Rate-dependent Model Research Articles

Study on Mechanical Failure Behavior of Steel-Wire Wound Reinforced Thermoplastic Pipe under Combined Internal Pressure and Soil Landslide Conditions.

A steel-wire wound reinforced thermoplastic pipe (SWW-RTP) has been widely utilized in many industrial areas, and a soil landslide is an inevitable hazardous extreme condition for the SWW-RTP as it is usually buried underground. It is imperative to study the mechanical failure behavior and the failure criterion of the SWW-RTP under the combination of internal pressure and soil landslide conditions, and this paper is the first study to investigate the topic. In this paper, groups of stress-strain curves of high-density polyethylene (HDPE) and steel wires were obtained by uniaxial tensile tests at different strain rates, with the help of a Digital Image Correlation device (DIC). A rate-dependent constitutive model was employed to represent the mechanical behavior of the HDPE and to help deduce the stress-strain curve of the HDPE under the required strain rate, estimated from the static simplification of the dynamic soil landslide. Afterwards, a finite element model of the SWW-RTP, embedded in a cubic of soil, was established with the software ABAQUS. The SWW-RTP model was composed of HDPE solid elements, embedded with steel-wire truss elements, and the soil was characterized with the extended Drucker-Prager model. A quartic polynomial displacement distribution was applied to the soil model to represent the soil landslide. Then, the mechanical response of the SWW-RTP was analyzed. It was found that the failure criterion of the HDPE yield was more suitable for the pipe subjected to internal pressure and soil landslide conditions, instead of the steel-wire strength failure criterion always used in traditional research on the SWW-RTP. Further, the influence of landslide width, internal pressure and steel-wire number were discussed. The larger the width of the landslide area, the gentler the deformation of the pipeline; this resulted in an increase in the maximum landslide and a decrease in the maximum curvature with the width of the landslide area. The relatively high internal pressure was beneficial to the safety of the SWW-RTP under landslide, because the internal pressure could increase the stiffness of the pipeline. The number of steel wires had a limited influence on the maximum landslide required for the SWW-RTP's failure. This work can be useful for the design and safe assessment of the SWW-RTP under internal pressure and soil landslide conditions.

Modelling the cyclic inelastic behaviour of a dissimilar metal/composite bonded joint at low frequencies

ABSTRACT The present paper is concerned with the investigation of the inelastic behaviour observed in load-unload cyclic tests performed at 50°C in single lap joints composed of a polyurethane based composite reinforced with fibreglass bonded to an ASTM A1020 steel substrate using an epoxy adhesive. The experiments presented in this research show that the inelastic behaviour of the joint is strongly dependent on the load frequency, eventually leading the structure to exhibit a progressive deformation when submitted to load-unload cyclic loading. The main goal of this study was to propose a preliminary rate-dependent mechanical model capable to describe the cyclic inelastic behaviour for an arbitrary load-unload history at low frequencies and a reasonable agreement was obtained between the experimental results and the model predictions.

Dynamic modeling and disturbance rejection compensation for hysteresis nonlinearity of high voltage piezoelectric stack actuators

High voltage piezoelectric stack actuators (HVPSA) are widely used in the field of active vibration control of engineering structures due to their strong load capacity, fast response rate, and high mechanical output efficiency. However, their inherent hysteresis will have a direct impact on the stability and control efficiency of the piezoelectric active control system. To compensate the hysteresis nonlinearity of HVPSA, a high-precision dynamic hybrid method based on linear active disturbance rejection control (LADRC) is proposed. Starting from the hysteresis analysis of piezoelectric actuators, an exponential function butterfly-shape hysteresis operator is constructed and combined with the asymmetric Bouc–Wen model to present a novel hybrid static hysteresis model. In order to implement rate-dependent hysteresis modeling, the Hammerstein rate-dependent hysteresis model of HVPSA is further established, and its inverse model is built for feedforward compensation. Subsequently, the LADRC is used to adjust the driving voltage in real time to form the hysteresis closed-loop compensator of HVPSA. The experimental results show that the Hammerstein rate-dependent hysteresis model established has satisfactory modeling accuracy in the working voltage range and frequency band under consideration. Furthermore, compared with the traditional inverse model feedforward compensation strategy, the proposed hybrid compensation method based on LADRC improves the compensation efficiency by more than 11% and reduces the hysteresis nonlinearity of HVPSA to less than 3%, with strong anti-disturbance ability.

