Strain Compatibility Research Articles

Compatibility of strains and the three-fold differentiability of the displacement field

The problem of the necessary class of smoothness of solutions to quasi-static problems of deformable solid mechanics in terms of displacements was discussed. It is shown that in order for the equations of compatibility of deformations to become identities when displacements are substituted in them, the existence of some third mixed derivatives of displacements is required. A counterexample for a linearly elastic compressible isotropic elastic medium was given. In this counterexample, the displacement field, being a doubly differentiable solution to the boundary value problem for the system of Lame equations in the entire domain, is not a solution to the displacement problem at all points in this domain.

Hybrid CFRP‐GFRP sheets for flexural strengthening of continuous RC beams: Experimentation and analytical modeling

AbstractContinuous reinforced concrete (RC) beams cast in place are commonly used in construction; however, there is a notable gap in the literature regarding the performance of continuous RC beams strengthened with fiber‐reinforced polymer (FRP) sheets. Strengthening RC beams with FRP sheets typically leads to reduced ductility and moment redistribution capacity due to the linear stress–strain behavior of FRP materials compared to non‐strengthened RC beams. Addressing this gap, this study explores the feasibility of enhancing the mechanical properties and ductility of strengthened elements through a hybrid approach, combining carbon‐fiber‐reinforced polymer (CFRP) and glass‐fiber‐reinforced polymer (GFRP) sheets. An experimental program was conducted, retrofitting two continuous two‐span RC beams (250 × 150 × 6000 mm) with hybrid CFRP‐GFRP (HCG) sheets. Concentrated loads were applied at the center of each span, and comprehensive data on strains in FRP sheets, longitudinal reinforcements, and crack propagation patterns were recorded and meticulously analyzed. The outcomes demonstrated that employing HCG sheets for strengthening RC continuous beams significantly improves ductility, load‐carrying capacity, and moment redistribution, surpassing the performance of beams strengthened with either CFRP or GFRP sheets. To ensure accurate predictions of the flexural response, an analytical model was developed and rigorously verified using the experimental results. The model takes into account the strain compatibility condition and provides insights into the behavior of continuous RC beams strengthened with CFRP, GFRP, and HCG sheets. This research contributes valuable knowledge to the understanding of FRP sheet strengthening techniques, emphasizing the efficacy of HCG sheets for achieving enhanced structural performance in continuous RC beams.

Development of a Novel Beam-Based Finite-Element Approach for the Computationally Efficient Prediction of Residual Stresses and Displacements in Large 3D-Printed Polymer Parts

Recently, 3D printing of large, structural polymer parts has received increasing interest, especially for the creation of recyclable structural parts and tooling. However, the complexity of large-scale 3D polymeric printing often dictates resource-intensive trial and error processes to achieve acceptable parts. Existing computational models used to assess the impact of fabrication conditions typically treat the 3D-printed part as a continuum, incorporate oversimplified boundary conditions and take hours to days to run, making design space exploration infeasible. The purpose of this study is to create a structural model that is computationally efficient compared with traditional continuum models yet retains sufficient accuracy to enable exploration of the design space and prediction of part residual stresses and deformations. To this end, a beam-based finite element methodology was created where beads are represented as beams, vertical springs represent inter-bead transverse force transfer and multi-point, linear constraints enforce strain compatibility between adjacent beads. To test this framework, the fabrication of a large Polyethylene terephthalate glycol (PETG) wall was simulated. The PETG was modeled as linearly elastic with an experimentally derived temperature-dependent coefficient of thermal expansion and elastic modulus using temperature history imported from an ABAQUS thermal model. The results of the simulation were compared to those from a continuum model with an identical material definition, showing reasonable agreement of stresses and displacements. Further, the beam-based model required an order of magnitude less run time. Subsequently, the beam-based model was extended to allow separation of the part from the printing bed and the inclusion of part self-weight during fabrication to assess the significance of these effects that pose challenges for existing continuum models.

