Plasticity Theory Research Articles

A Lipid-Raft Theory of Alzheimer's Disease.

I present a theory of Alzheimer's disease (AD) that explains its symptoms, pathology, and risk factors. To do this, I introduce a new theory of brain plasticity that elucidates the physiological roles of AD-related agents. New events generate synaptic and branching candidates competing for long-term enhancement. Competition resolution crucially depends on the formation of membrane lipid rafts, which requires astrocyte-produced cholesterol. Sporadic AD is caused by impaired formation of plasma-membrane lipid rafts, preventing the conversion of short- to long-term memory and yielding excessive tau phosphorylation, intracellular cholesterol accumulation, synaptic dysfunction, and neurodegeneration. Amyloid β (Aβ) production is promoted by cholesterol during the switch to competition resolution, and cholesterol accumulation stimulates chronic Aβ production, secretion, and aggregation. The theory addresses all of the major established facts known about the disease and is supported by strong evidence.

A Transition State Theory-Based Continuum Plasticity Model Accounting for the Local Stress Fluctuation

Based on the transition state theory, a continuum plasticity theory is developed for metallic materials. Moreover, the nature of local stress fluctuation within a material point is considered by incorporating the probability distribution of the stresses. The model is applied to investigate the mechanical behaviors of 316 L stainless steel under various loading cases. The simulated results closely match the results obtained by the polycrystal plasticity model and experiments. The mechanical behaviors associated with strain rate sensitivity, temperature dependence, stress relaxation, and strain creep are correctly captured by the model. Furthermore, the proposed model successfully characterizes the Bauschinger effect, which is challenging to capture with a conventional continuum model without additional assumptions. The proposed model could be further employed in the design, manufacturing, and service of engineering components.

Fatigue life prediction of film-cooling Hole specimens with initial damage

This study investigates a Nickel-based single crystal (SX) superalloy with femtosecond laser-drilled film-cooling holes (FCHs) under varying temperatures (room temperature, 850 °C, and 980 °C), employing a novel framework for predicting fatigue life based on initial manufacturing damage quantification. For all tested anisotropic SX superalloy specimens (including smooth and FCH specimens), the initial damage state is characterized as an equivalent initial flaw size (EIFS), and an EIFS calculation model considering stress concentration is established. Subsequently, the fatigue crack paths and microstructural characteristics of the FCH specimens at different temperatures are analyzed, elucidating crack initiation mechanisms and propagation patterns. A novel incremental plasticity J-integral driving force for fatigue crack propagation is introduced. By incorporating the closure effect of small crack propagation and employing Markov Chain Monte Carlo simulations for determining crack growth rate probabilities, a more accurate expression for the crack growth rate in relation to ΔJfat − ΔJth is derived. This expression comprehensively captures crack patterns on crystallographic planes and Type I mixed mode behavior. Finally, the total fatigue life of the FCH structures, featuring a threefold dispersion zone in both room and high-temperature environments, is predicted through experimental observations and description of crack growth rates. The predicted outcomes significantly outperform those of the conventional life prediction models reliant on crystal plasticity theory.

Elastic–plastic solutions of reserved deformation for soft rock circular tunnel under high stress

The determination of reserved deformation is typically based on referring to relevant codes or the engineering analogy method, lacking a certain theoretical approach. The purpose of this study is to provide a theoretical basis for determining reserved deformation and to analyze the variation law of the surrounding rock affected by reserved deformation. Considering the reserved deformation under the condition of asymmetric load, the expression of optimal reserved deformation, the expression of support resistance reflecting the strength of surrounding rock, the strength of support material and the magnitude of in situ stress, the displacement expression of surrounding rock are derived by approximate solution based on the classical elastic–plastic theory. Numerical simulation software is used to simulate the displacement expression of the surrounding rock considering the reserved deformation and the expression of the optimum reserved deformation under the condition of asymmetric load. The results of the numerical simulation were compared with those of the analytical solutions, and the analytical results show that the errors between the two are within 12% and that the consistency is good.