Explicit phase-field material point method with the convected particle domain interpolation for impact/contact fracture in elastoplastic geomaterials

A novel explicit phase-field material point method with the convected particle domain interpolation (ePF-CPDI) is proposed for solving large deformation dynamic impact/contact fracture problems in elastoplastic geomaterials. In this method, we derive an explicit rate-dependent phase-field fracture model relying on the microforce balance law and the second law of thermodynamics. A coupled explicit phase-field plasticity model is then developed to describe dynamic elastoplastic fracture responses of geomaterials. Here the explicit time integration strategy and the staggered solution scheme are utilized in this work to solve the coupled-field governing equations based on the material point method. To eliminate the numerical noises caused by material points crossing cell boundaries, the convected particle domain interpolation technique is adopted to improve the computational accuracy in large deformation simulation. Furthermore, the proposed approach combining with the particle to particle contact algorithm is extended to deal with more complicated high-velocity impact and multi-body contact elastoplastic fracture problems. Numerical experiments are employed to validate the high accuracy and excellent capability of the proposed method and discuss the influences of main parameters on the phase-field fracture modeling.

GPU-optimized LBM-MRT simulation of free convection and entropy generation of non-Newtonian power-law nanofluids in a porous enclosure at REV scale

The present research investigates the heat transfer and entropy generation of a non-Newtonian power-law Cu-water nanofluid in a square porous enclosure at a representative elementary volume (REV) scale using the multiple-relaxation-time lattice Boltzmann method (MRT-LBM). The Graphics Processing Unit (GPU) accelerated the computations involved. The Brinkman-Forchheimer-extended Darcy model and the shear rate dependent power-law viscosity model were taken into account to characterise the non-Newtonian fluid flow in porous medium. Three types of model validations have been conducted, followed by the mandatory grid independence test, to demonstrate the precision and accuracy of the computational code. The numerical results were obtained by varying five key parameters namely, Darcy number (Da = 10−3, 10−2, 10−1); power-law index (n = 0.6–1.0); Rayleigh number (Ra = 104, 105, 106); porosity parameter (ϵ = 0.6); volume fraction of nanoparticles (ϕ = 0.0–0.05), and the Darcy Rayleigh number (Ram = 100, 1000). The numerically simulated outcomes were presented in terms of streamlines, isotherms, velocity, and temperature profiles as well as the Nusselt (Nu) numbers. Furthermore, a correlation among the parameters to determine the average Nu was developed using the Levenberg-Marquardt (LM) algorithm. The mathematical correlation was also subject to validations, and, in general, good correlation coefficients were obtained.

Damage in hybrid corrugated core sandwich structures under high velocity hail ice impact: A numerical study

Potential damage in composite structures caused by hail ice impact is an essential safety threat to the aircraft in flight. In this study, a nonlinear finite element (FE) model is developed to investigate the dynamic response and damage behavior of hybrid corrugated sandwich structures subjected to high velocity hail ice impact. The impact and breaking behavior of hail are described using the FE-smoothed particle hydrodynamics (FE-SPH) method. A rate-dependent progressive damage model is employed to capture the intra-laminar damage response; cohesive element and surface-based cohesive contact are implemented to predict the inter-laminar delamination and sheet/core debonding phenomena respectively. The transient processes of sandwich structure under different hail ice impact conditions are analyzed. Comparative analysis is conducted to address the influences of core shape and impact position on the impact performance of sandwich structures and the corresponding energy absorption characteristics are also revealed.

Strain Rate Effect on the Thermomechanical Behavior of NiTi Shape Memory Alloys: A Literature Review

A review of experiments and models for the strain rate effect of NiTi Shape Memory Alloys (SMAs) is presented in this paper. Experimental observations on the rate-dependent properties, such as stress responses, temperature evolutions, and phase nucleation and propagation, under uniaxial loads are classified and summarized based on the strain rate values. The strain rates are divided into five ranges and in each range the deformation mechanism is unique. For comparison, results under other loading modes are also reviewed; however, these are shorter in length due to a limited number of experiments. A brief discussion on the influences of the microstructure on the strain-rate responses is followed. Modeling the rate-dependent behaviors of NiTi SMAs focuses on incorporating the physical origins in the constitutive relationship. Thermal source models are the key rate-dependent constitutive models under quasi-static loading to account for the self-heating mechanism. Thermal kinetic models, evolving from thermal source models, address the kinetic relationship in dynamic deformation.