Asymmetrical plastic deformation during spherical micro-indentation of magnesium

The complex deformation of magnesium (Mg) and its alloys has been the focus of many studies in lightweight technologies. In this paper, spherical micro-indentation tests followed by post-test electron microscopy were carried out on large grain pure Mg to isolate the effects of crystal orientation on the activation of deformation along different slip or twinning systems. Both pre- and post-indentation crystal orientations were measured using electron backscatter diffraction (EBSD). The pre-indentation orientations were mapped into a crystal plasticity finite element (CPFE) model to further analyze the results. It is shown that the resulting deformation twinning and the degree of indentation-induced misorientation were strongly correlated with the crystal orientation in the region of the indentation. Depending on the crystal orientation, multiple waves of basal slip were observed to form asymmetrically around the indents. These slip bands lead to more than 12° lattice rotations that are captured by CPFE modeling. For the first time, it is shown that indentation can lead to significant out-of-plane displacement field that can induce twin nucleation at the interface of far-field (>100 μm) neighbouring grains. CPFE simulations indicate that maintaining far-field strain compatibility leads to the nucleation of twins rather than a slip transfer or slip-induced twinning mechanism.

Solution of the plane thermoelasticity problems based on a new set of equations

The interaction of thermal and mechanical fields in modern technologies for the synthesis and processing of materials attracts more and more attention. This is due to the need to predict the behavior and properties of new materials and products depending on the conditions of their creation. In the present work, attention is focused on the comparison of the solutions to the thermoelasticity plane problems with and without accounting for the temperature dependence of the material properties. It is assumed that an external heat source traveling over the surface with a specific velocity and following a given trajectory is responsible for a significant temperature increase. It may correspond to a laser source, for example. The new way of problem formulation in stresses is used. The temperature dependence of the characteristics leads to nonlinear thermoelasticity equations when the equilibrium equations, the requirement of strain compatibility, and the Duhamel-Neuman relation for the plane stress state case are combined. To determine the temperature field, a nonlinear thermal conductivity equation is used. To solve the problem numerically, the use of an implicit finite-difference scheme and coordinate splitting for the thermal conductivity equation and the finite-difference method of successive over-relaxation with Chebyshev acceleration for the equations for stresses was made. As a result, the difference in the solution of linear and nonlinear problems is demonstrated for the considered cases. Using the example of a mixture of titanium and aluminum powders, numerical modeling demonstrated that some stress components can reach values up to 3.5 times higher than those obtained in the case of temperature-independent material properties when there is a 500-degree local temperature increase.

Investigation into the stress‒strain compatibility and fracture behaviour of a TC18 titanium alloy with a multistage lamellar microstructure

Understanding the fracture mechanism is essential for optimizing the mechanical properties of titanium alloys. The relationship between fracture behaviour and the multistage lamellar microstructure of the TC18 (Ti–5Al–5Mo–5V–1Cr–1Fe) alloy was investigated via in situ tensile and three-point bending tests. The results indicate that the TC18 alloy, featuring a multistage lamellar microstructure (including a β matrix, primary lamellar α phase, bundles, and secondary lamellar α phase), exhibits an excellent combination of strength and ductility. The precipitation of the secondary lamellar α phase significantly enhances the alloy's strength but weakens the stress‒strain compatibility of the microstructure. This results in a smaller crack-tip plastic zone (CTPZ) and causes dislocations to concentrate more at the grain boundaries and, to a lesser extent, at the phase interfaces. Consequently, in the later stages of crack propagation, microvoids and microcracks tend to form at dislocation pile-ups. With increasing stress, these microvoids and microcracks rapidly coalesce, leading to a greater proportion of intergranular fracture and thus reducing the fracture toughness of the alloy.

The mechanical anisotropy of Mg-Zn-Y alloys with columnar crystals in specific orientation

The Mg99.2Zn0.2Y0.6 alloys were prepared by directional solidification, and the effect of loading modes on mechanical anisotropy and deformation mechanism of the alloys was studied. The microstructure of the alloy is columnar crystals whose growth orientations are mainly concentrated in <112(_)0>. When the tensile load is parallel to longitudinal grain boundaries of columnar crystals, the alloy has high yield strength (232 MPa), owing to basal <a> slip with hard orientation and {101(_)1} contraction twinning with high critical resolved shear stress (CRSS), but work hardening is not obvious. When the compressive load is parallel to longitudinal grain boundaries of columnar crystals, the alloy has high compressive strength (337 MPa) and good plasticity (maximum strain, 24 %), as well as distinct work hardening, which are related to (112(_)1) [112(_)6(_)] twins and good strain compatibility of grain boundaries. When the compressive load is perpendicular to longitudinal grain boundaries, the alloy shows high plasticity (maximum strain, 31 %) because the strip-like extension twins are parallel to the longitudinal grain boundaries during deformation.

