set of first- and second-order (two components) reactions was developed using three material specimens containing different phosphorus concentrations. Subsequently, the extrapolative power of the developed reaction model was demonstrated by accurately predicting the experimental measurements obtained for several compositions not used in the model development process.

A methodology for predicting and comparing the full‐scale fire performance of similar materials based on small‐scale testing

SummaryReconstructive fire testing is an important tool used by fire investigators to determine the cause, origin, and progression of a particular fire. Accurate reconstruction of the fire requires the laboratory structure to be outfitted with materials that, in terms of contribution to fire growth, perform similarly to the original materials found at the fire scene. Therefore, a procedure was developed to enable fire investigators to select these replacement materials on the basis of a quantitative assessment of their relative fire performance. This procedure consists of gram‐scale and/or milligram‐scale standard testing accompanied by inverse numerical modeling of these tests, which is used to obtain relevant material properties. A numerical model composed of a detailed pyrolysis submodel and empirical flame heat feedback submodels, which were developed in this study, is subsequently employed to simulate the early stages of the Room Corner Test, which was selected to represent full‐scale material performance. The results of these simulations demonstrate that this procedure can successfully differentiate between fire growth propensities of several commercially available medium density fiberboards.

A novel inverse numerical modeling method for the estimation of water and salt mass transfer coefficients during ultrasonic assisted-osmotic dehydration of cucumber cubes

The objective of this paper was to study the moisture and salt diffusivity during ultrasonic assisted-osmotic dehydration of cucumbers. Experimental measurements of moisture and salt concentration versus time were carried out and an inverse numerical method was performed by coupling a CFD package (OpenFOAM) with a parameter estimation software (DAKOTA) to determine mass transfer coefficients. A good agreement between experimental and numerical results was observed. Mass transfer coefficients were from 3.5 × 10−9 to 7 × 10−9 m/s for water and from 4.8 × 10−9 m/s to 7.4 × 10−9 m/s for salt at different conditions (diffusion coefficients of around 3.5 × 10−12–11.5 × 10−12 m2/s for water and 5 × 10−12 m/s–12 × 10−12 m2/s for salt). Ultrasound irradiation could increase the mass transfer coefficient. The values obtained by this method were closer to the actual data. The inverse simulation method can be an accurate technique to study the mass transfer phenomena during food processing.

High strain rate and high temperature response of two armour steels: Experimental testing and constitutive modelling

Under ballistic impact or blast loading, the high strain rate and high temperature behaviour of armour steels is key to their response to a given threat. This experimental and numerical investigation examines the tensile response of a class 4a improved rolled homogenous armour steel (IRHA) and a high hardness armour steel (HHA). Cylindrical tensile specimens were tested at a range of strain rates from 0.001 s-1 to 2700 s-1. Quasi-static, elevated temperature tests were performed from room temperature up to 300° C. While the HHA is strain rate insensitive, the IRHA displays a significant increase in strength across the range of loading rates reducing the ultimate strength difference between the materials from 19% at 0.001s-1 to 4.6% at 2700s-1. An inverse numerical modelling approach for constitutive model calibration is presented, which accurately captured the dynamic material behaviour. The modified Johnson-Cook strength and Cockcroft-Latham (C-L) fracture models were capable of predicting the ballistic limit of each material to within 5% of the experimental result and to within 10% for deformation under blast loading. The blast rupture threshold of both materials was significantly over-estimated by the C-L model suggesting stress state or strain rate effects may be reducing the ductility of armour steel under localised blast loading.