A viscoelastic–viscoplastic constitutive model for polymer bonded explosives under low impact loading

Viscoplastic work is very important to explosive ignition under impact loading. At present, a large number of constitutive models only consider the viscoelastic and damage behavior of explosives, ignoring the plastic effect under low impact loading. A new viscoelastic–viscoplastic (VE–VP) model was developed and studied to describe the dynamic mechanical behaviors of polymer-bonded explosives (PBXs). The total strain was assumed to be the sum of the viscoelastic (VE) and viscoplastic (VP) components. A generalized Maxwell model was used to determine the VE responses. A VP model was developed by using the classical J2 rate-dependent model with isotropic hardening. Viscoplastic flow was considered in hyperbolic sinusoidal form. The explicit algorithms of VE model were proposed and assessed by using two different integration methods. The accuracy and efficiency of these two methods are similar at high strain rates. The coupled algorithms of VE–VP model were developed by referring to the classical elasto-viscoplasticity (EVP) provided and using the expression of incremental relaxation modulus. The proposed model was implemented in the ABAQUS using a user-subroutine (VUMAT) to predict the response behaviors of PBX 9501 under low impact loading. Several numerical simulations illustrated the computational efficiency and the accuracy of the proposed methods. The model predictions were compared with experimental data, and reasonable agreement was obtained.

Spatiotemporal distributions of afterslip and locking on the plate interface associated with the 2011 Tohoku-Oki earthquake using a 3-D temperature and strain rate-dependent heterogeneous viscosity model

We introduced a novel approach to produce a 3D heterogeneous viscosity distribution model of the upper mantle below Northeast Japan. The viscoelastic relaxation constitutes a significant portion of the postseismic deformation associated with a megathrust earthquake. Our viscosity distribution was based on a 3D simulation of thermomechanical modeling with realistic 3D oceanic plate geometry and subduction velocity of the Pacific plate in the upper mantle. After obtaining the thermal and strain-rate distributions obtained from the thermomechanical modeling, 3D viscosity distribution was calculated. We used the resulting viscosity distribution in a viscoelastic relaxation model to calculate the viscoelastic response associated with the MW 9.0 2011 Tohoku-Oki earthquake, using a finite element method. We found it necessary to include an elastic cold nose in the mantle wedge and a low-viscosity layer at the subducted lithosphere-asthenosphere boundary to reproduce the observed onshore uplifts and landward horizontal displacements of the seafloor, respectively. We then divided the calculated viscoelastic displacements into 7 one-year intervals and subtracted them from the corresponding observed postseismic displacements to obtain yearly residual displacements. Assuming the residual displacements were the result of afterslip and subduction fault locking on the plate interface, we employed a time-dependent inversion to estimate the spatiotemporal distributions of afterslip and subduction fault locking. Our results showed decrease in the afterslip amount and extent over time, which primarily occurred during the first two years following the 2011 event, which is followed by gradual extension of the subduction fault locking region. We concluded that the plate interface off Northeast Japan is gradually entering an interseismic stage of interplate coupling and elastic strain accumulation within several years after the occurrence of the Tohoku-Oki earthquake.

Efficient computational framework for image-based micromechanical analysis of additively manufactured Ti-6Al-4V alloy

The increase in additively manufactured (AM) Ti-6Al-4V alloys in high-performance industrial applications has necessitated the development of robust computational models that can aid in their qualification and certification. Physics-based micromechanical models, relating the AM-processed material microstructure and defect state with the overall material response and life, can play an important role in reducing uncertainty in component behavior and increasing acceptance. Motivated by this need, the present paper develops a novel image-based crystal plasticity finite element model (CPFEM) for efficient micromechanical simulation of the additively manufactured Ti-6Al-4V alloy, whose Widmanstätten microstructure is characterized by 12 HCP α lath variants in the parent β grain. A unique feature of this work is the creation of an efficient crystal plasticity framework for the parent β grain polycrystalline ensembles with parametric representation of the α lath statistics of size, shape, orientation, and crystallography. This statistical representation is expected to significantly enhance its efficiency over models that represent each α lath explicitly in the microstructure. Defects in the form of voids are represented at two scales. The smaller voids in the microstructure are manifested as porosity or void volume fraction distribution in the crystal plasticity model. Larger voids are represented explicitly in the statistically equivalent microstructural volume element (SEMVE) model. The models are built from experimentally acquired electron back scatter diffraction (EBSD) and micro-focus X-ray computed tomography (XCT) images and calibrated and validated with mechanical testing data. This paper extends the developments in Pinz et al. (2022) through the development of a special self-consistent boundary condition in the context of a concurrent model to overcome limitations of periodicity boundary conditions. The concurrent model embeds the SEMVE in a homogenized exterior domain represented by a rate-dependent isotropic plasticity model. Parametric studies are conducted to comprehend the effect of void size, shape and orientation on the overall material response.