Experimental study of ultra-high-performance fibre-reinforced concrete (UHPFRC)-encased CFST short columns under axial and eccentric compression

This study presents a comprehensive experimental programme and analysis of ultra-high-performance fibre-reinforced concrete (UHPFRC)-encased concrete-filled steel tube (CFST) columns subjected to axial and eccentric compression. Twelve short columns were tested, with six of them utilising UHPFRC encasement while the other six employing normal strength fibre-reinforced concrete (FRC) encasement for comparison purpose. The study focused on the effects of load eccentricity ratio, concrete encasement type, and steel tube configuration. Key findings from the test results including failure modes, load-deflection behaviour, moment-curvature relationships and curvature ductility were examined. The findings showed that UHPFRC-encased CFST columns exhibited significantly enhanced strength and bending capacity, while FRC-encased columns showed remarkable ductility. A notable shift in failure mode was observed with increasing load eccentricity ratio, transitioning from crushing of concrete to compression, and then to balanced failure. Furthermore, applicability of prevalent design codes such as EC4, AIJ, and ACI 318 in calculating the peak loads of UHPFRC- and FRC-encased CFST columns was assessed. The plastic stress distribution methods in EC4 and AIJ overestimated peak loads, while ACI 318's strain compatibility approach accurately predicted FRC-encased columns but not UHPFRC-encased columns. To address this, modifications of the parameters α and β were incorporated into the ACI design method to reflect the relative brittle nature of UHPFRC, resulting in accurate predictions.

Animal Models of Helicobacter pylori Infection and Vaccines: Current Status and Future Prospects.

Helicobacter pylori infection causes chronic gastritis, ulcers, and gastric cancer, making it a threat to human health. Despite the use of antibiotic therapy, the global prevalence of H. pylori infection remains high, necessitating early eradication measures. Immunotherapy, especially vaccine development, is a promising solution in this direction, albeit the selection of an appropriate animal model is critical in efficient vaccine production. Accordingly, we conducted a literature, search and summarized the commonly used H. pylori strains, H. pylori infection-related animal models, and models for evaluating H. pylori vaccines. Based on factors such as the ability to replicate human diseases, strain compatibility, vaccine types, and eliciting of immune responses, we systematically compared the advantages and disadvantages of different animal models, to obtain the informed recommendations. In addition, we have proposed novel perspectives on H. pylori-related animal models to advance research and vaccine evaluation for the prevention and treatment of diseases such as gastric cancer.

Experimental evaluation and design of fillet welds under in-plane eccentric loads

The principal objective of this investigation is to furnish equations to compute the design strength of fillet welds under in-plane eccentric loads suitable for load and resistance factor design (LRFD) applications. Over the years, experimental and analytical techniques have been used to arrive at safe estimates for the strength of such welds in common practical applications. The conventional elastic design (ED) method is very conservative and is not compatible with the LRFD design philosophy. In addition, the ED method neglects the weld group's ductility and strain compatibility. On the other hand, the instantaneous center of rotation (IC) method considers the above parameters but requires complex calculations. In the present study, a method for designing fillet welds under eccentric loading is introduced called the plastic design (PD) method. This method considers the inelastic properties of the welds in a simple manner while providing an accurate prediction of the weld group's capacity. The performance of the proposed PD method was compared with the IC method for several cases. The ultimate loads obtained were mostly within 10% difference on the conservative side and only marginally different for a few. Additionally, the fillet weld group's resistance under in-plane eccentric loads was evaluated experimentally using 12C-shaped specimens with the load applied at different angles of 0, 45, and 75°. The test results also confirmed the efficacy of the proposed PD method in evaluating the design strength of such weld groups.

Calculating the grain size effect during strain hardening through a probabilistic analysis of the mean slip distance in polycrystals

Grain refinement is an important mechanism to produce stronger alloys. Strain hardening is an essential phenomenon in metal forming processes. The interaction between grain size and strain hardening is evident: a decrease in grain size (dg)causes an increase in ultimate tensile strength but a decrease in uniform elongation. The Kocks-Mecking (KM) model for strain hardening is based on the relationship between shear strain and the path length for dislocation slip. It provides good general estimates for stress-strain curves, and empirical modifications have been made to include dg. Here, the empirical approach is substituted by theoretical probability calculations, accounting for the fact that the grain size imposes a bound on the mean slip distance, while strain compatibility defines a relationship between grain boundary-dislocation interaction and bulk storage and annihilation. The resulting differential only uses the two parameters inherent to KM. Fitting to published tensile curves for Al, Cu, and Ni produces excellent results. The fitting parameters allow to predict the tensile strength as a function of dgto good approximation, for dg>1μm. Below this limit, fundamental changes in dislocation statistics impose the activation of grain boundary dislocation sources and may induce dislocation density gradients, which seem to determine the flow stress in the sub-μm range.