A Wedge-DCB Test Methodology to Characterise High Rate Mode-I Interlaminar Fracture Properties of Fibre Composites

A combined numerical-experimental methodology is presented to measure dynamic Mode-I fracture properties of fiber reinforced composites. A modified wedge-DCB test using a Split-Hopkinson Bar technique along with cohesive zone modelling is utilised for this purpose. Three different comparison metrics, namely, strain-displacement response, crack propagation history and crack opening history are employed in order to extract unique values for the cohesive fracture properties of the delaminating interface. More importantly, the complexity of dealing with the frictional effects between the wedge and the DCB specimen is effectively circumvented by utilising right acquisition techniques combined with an inverse numerical modelling procedure. The proposed methodology is applied to extract the high rate interlaminar fracture properties of carbon fiber reinforced epoxy composites and it is further shown that a high level of confidence in the calibrated data can be established by adopting the proposed methodology.

High‐Resolution Shortwave Infrared Imaging of Water Infiltration into Dry Soil

Core Ideas SWIR imaging for quantification of soil moisture dynamics is introduced. High spatiotemporal resolution images yield accurate soil moisture profile. Flux density profiles during water infiltration were quantified with this method. The new technique opens potential avenues for soil hydraulic properties estimation. A novel proximal sensing framework for high‐resolution soil water content profile retrieval under laboratory conditions has been developed. Constant‐head upward‐flow experiments were conducted for a number of soils that cover a wide textural range. The soils were packed into quartz Hele–Shaw cells, and the profile was imaged at high temporal frequency with a shortwave infrared (SWIR) camera in the 900‐ to 1700‐nm electromagnetic domain during upward infiltration of water. The SWIR reflectance recorded for each spatial pixel was converted to soil water content with a recently developed linear physical model. Because of the linearity of the model, its parameters were assumed to be identical at both the pixel and column scales, and this allowed simple self‐calibration during the experiment. The obtained water content profiles were in good agreement with soil water content data measured independently with a recently developed time domain reflectometry array with 1‐cm depth resolution. In addition, the accuracy of the soil water content profiles was verified based on the water mass balance. The high‐spatiotemporal‐resolution SWIR reflectance‐derived water content profiles allow calculation of water flux densities, which provides a potential new avenue for the rapid estimation of soil hydraulic properties and processes via inverse numerical or analytical modeling.

Dating the topography through thermochronology: application of Pecube Code to inverted vertical profile in the Eastern Sila Massif, Southern Italy

The Sila Massif is a small part of an orogenic wedge that sits on top of the narrow and active Calabrian subduction zone. The topography of the Sila Massif is characterized by a plateau region whose age and origin has been long debated. Here we integrate new apatite (U-Th)/He data from the eastern flank of the massif with existing apatite fission-track (AFT) data, to constrain the topographic evolution of the massif. The new AHe ages range from 9.7 Ma to 49.8 Ma and overlap the AFT ages indicating that a phase of rapid Cenozoic exhumation was followed by an abrupt decrease of the exhumation rate. A steep/inverse AFT age-elevation relationship from a vertical profile on top of the summit area of the north-eastern Sila may records post-exhumation relief degradation, which is consistent with the low-relief upland topography. To test this hypothesis we performed inverse numerical modeling using Pecube code. Integrating the new AHe ages and the numerical modelling results with the geological constraints we propose a new model for the regional topographic evolution from 30 Ma to the present.

Multi-well and multi-tracer tests to characterize the groundwater aquifers in southern Kuwait