Assessment of Free Energy Functions for Sand

ABSTRACTThe advantages of constitutive models in energy‐conservation frameworks have been widely addressed in the literature. A key component is choosing an appropriate energy potential to derive the hyperelastic constitutive equations. This article investigates the advantages and limitations of different energy potentials found in the literature based on mathematical conditions to guarantee numerical stability, such as the desired order of homogeneity, positive and non‐singular stiffness within the application range, and equivalent Poisson's ratio from a constitutive modelling standpoint. Potentials meeting the aforementioned criteria are employed to simulate the response envelopes of Karlsruhe fine sand (KFS). Moreover, the performance of the potentials, in conjunction with plasticity theories, is examined. To achieve this, the hyperelastic constitutive equations have been coupled with the bounding surface plasticity model of Dafalias and Manzari to reproduce the soil response in a hyperelastic–plastic frame. Finally, one of the potentials is modified, whereas recommendations for incorporating other appropriate free energy functions into different soil constitutive models are presented. Furthermore, 100 closed elastic strain cycles have been simulated with the bounding surface plasticity model of Dafalias and Manzari considering the original hypoelastic stiffness and hyperelastic–plastic constitutive equations. Using the hypoelastic framework in the simulation led to stress accumulation after 100 closed elastic strain loops, while a reversible response was predicted using the hyperelastic stiffness tensor.

Mesoscopic coupled plasticity-damage model of rough surface considering size-dependent plasticity

Metallic materials exhibit significant size effect at mesoscopic scale have been revealed by many experiments. Thus, it is essential to consider size effect when conducting mesoscopic scale studies in tribology. However, there is no constitutive model considering both ductile fracture and size effects of rough surface in the literature. At the same time, the simulation of friction and wear at the mesoscopic scale suffer from computational inefficiency using the conventional theory of mechanism-based strain gradient (CMSG) plasticity theory. To address the aforementioned challenges, we propose a mesoscopic coupled plasticity-damage model by combining the coupled plasticity-damage model and the simplified CMSG plasticity theory. This model can take into account not only the effect of stress state, temperature, strain rate on plasticity and fracture, but also the effect of the effective plastic strain gradient. Meanwhile, the model is able to solve the effective plastic strain gradient by a simplified method, thereby enhancing the computational efficiency. Then, model parameters for bearing bushing material of an engine are calibrated. Finally, scratch simulation and scratch tests of bearing bushing material at the mesoscopic scale are conducted to validate the effectiveness of the mesoscopic constitutive model. The residual scratch depth and width, coefficient of friction at different normal loads are investigated by experiment and simulation, respectively. Results proved the effectiveness of mesoscopic coupled plasticity-damage model, which is applicable for investigating issues related to wear, friction, and contact.

Constitutive relationship of soil in contact with mortar under continuous loading

Mortars will remain critical in future land wars due to their flexibility and versatility. When mortars are fired continuously, the contact soil is gradually compacted by the mortar base plate, and dynamic research into this process is the basis for innovative mortar design. However, the discontinuity and nonlinearity of soil contact absolutely necessitate the constitutive relationship of soil contact, which is difficult to study. Therefore, this study conducted experimental research and theoretical derivation to establish an accurate dynamic model of the mortar system. First, based on the nonlinear elastic–plastic theory and the stress–strain relationship of soil under cyclic loading, a theoretical analysis method for the constitutive relationship of contact soil under continuous loading was proposed. Second, an experimental and testing system was designed to simulate launch loads, and the stress–strain response of soil under continuous impact loads was obtained experimentally. Subsequently, based on theoretical analysis and experimental data, the stress–strain relationship during the gradual compaction of soil was established using the least squares method. Finally, a constitutive relationship model of the contact soil in the mortar system was established in ABAQUS using the VUMAT subroutine interface, and the calculated results were compared and analyzed with traditional calculation results. The results indicated that studying the constitutive relationship of mortar in contact with soil during continuous firing using this method can improve the accuracy of dynamically modeling mortar systems. Moreover, this study has practical value in the engineering design of mortar systems.