Rate-dependent constitutive model of high-strength reinforcing steel HTRB600E in tension

High-strength reinforcing steel HTRB600E has significant potential application in reinforced concrete (RC) structures because of its high strength and ductility. Under the risk that structures with HTRB600E are subjected to severe dynamic loadings, the rate-dependent behavior and constitutive model of HTRB600E need to be investigated to provide a basis for the structural analysis. A series of tension tests were carried out to acquire the engineering stress–strain curves of HTRB600E in the strain rate range from 0.00025 to 590 s−1. Moreover, a hybrid experimental–numerical converse method was used to obtain the true stress–strain curves beyond the necking of HTRB600E at different strain rates. The test results indicate that the strain rate significantly affects the mechanical properties of HTRB600E. The effect of strain rate on yield and ultimate tensile strength, uniform elongation, and yield to tensile ratio of HTRB600E was discussed. Three commonly-used models were calibrated or modified to predict the dynamic increase factors (DIFs) for yield and ultimate tensile strength of HTRB600E. A rate-dependent constitutive model for the engineering stress–strain curves modified from the Mander model was presented for the structure's analytical model based on the section analysis technique. A new rate-dependent constitutive model for the true stress-plastic strain relationship with necking behavior was proposed for the structure's nonlinear finite element analysis model. The formulations of DIFs and constitutive models agree with the test results well.

Using experimental design to assess rate-dependent numerical models

To enhance the accuracy of advanced constitutive models for soft natural clays, several parameters are necessary, resulting in complexity of numerical modelling. However, the detailed effects of these parameters are not rigorously quantified towards their constitutive relationships. Thus, the aim of the paper is to assess such advanced models in order to determine the most significant parameters over the time series data. Two methods for Global Sensitivity Analysis (GSA), i.e. Experimental Design and the Sobol method, were used and benchmarked to assess the model predictions on a discretised domain in time and space. A rate-dependent Finite Element model using Creep-SCLAY1S and a hydro-mechanically coupled formulation for consolidation was used to study a Constant Rate of Strain (CRS) test. The value of GSA approaches adopted herein was to investigate the model predictions both in the temporal and spatial domain. The temporal analyses indicate three sets of significant model parameters in different portions of the CRS compression curve. Furthermore, the non-stationary nature of sensitivity results is exposed, identifying the parameters that lead to unique solutions for the CRS loading path. The FE implementation enabled the quantification of the most sensitive model parameters in the spatial domain. The spatial results that are governed by the rate-dependent processes in the soil (i.e. consolidation and creep) illustrated that Experimental Design was capable of providing sensitivity maps with satisfactory accuracy similar to the Sobol method. Experimental Design was found to be the most efficient method, concerning execution time and storage costs, to assess rate-dependent problems in Geotechnics.

A Strain Rate Dependent Damage Model for Evaluating the Dynamic Response of CFRTP Laminates with Different Stacking Sequence

Carbon fiber reinforced thermoplastic polymer (CFRTP) laminates can be used in packaging electronics components to reduce weight and shield external disturbance. The CFRTP structures in operation are inevitably to suffer dynamic loading conditions such as falling rocks, tools and impacts. In this study, a strain rate dependent material model for accurately evaluating the dynamic response of CFRTP laminates with different stacking sequence was proposed. The model was composed of three components: a strain rate dependent constitute model, a strain rate related damage initiation model and an energy-based damage evolution model. The strain rate effect of modulus and strength was described by a stacking sequence related matrix, and the damage initiation model could describe the matrix, fiber and delamination damage of CFRTP laminates without introducing cohesive elements. The material model was implemented into finite element software ABAQUS by user defines subroutine VUMAT. The low velocity impact tests of CFRTP laminates with quasi-isotropic and angle-ply stacking sequence were used to provide validation data. The dynamic response of CFRTP laminates from numerical results were highly consistent with the experimental results. The mechanical response of CFRTP laminates were affected by stacking sequence and impact energy, and the numerical error of proposed material model significantly decreased with the increasing impact energy especially for the laminae with damage occur.