In the water-starved arid climate of Kuwait, useable (both fresh and brackish) reserves of groundwater constitute a strategic resource. Therefore, effective management policies are essential for ensuring sustainable management of the groundwater resources in the state. Although the general pattern of groundwater flow is known, the detailed pattern of the flow paths of water within the Kuwait aquifer system and the variation of hydraulic and transport properties are not known. Applied tracers are powerful hydrogeological investigative tools because the tracer application (source term) is controlled and well characterized which permits quantification of subsurface properties often unmatched by standard physical methods. Aquifer pumping tests and multi-well and multi-tracer (rhodamine-WT, fluorescein, sodium bromide) tests were carried out, under both natural and forced gradient conditions, at Al-Shegaya and Umm-Gudair sites. The objectives of the tracer tests are to determine the groundwater flow directions, flow rates, inter- and intra-aquifer hydraulic communications, effective porosity, dispersivity, etc., in the established groundwater well fields of southern Kuwait at Al-Shegaya Umm-Gudair. The tests involved drilling, construction and development of groundwater wells, and injection of tracers in the injection wells and monitoring its concentrations in the injection and monitoring wells. Inverse numerical modeling (MODFLOW and MT3DMS codes) was used for data interpretation. The Kuwait Group and Dammam Formation have a high degree of hydraulic separation, and it is likely that there is little recharge of the Dammam Formation from downward leakage from the Kuwait Group (at least in the study area). Groundwater resources in the Dammam Formation may be largely restricted to the flow into Kuwait from Saudi Arabia. The lower Kuwait Group aquifer has dual-porosity conditions: likely a rapid flow through fracture and/or conduit system (neff = 0.5 %) and a slow flow through the formation (calcareous) matrix (neff = 20 %), with very low dispersivity (longitudinal and transverse/vertical dispersivities of 0.1 and 0.01 m, respectively). The injection wells indicate more than one linear line segment in the tracer dilution plot (concentration in natural logarithmic vs. time), which suggests varying transmissivity across the well screen depths. The filtration velocity, hydraulic conductivity and transmissivity of the aquifers have also been estimated. At both the sites, the groundwater flow in the underlying carbonate formation is very slow (0.028 m/d). The hydrogeological parameters obtained from the present tracer study will be used for more reliable conceptualization, development and calibration of a suitable statewide flow and solute transport model for the regional groundwater system of Kuwait.

Extending thermal response test assessments with inverse numerical modeling of temperature profiles measured in ground heat exchangers

Thermal response tests conducted to assess the subsurface thermal conductivity for the design of geothermal heat pumps are most commonly limited to a single test per borefield, although the subsurface properties can spatially vary. The test radius of influence is additionally restricted to 1–2 m, even though the thermal conductivity assessment is used to design the complete borefield of a system covering at least tens of squared meters. This work objective was therefore to develop a method to extend the subsurface thermal conductivity assessment obtained from a thermal response test to another ground heat exchanger located on the same site by analyzing temperature profiles in equilibrium with the subsurface. The measured temperature profiles are reproduced with inverse numerical simulations of conductive heat transfer to assess the site basal heat flow, at the location of the thermal response test, and evaluate the subsurface thermal conductivity, beyond the thermal response test. Paleoclimatic temperature changes and topography at surface were considered in the model that was validated by comparing the thermal conductivity estimate obtained from the optimization process to that of a conventional thermal response test.

Determination of kinetics and thermodynamics of thermal decomposition for polymers containing reactive flame retardants: Application to poly(lactic acid) blended with melamine and ammonium polyphosphate

A methodology for parameterization of kinetics and thermodynamics of decomposition of polymeric materials has been extended to blends of a polymer with condensed-phase active flame retardants. This methodology is based on Thermogravimetric Analysis, Differential Scanning Calorimetry, Microscale Combustion Calorimetry and inverse numerical modeling of these experiments. Material systems consisting of poly(lactic acid), melamine and ammonium polyphosphate were used to demonstrate this parameterization process. The resulting model consists of a set of first and second order (two component) reactions that define the rate of gaseous pyrolyzate production, heats of these reactions, heat capacities of the condensed-phase reactants and products and heats of combustion of the components of the gaseous pyrolyzate. This model is shown to reproduce results of all aforementioned experiments with a high degree of detail and predict relation between the outcome of these experiments and material composition. It is expected that a combination of this model with thermal transport parameters, which determination will be a subject of separate study, will yield a complete pyrolysis model capable of predicting the dynamics of burning and flame spread on these materials and dependence of this dynamics on the flame retardant content.