Interlayer reinforced 3D printed concrete with recycled coarse aggregate: Shear properties and enhancement methods

In reinforced 3D printed concrete structures, the shear interaction between the rebar and the 3D printed filaments influences both the performance and safety of the concrete structures during service. In this study, the shear performance of the interlayer reinforced interface (IRI) of 3D printed concrete with recycled coarse aggregates (3DPRAC) was investigated, focusing on the pore structure characteristics of the interlayer interface. An enhancement method for the IRI was proposed by varying the number of anchored rebar nails (ARNs) and comparing the results with those of 3D printed concrete with natural coarse aggregates (3DPNAC) and 3D printed mortar (3DPM). The results showed that the ARNs significantly improved the IRI shear strength of 3DPRAC. Specifically, the IRI shear strength of 3DPRAC was 6.1% lower than that of 3DPNAC but 43.6% higher than that of 3DPM. By examining the structural characteristics of the rebar-3DPRAC bonding area, a relationship between pore defects and shear strength was established. This established relationship led to the proposal of a partition model for the interlayer bonding interface. A finite element model of 3D printed concrete incorporating real pore structure characteristics was developed to analyze the stress distribution and damage characteristics of the interface under shear stress. The fracture mode induced by local pores with the crack propagation mechanism was also analyzed. Finally, a unified formula for calculating the shear strength of the 3DPRAC IRI was derived based on the principles of virtual work and plastic limit theory. This study provides theoretical support for engineering applications of 3D-printed reinforced concrete structures.

Time-Varying Stability Analysis of the Trenching Construction Process of Diaphragm Wall

The stability of underground diaphragm walls is crucial for ensuring the safety and integrity of trench excavations in geotechnical engineering. This study addresses this critical issue by proposing a novel destabilization mechanism based on a sliding body model specifically designed for diaphragm wall trenching operations. The research employs an analytical framework rooted in soil mechanics and plasticity theory, utilizing limit equilibrium analysis to develop a method for calculating the minimum required slurry density and corresponding safety factor for trench stability. The study compares two distinct approaches to slurry density computation, analyzing their sensitivity to various influencing factors. Theoretical findings are validated through multiple real-world engineering case studies. Comparative analysis demonstrates the superiority of the proposed method, particularly in assessing trench stability within clay layers. Key variables influencing the safety factor are identified, including trench length, slurry density, soil friction angle, and the relative height difference between slurry and groundwater levels. Results indicate that actual slurry densities observed in practice consistently fall within the bounds predicted by the theoretical calculations. This research contributes a valuable theoretical framework to the field of diaphragm wall construction, offering improved accuracy in stability assessments and potentially enhancing safety in geotechnical engineering projects.

Fatigue life predictions for welded boiler water walls

Boiler water walls experience in-phase thermo-mechanical loading during start-ups and shut-downs, leading to low cycle fatigue (LCF) failure. This study aims at establishing an FEA-based failure prediction method for estimating the fatigue performance and service life of the welded water walls. The developed model is validated for predicting failure in the defect-free uniaxial fatigue specimens. Stress-mechanical strain hysteresis loops and accumulated inelastic strain energy density per cycle parameters are extracted from fatigue tests at 0.4%, 0.6%, and 0.7% strains. A combination of cyclic plasticity and continuous damage mechanics (CDM) theory is utilized to predict fatigue crack initiation sites and estimate the specimen fatigue life. Accumulated damage has been calculated for the life cycle of each specimen. FEA model predicted failure and service life agrees well with the experimental results. The established failure analysis parameters are then transferred from the specimen level to the water wall component level, thereby estimating the service life of defect-free water walls at 750 cycles.

In situ study of microstructure evolution and α → ω phase transition in annealed and pre-deformed Zr under hydrostatic loading

The detailed study of the effect of the initial microstructure on its evolution under hydrostatic compression before, during, and after the irreversible α→ω phase transformation and during pressure release in Zr using in situ x-ray diffraction is presented. Two samples were studied: one is plastically pre-deformed Zr with saturated hardness and the other is annealed. Phase transformation α→ω initiates at lower pressure for a pre-deformed sample but for a volume fraction of ω Zr, c>0.7, a larger volume fraction is observed for the annealed sample. This implies that the proportionality between the athermal resistance to the transformation and the yield strength in the continuum phase transformation theory is invalid; an advanced version of the theory is outlined. Phenomenological plasticity theory under hydrostatic loading is outlined in terms of microstructural parameters, and plastic strain is estimated. During transformation, the first rule is suggested, i.e., the average domain size, microstrain, and dislocation density in ω Zr for c<0.8 are functions of the volume fraction, c of ω Zr only, which are independent of the plastic strain tensor prior to transformation and pressure. The microstructure is not inherited during phase transformation. Surprisingly, for the annealed sample, the final dislocation density and the average microstrain after pressure release in the ω phase are larger than for the severely pre-deformed sample. The results suggest that an extended experimental basis is required for the predictive models for the combined pressure-induced phase transformations and microstructure evolutions.