Experimental Analysis and Constitutive Modeling of Cyclic Behavior of 304 L Stainless Steel: Introduction of Isotropic Hardening Fading Effect

Abstract In this study, the mechanical behavior of austenitic stainless steel 304 L under low cycle fatigue was investigated under different uni-axial strain-controlled loadings of 0.5%, 0.8%, 1.0%, 1.2%, and 1.5%. The analysis of the experimentally determined strain versus stress hysteresis curves was carried out to achieve stress quantities such as amplitude stress, peak effective stress, and peak back stress. It was observed that in the early stage of cyclic loading, material underwent initial hardening, followed by softening phenomena which were more considerable in the lower strain range. Before the failure, the secondary hardening was observed at the final stage. In addition to accumulated plastic strain, it was shown that the peak back stress and peak effective stress which is associated with isotropic hardening and kinematic hardening behavior, respectively, are influenced by the strain range effect. Therefore, the coefficient of recall term that appeared in the Armstrong–Frederick nonlinear kinematic hardening model was considered to be dependent on the radius of the memory surface. Furthermore, to increase the ability of the plasticity constitutive model to show a smooth transition between various hardening stages, the radius of the yield surface which is associated with the isotropic hardening rule was equipped with the fading effect. Finally, by the comparison of numerical and experimental results, the capability of the rate-dependent constitutive model over classical rate-independent plasticity in the prediction of mechanical behavior of steel 304 L under strain-controlled cyclic loading was revealed.

Damage evolution and failure mechanism of three-dimensional braided composite subjected to varied high strain-rate loadings

Three-dimensional (3D) braided composite exhibit the excellent integrity of a braided structure, which gives the composites the advantages of high-impact damage tolerance, excellent delamination resistance, and high fatigue resistance. They have been widely used in the fields of aerospace and transport. Composites are always subjected to high strain-rate loading in these application cases. Braided composites show significantly different damage evolution under varied high strain-rate loadings. A bridge which can connect the strain rate variation to the different damage evolution of composites is urgently needed for composite strength design. This research demonstrated how the strain rate variation induced the change of damage evolution and failure mode of 3D braided composite. A high-speed camera system was used to capture damage process information. A micro-scale rate-dependent finite-element model (FEM) was established to study the underlying mechanisms. The results show that the velocity gap between yarns and resin becomes more obvious at higher strain-rate loading. Damage morphology of composites under lower strain rate resulted from the higher transverse stress at the output-bar area. Higher strain-rate loading induces plastic deformation, which occurs earlier in composites. The deformation distributes more haphazardly under higher strain-rate loading. Optimizing suggestions are given to improve the impact resistance of 3D braided composites.

Online Optimization Method for Nonlinear Model-Predictive Control in Angular Tracking for MEMS Micromirror.

In this brief, a precise angular tracking control strategy using nonlinear predictive optimization control (POC) approach is address. In order to deal with the model uncertainty and noise interference, a online Hammerstein-model-based POC is designed using online estimated parameters and model residual. Above all, a rate-dependent Duhem model is used to describe the nonlinear sub-model of the whole Hammerstein architecture for depicting multi-valued mapping nonlinear characteristic. Then, predictive output of angular deflection is obtained by Diophantine function based on linear submodel. Subsequently, the iterative control value depends on estimated parameters through data-driven is acquired. Later, based on the cost function, the iteratively optimization control quantity is fed back to the electromagnetic driven deflection micromirror (EDDM) system on the basis of Hammerstein architecture. It should be stressed that the control value is determined by real-time update model residual and defined cost function. Moreover, the stability of POC strategy is proposed. In addition, experimental result is proposed to validate the effectiveness of the control technique adopted in this paper.