Landslide Kinematical Analysis through Inverse Numerical Modelling and Differential SAR Interferometry

The aim of this paper is to propose a methodology to perform inverse numerical modelling of slow landslides that combines the potentialities of both numerical approaches and well-known remote-sensing satellite techniques. In particular, through an optimization procedure based on a genetic algorithm, we minimize, with respect to a proper penalty function, the difference between the modelled displacement field and differential synthetic aperture radar interferometry (DInSAR) deformation time series. The proposed methodology allows us to automatically search for the physical parameters that characterize the landslide behaviour. To validate the presented approach, we focus our analysis on the slow Ivancich landslide (Assisi, central Italy). The kinematical evolution of the unstable slope is investigated via long-term DInSAR analysis, by exploiting about 20 years of ERS-1/2 and ENVISAT satellite acquisitions. The landslide is driven by the presence of a shear band, whose behaviour is simulated through a two-dimensional time-dependent finite element model, in two different physical scenarios, i.e. Newtonian viscous flow and a deviatoric creep model. Comparison between the model results and DInSAR measurements reveals that the deviatoric creep model is more suitable to describe the kinematical evolution of the landslide. This finding is also confirmed by comparing the model results with the available independent inclinometer measurements. Our analysis emphasizes that integration of different data, within inverse numerical models, allows deep investigation of the kinematical behaviour of slow active landslides and discrimination of the driving forces that govern their deformation processes.

Dispersivity Determination Through a Modeling Approach From a Tracer Test Based on Total Br Concentration in Soil Samples

Determination of reliable solute transport parameters is an essential aspect for the characterization of the mechanisms and processes involved in solute transport (e.g., pesticides, fertilizers, contaminants) through the unsaturated zone. A rapid inexpensive method to estimate the dispersivity parameter at the field scale is presented herein. It is based on the quantification by the X-ray fluorescence solid-state technique of total bromine in soil, along with an inverse numerical modeling approach. The results show that this methodology is a good alternative to the classic Br− determination in soil water by ion chromatography. A good agreement between the observed and simulated total soil Br is reported. The results highlight the potential applicability of both combined techniques to infer readily solute transport parameters under field conditions.

A method for automated, daily, temperature-based vertical streambed water-fluxes

Heat is increasingly used as a natural tracer to quantify water fluxes at the groundwater-surface waterinterface. We present a systematic approach to monitor and evaluate stream and streambed temperatures to derive daily-updated temperature-based water exchange fluxes between the stream and the streambed. Specifically designed multi-level temperature sensors coupled with a data logger and GSM modem are used to monitor temperature in the stream and streambed and transfer this data daily to a database. A suite of MATLAB scripts with structured query language (SQL) commands is applied to extract the data for processing using an inverse numerical model to estimate water flow based on the measured temperatures. Compared to common analytical approaches, which typically require sinusoidal diurnal temperature pattern, our numerical model can utilize temperature records without daily variations. Temperature-based calculations to quantify vertical water fluxes at the stream-groundwater interface can provide a supplement to, or even a replacement of, calculations based on vertical hydraulic gradients and Darcy’ law.

Numerical models of tsunami sediment transport — Current understanding and future directions

Abstract Researchers who study tsunami deposits share common ultimate goals of their work, which are to better assess the magnitude information of paleotsunamis and to contribute to the assessment of future tsunami risks. Numerical modeling of tsunami sediment transport is an important piece of interdisciplinary research that fills the gap between geological studies and practical utilization of tsunami deposits. Forward and inverse numerical models that address tsunami transport of sand and boulders have been developed over the last two decades. Forward models are capable of delineating the time evolution of tsunami hydrodynamics, sediment transport and the resulting morphological changes associated with erosion and deposition. Inverse models estimate tsunami characteristics, such as flow speed and depth, from deposits. Numerical modeling can be used not only to quantify paleotsunamis but also to enhance our understanding of tsunami sedimentology and hydrodynamics. To make progress towards the ultimate goal of improved tsunami risk assessment, development of an in-depth mutual understanding between modelers and geologists of the advantages, limitations and uncertainties in both numerical modeling and geological records is an important challenge.