Mechanical Properties of Silicon Nitride in Different Morphologies: In Situ Experimental Analysis of Bulk and Whisker Structures.

Silicon nitride (Si3N4) is widely used in structural ceramics and advanced manufacturing due to its excellent mechanical properties and high-temperature stability. These applications always involve deformation under mechanical loads, necessitating a thorough understanding of their mechanical behavior and performance under load. However, the mechanical properties of Si3N4, particularly at the micro- and nanoscale, are not well understood. This study systematically investigated the mechanical properties of bulk Si3N4 and Si3N4 whiskers using in situ SEM indentation and uniaxial tensile strategies. First, nanoindentation tests on bulk Si3N4 at different contact depths ranging from 125 to 450 nm showed significant indentation size effect on modulus and hardness, presumably attributed to the strain gradient plasticity theory. Subsequently, in situ uniaxial tensile tests were performed on Si3N4 whiskers synthesized with two different sintering aids, MgSiN2 and Y2O3. The results indicated that whiskers sintered with Y2O3 exhibited higher modulus and strength compared to those sintered with MgSiN2. This work provides a deeper understanding of the mechanical behavior of Si3N4 at the micro- and nanoscale and offers guidance for the design of high-performance Si3N4 ceramic whiskers.

A framework toward fatigue life modeling of machining process verified in burnishing

In the present work a multiscale model was developed to predict fatigue lives of Inconel 718 after a machining process. The model captures the effects of surface integrity like residual stress, microstructure, hardness and roughness. Within this holistic predictive model, firstly burnishing process factors (viz static force, feed rate, spindle speed and pass number) are correlated to surface integrity aspects. Herein, residual stress is modeled using theory of incremental plasticity; also grain size and hardness were correlated to process factors through dislocation density evolution. In order to model the surface roughness, the Z-map approach considering the work hardening of the surface layers was utilized. The foresaid developed models of surface integrity aspects were utilized to predict the fatigue life using Navaro-Rios crack propagation together with Chen’s crack initiation models. Thus, a novel holistic model correlating machining parameters directly to fatigue life has been developed through this hybrid approach. The developed models of fatigue life and surface integrity aspects were then confirmed by series of burnishing experiments on Inconel 718. Later, the confirmed model was utilized to identify the parametric influence of burnishing process on variation of fatigue life where the results were justified using variation of surface integrity factors. Through this developed model, it was found that burnishing setting of 1000 N static force, 0.05 mm/rev feed rate, 300RPM spindle speed and 2 pass number results in improvement of HCF, MCF and LCF of 242 %, 184 % and 212 % where the obtained results from the developed framework were compatible well with experimental values.

The crack propagation behaviors, microstructure and mechanical properties of T-welded joints for TIGW with crystal plasticity model and XFEM

In view of the significant impact of welding defects on the fracture behaviors involving the strength, stress concentration and bearing capacity of welded joint, etc., the propagation behaviors and mechanical properties of welded joints with porosity and micro crack are deeply investigated using a multiscale method. In this work, a crack nucleation and propagation model based on crystal plasticity theory, combined with the extended finite element method (XFEM), is established for the T-welded joint. The maximum slip on the predominant slip system method is applied to predict the crack propagation path of pores and micro cracks in the weld zone (WZ), and the effect of crystal orientation on crack growth is explored. Then, a continuous model is used to analyze the micro and macro fracture behaviors near the weld under tensile load, combined with the maximum principal stress method. The WZ and heat affected zone (HAZ) are observed using electron backscatter diffraction (EBSD) to study the microstructure evolution. Considering grain boundaries, the image information of crystal morphology is processed through binary image analysis for FE modeling. The local mechanical properties testing is carried out using micro-specimens of HAZ and WZ to calibrate the crystal plastic parameters. The results show that the resolved shear stress of the predominant slip system of crack initiation and propagation elements is increased by pore and crack defects. The fracture positions of tensile specimens through numerical simulation are in good agreement with the macroscopic experimental results. It will provide an analysis basis for preventing fracture failure and improving the service performance of thin-walled structures in future.