Strengthening and toughening behaviors and dynamic constitutive model of carbon-based hierarchical fiber modified concrete: Cross-scale synergistic effects of carbon nanotubes and carbon fiber

Considering the synergistic effects (filling, activating, bridging, anti-cracking, and interface-optimizing) of combined carbon fiber and carbon nanotubes, the strategy of using carbon nanotubes-carbon fiber cross-scale reinforcement (CNTs-CF) to enhance concrete was proposed. The strengthening and toughening behaviors of CNTs-CF modified concrete (CCMC) were experimentally investigated. The results showed that CCMC had good crushing resistance capacity, and the addition of an appropriate amount of CNTs-CF was conducive to alleviating the brittle failure characteristics of concrete materials. Compared with ordinary concrete, the static and dynamic strength properties and toughness indexes of CCMC were greatly improved. When the volume content of CNTs-CF in concrete was 0.3%, CCMC showed the most superior strengthening and toughening behaviors. The hierarchical assembly and synergistic effect of carbon fiber and carbon nanotubes realized the combination of high strength and high toughness of concrete materials. The proposed rate-dependent constitutive model with damage based on Weibull statistical theory in this study can be used to accurately predict the dynamic compressive stress-strain relationship curve of concrete under different fiber content and strain rate.

Corrosion Crack Morphology and Creep Analysis of Members Based on Meso-Scale Corrosion Penetration.

In this paper, to study the development of load-carrying capacity and long-term creep performance of reinforced concrete beams under different corrosion patterns, the rate-dependent model of concrete is used as the basis to consider the creep development process from the meso-scale level. The porosity mechanics method is used to simulate the generation and penetration process of corrosion products. Three corrosion conditions are set: bottom longitudinal reinforcement corrosion, top longitudinal reinforcement corrosion and all reinforcement corrosion. The corrosion rate is used as the variable in each corrosion condition. The results show that: (1) the greater the corrosion rate in all conditions, the lower the bearing capacity. In addition, the corrosion of top longitudinal reinforcement causes the damage form of the beam to change to brittle damage; (2) the creep coefficient decreases with the increase in corrosion rate in all working conditions, but the main factor for this phenomenon is the obvious increase in initial deformation. Consequently, it is not suitable to follow the conventional creep concept (deformation development/initial deformation) for the development of plastic deformation of damaged members. It is more reasonable to use the global deflection to describe the long-term deformation of corrosion-damaged members.

A long term resilient modulus rate dependent model for coarse fine mixtures geomaterials under freezing and thawing cyclic

The cyclic loading frequency (fcyc) effects on the resilient modulus (Mr) of freezing–thawing coarse–fine mixtures geomaterials (FTCFG) have always been a research hotspot. A series of long-term cyclic triaxial tests were conducted on FTCFG having different fines content (FC) under different number of freeze–thaw cycles (NFT) to investigate the effect of fcyc and deviator stress amplitude (qcyc) on the Mr of FTCFG. The freezing–thawing cyclic was found to improve the Mr of FTCFG. Additionally, Mr of FTCFG shown an obviously rate-dependent characteristics. Then three kinetic effects (rate effect, piston effect, and fatigue effect) are discussed in systemically which are related to qcyc, fcyc and moisture holding capacity (wh). Finally, a rate dependent model of long-term resilient modulus was developed to predict FTCFG materials’ resilient moduli as a function of qcyc, fcyc and wh. The comparisons between the calculation and experimental results reveal that the present model describes the Mr of FTCFG well.

Estimation of undrained shear strength in rate-dependent and strain-softening surficial marine clay using ball penetrometer

The spherical penetrometer (known as ball) has been widely used in laboratory tests and in-situ investigation to determine the undrained shear strength of fine-grained sediments in offshore geotechnical engineering. The conventional interpretation of the ball penetration tests suffers from either neglecting the effect of the strain softening and strain rate for steady state penetration or inaccurate accounting for the evolving bearing factor during the shallow failure stage of soil. In this study, the continuous penetration of the ball is simulated using the “Remeshing and Interpolation Technique with Small Strain” (RITSS) with a strain softening and rate-dependent soil model. Three stages from shallow failure mechanism to deep flow-round mechanism are clarified. The strength distribution of ball penetration into softening and rate-dependent soil is also revealed. A parametric study is performed to investigate the effect of strain rate and softening parameters on the failure mechanism and the evolved bearing factor profile. The effects of the dimensionless soil strength sum /γ′D and the frictional condition of the soil-ball interface are explored. Empirical formulas are developed to estimate the critical depths of the ball penetration test. A practical interpretation framework, incorporating the effects of strain rate and softening, is developed to assess the soil undrained shear strength using the ball penetrometer.