Towards mechanical characterization of intact endarterectomy samples of carotid arteries during inflation using Echo-CT

In this study, an experimental framework is described that allows pressurization of intact, human atherosclerotic carotid samples (inflation testing), in combination with ultrasound imaging. Eight fresh human carotid endarterectomy samples were successfully pressurized and tested. About 36 2-D (+t) ultrasound datasets were acquired by rotating the vessel in 10° steps (Echo-CT), from which both 3-D geometry and 3-D strain data were obtained. Both geometry and morphology were assessed with micro-CT imaging, identifying calcified and lipid rich regions. US-based and CT-based geometries were matched for comparison and were found to show good agreement, with an average similarity index of 0.71. Realistic pressure–volume relations were found for 6 out of 9 samples. 3-D strain datasets were reconstructed, revealing realistic strain patterns and magnitudes, although the data did suffer from a relatively high variability. The percentage of fat and calcifications (micro-CT) were compared with the median, 75th and 99th percentile strain values (Echo-CT). A moderate trend was observed for 75th and 99th percentile strains, higher strains were found for more lipid rich plaques, where lower strains were found for highly calcified plaques. However, an inverse numerical modeling technique is necessary for proper mechanical characterization the of plaque components, using the geometry, morphology and wall deformation as input.

Anisotropic frequency-dependent spreading of seismic waves from first-arrival vertical seismic profile data analysis

A model of first-arrival amplitude decay combining geometric spreading, scattering, and inelastic dissipation is derived from a multioffset, 3D vertical seismic profile data set. Unlike the traditional approaches, the model is formulated in terms of path integrals over the rays and without relying on the quality factor ([Formula: see text]) for rocks. The inversion reveals variations of geometric attenuation (wavefront curvatures and scattering, [Formula: see text]) and the effective attenuation parameter ([Formula: see text]) with depth. Both of these properties are also found to be anisotropic. Scattering and geometric spreading (focusing and defocusing) significantly affect seismic amplitudes at lower frequencies and shallower depths. Statistical analysis of model uncertainties quantitatively measures the significance of these results. The model correctly predicts the observed frequency-dependent first-arrival amplitudes at all frequencies. This and similar models can be applied to other types of waves and should be useful for true-amplitude studies, including inversion, inverse [Formula: see text]-filtering, and amplitude variations with offset analysis. With further development of petrophysical models of internal friction and elastic scattering, attenuation parameters [Formula: see text] and [Formula: see text] should lead to constraints on local heterogeneity and intrinsic physical properties of the rock. These parameters can also be used to build models of the traditional frequency-dependent [Formula: see text] for forward and inverse numerical viscoelastic modeling.

Influence of Carbonation on the Microstructure and Hydraulic Properties of a Basic Oxygen Furnace Slag

Basic oxygen furnace (BOF) slag is considered as a potential alternative construction material and is used here on an experimental plot to accurately quantify the risk of pollutant release. Since pollutant release depends on flow, this initially requires characterizing BOF slag hydraulic properties. These were monitored and estimated at plot scale by carrying out water infiltration experiments and inverse numerical modeling. Monitoring the plot showed that the BOF slag studied crusted at the surface as a result of weathering processes. Numerical inversion proved that the crusted material differed from the unaltered slag in terms of water retention and hydraulic conductivity functions. Although all the data pointed to a decrease in saturated hydraulic conductivity with crusting, the trends depended on the infiltration devices used for the capillary length (tension disc vs. Beerkan). Scanning electron microscope (SEM) microanalysis of laboratory weathering cells and lysimeter measurements were monitored in parallel to study the microstructure more precisely and highlighted a reduction of porosity by clogging. On the basis of SEM observations, two conceptual models of pore reduction, based on two different pore clogging hypotheses, were applied to predict hydraulic properties. This step demonstrated that the effect on water retention and hydraulic conductivity strongly depended on the way precipitated phases form and coat grains and could explain the evolution of the transport properties observed. This study contributes to knowledge on the hydraulic properties of BOF slag and their evolution due to carbonation.