Numerical and Theoretical Study on Flexural Performance and Reasonable Structural Parameters of New Steel Grating–UHPFRC Composite Bridge Deck in Negative Moment Zone

As the bridge’s structural component is directly subjected to vehicle loads, the stress performance of the bridge deck has a significant impact on the safety, durability, and driving comfort of the bridge. In order to improve the bending performance of the bridge deck in the negative moment zone, a new type of steel grating–UHPFRC composite bridge deck was proposed in this paper. Firstly, structural details and advantages of the new steel grating-UHPFRC composite bridge deck were introduced. Secondly, the finite element program ABAQUS was used to establish a refined solid finite element model of the new bridge deck. The mathematical program MATLAB (PYTHON) was also used to analyze the effects of the structural parameters on bending bearing capacity and put forward reasonable structural parameters of the new bridge deck, considering the technical and economic indexes. Thirdly, the simplified plasticity theory was applied to analyze the bending bearing capacity of the new bridge deck, and the corresponding formula for bending bearing capacity calculation was derived and verified by numerical model results. In addition, the cost–benefit analysis and environmental impact assessment of the new bridge deck were also conducted. The results show that the bending bearing capacity of the new bridge deck in the negative moment zone increases with the increase of the width of the bridge deck, the thickness of the wing plate, and the height of the web plate, with a trend of increasing and then decreasing when the horizontal inclination of the web plate decreases. The bridge deck width does not have a significant effect on improving the bearing capacity. The bearing capacity calculated by theoretical formulas is close to that calculated by numerical models and the maximum relative deviation is 9.1%. The new steel grating-UHPFRC composite bridge deck proposed in this paper is superior to conventional steel-UHPC composite bridge deck in terms of cost-benefit and environmental impact.

Non-coaxial plasticity of similar weakly cemented soft rock under directional shear stress path

The plastic flow behavior of soft rock exhibits non-coaxial features under complex stress paths, while traditional plasticity theories are ill-equipped to adequately represent this, which leads to the mechanism of soft rock failure still unclear. To investigate the evolution law of strain increments and non-coaxial characteristics of weakly cemented soft rock, the directional shear tests are conducted using the hollow cylinder apparatus (HCA). The results show that non-coaxiality does not occur when α is distinct from 0° or 90°. The oscillation of the non-coaxial angle is significantly more variable in soft rock experiencing combined tension–torsion (45° < α < 90°), as opposed to those under the influence of combined compression-torsion (0° < α < 45°). The non-coaxiality swiftly dissipates when the sample is approaching the failure state. The stress rate is decomposed into stress magnitude and direction to describe non-coaxial features of plastic strain. And a new method for non-coaxial stress rate is proposed which can express the plastic strain increment directions. The spherical interpolation coefficient method is utilized to describe the continuous change in non-coaxial plastic flow direction between tangential and normal directions of the yield surface. The non-coaxial parameter (Δ) is introduced to quantify the non-coaxial characteristics of soft rock and its validity is confirmed through test results. This method effectively captures the principal stress direction influence on non-coaxial behavior of soft rock and have significance for rock mechanics.

Material plasticity – Development of stiffness tetrads in fiber‐reinforced materials with large plastic deformations

AbstractThe main objective of this work is to follow the evolution of the stiffness tetrad during large plastic strains. For this purpose, the framework of a general theory of finite plasticity is developed. Some special cases are investigated and the case of a material plasticity theory is considered in more detail. Its main feature is that the elasticity law changes during plastic deformations, for which we develop an approach. We use three types of fiber‐reinforced composites as example materials. Finite element simulations of representative volume elements for uni‐, bi‐ and tri‐directionally reinforced materials with periodic boundary conditions are used for numerical experiments and verification of the model's predictions. From these, we extract the stiffness tetrads before and after large deformations of the material. We quantify the change in stiffness tetrads due to fiber reorientation. Finally, we propose an analytical evolution with three parameters that reproduces reasonably well the evolution of the stiffness tetrads.

Evolution of local relaxed states and the modeling of viscoelastic fluids

We introduce a class of continuum mechanical models aimed at describing the behavior of viscoelastic fluids by incorporating concepts originated in the theory of solid plasticity. Within this class, even a simple model with constant material parameters is able to qualitatively reproduce a number of experimental observations in both simple shear and extensional flows, including linear viscoelastic properties, the rate dependence of steady-state material functions, the stress overshoot in incipient shear flows, and the difference in shear and extensional rheological curves. Furthermore, by allowing the relaxation time of the model to depend on the total strain, we can reproduce some experimental observations of the non-attainability of steady flows in uniaxial extension and link this to a concept of polymeric jamming or effective solidification. Remarkably, this modeling framework helps in understanding the interplay between different mechanisms that may compete in determining the rheology of non-Newtonian materials.

Advanced modeling of higher-order kinematic hardening in strain gradient crystal plasticity based on discrete dislocation dynamics

An extensive study of size effects on the small-scale behavior of crystalline materials is carried out through discrete dislocation dynamics (DDD) simulations, intended to enrich strain gradient crystal plasticity (SGCP) theories. These simulations include cyclic shearing and tension-compression tests on two-dimensional (2D) constrained crystalline plates, with single- and double-slip systems. The results show significant material strengthening and pronounced kinematic hardening effects. DDD modeling allows for a detailed examination of the physical origin of the strengthening. The stress–strain responses show a two-stage behavior, starting with a micro-plasticity regime with a steep hardening slope leading to strengthening, and followed by a well-established hardening stage. The scaling exponent between the apparent (higher-order) yield stress and the geometrical size h varies depending on the test type. Scaling relationships of h−0.2 and h−0.3 are obtained for respectively constrained shearing and constrained tension-compression, aligning with some experimental observations. Notably, the DDD simulations reveal the occurrence of the uncommon type III (KIII) kinematic hardening of Asaro in both single- and double-slip cases, emphasizing the relevance of this hardening type in the realm of small-scale plasticity. Inspired by insights from DDD, two advanced SGCP models incorporating alternative descriptions of higher-order kinematic hardening mechanisms are proposed. The first model uses a Prager-type higher-order kinematic hardening formulation, and the second employs a Chaboche-type (multi-kinematic) formulation. Comparison of these models with DDD simulation results underscores their ability to effectively capture the observed strengthening and hardening effects. The multi-kinematic model, through the use of quadratic and non-quadratic higher-order potentials, shows a notably better qualitative congruence with DDD findings. This represents a significant step towards accurate modeling of small-scale material behaviors. However, it is noted that the proposed models still have limitations, especially in matching the DDD scaling exponents, with both models producing h−1 scaling relationships (i.e., Orowan relationship for precipitate size effects). This indicates the need for further improvements in gradient-enhanced theories in order to guarantee their suitability for practical engineering applications.

Effect of plastic deformability and fracture behaviour on interfacial toughening mechanism at Fe/Ni interfaces

Fracture at interface causes plastic deformation in the vicinity region. Conventional plastic energy dissipation theory indicates that ductile vicinity toughens the interface by absorbing plastic deformation energy. However, the microstructure in the vicinity directly affects local plastic deformability and fracture behaviour, implying a more complicated toughening mechanism. In this study, the effect of microstructure and hardness on fracture behaviour of Fe/Ni interface was investigated. By experimental approach, interfaces with and without dynamic recrystallization (DRX) were fabricated by controlling the bonding conditions. It showed that compression-induced plastic deformation is the main source of the hardening behaviour in the vicinity. Moreover, the interfaces with hardened DRX vicinities exhibited improved fracture toughness, which is inconsistent with the plastic energy dissipation theory. To clarify this observation, the crystal plasticity finite element method (CPFEM) approach was employed to distinguish the effects of plastic deformation and interfacial microstructure. The result showed that although higher plastic deformability in the vicinity absorbs more dissipated plastic energy, severe stress concentration at the interface leads to early fracture and poor toughness. On the other hand, the interfacial hardened DRXed grains disperse interfacial stress distribution and provide potential sub-crack sites. A combined result of uniform plastic deformation and fracture energy dissipation is responsible for the improved toughness at interfaces with DRXed grains.