Capacity of Reinforced/Prestressed Concrete Compression Members Strengthened/Repaired Using Ultra-High-Performance Concrete Encasement

Currently, 36% of bridges in the United States need major repair work or replacement and 7% of them are classified as structurally deficient. Most of these bridges can be repaired or strengthened to meet the current load demands and withstand the environmental impacts for the remaining service life. Ultra-high-performance concrete (UHPC) has shown immense potential as a repair and strengthening material thanks to its exceptional characteristics such as high workability, excellent strength and durability, and remarkable energy absorption capacity. This paper presents an analytical approach to predict the capacity of reinforced or prestressed concrete compression members with UHPC encasement (jacket) under combined axial and bending effects. The approach is based on strain compatibility and uses idealized UHPC material models in tension and compression according to the new AASHTO Guide Specifications. The approach uses integration to develop accurate interaction diagrams for any section with complex geometry, which overcomes the approximations of the lamina approach. The paper also provides a comprehensive literature review on UHPC usage in repairing and strengthening concrete bridge columns and piers. A design example of a circular reinforced concrete column is presented to illustrate the proposed approach and to calculate the nominal and design capacities of the composite section. This example has shown that increasing the thickness of the UHPC jacket has a prominent effect on enhancing the axial capacity but only a slight effect on the flexural capacity of compression members.

A stability evaluation method for deep-seated toppling in the upper Lancang river, Southwestern China

Deep-seated toppling in the upper reaches of the Lancang River, southwest China involves deformations exceeding 100 m in depth. The slope deformation is initiated by river downcutting and evolves distinctive characteristics with a depth of river incision. In this study, we propose a system for evaluating the stability of deep-seated toppled slopes in different evolutionary stages. This system contains identification criteria for each evolutionary stage and provides the corresponding stability evaluation methods. Based on the mechanical and kinematic analysis of slope blocks, the specific stage of slope movement can be identified in the field through outcrop mapping, in situ tests, surface displacement monitoring, and adit and borehole explorations. The stability evaluation methods are established based on the limiting equilibrium theory and the strain compatibility between the undisturbed zone and the toppled zone. Finally, several sample slopes in different evolution stages have been investigated to verify the applicability and accuracy of the proposed stability evaluation system. The results indicate that intense tectonic activity and rapid river incision lead to a maximum principal stress ratio exceeding 10 near the slope surface, thus triggering widespread toppling deformations along the river valley. When considering the losses of joint cohesion during the further rotation process, the safety factor of the slope drops by 7%–28%. The self-stabilization of toppling deformation can be recognized by the layer symmetry configuration after the free rotation of the deflected layers. Intensely toppled rock blocks mainly suffer sliding failures beyond the layer symmetry condition. The factor of safety of the K73 rockslide decreased from 1.17 to 0.87 by considering the development of the potential sliding surface and the toe-saturated zone.

Compatibility of Native Strains of Beauveria peruviensis and Metarhizium sp. as Strategy for Biological Control of Coffee Berry Borer (Hypothenemus hampei, Ferrari)

Coffee is a crop of global importance, and it is especially important in countries such as Peru. However, the presence of the pest Hypothenemus hampei represents a significant challenge with a notable economic impact. This study addresses this challenge using entomopathogenic fungi such as Beauveria peruviensis and Metarhizium sp. The compatibility of three strains of Beauveria peruviensis (F5, P19, and P4) and seven strains of Metarhizium sp. (MMR-M1, LLM-M2, MHR-M4, PMR-M12, MMR-M15, TOR-M16, and GOR-M18) was evaluated for approximately 2 months. A total of 14 treatments were designed, each consisting of one strain of B. peruviensis and one strain of Metarhizium sp. The Skott–Knott test (p ≤ 0.05) revealed that strain LLM-M2 (Metarhizium sp. strain) had the highest conidial production (3.75 × 107 conidia/mL). Except for T6 (MMR-M1/F5), which showed a mutual growth type interaction (type A), all other strain combinations showed a type B interaction (mutual inhibition by contact or separation between colony margins (&lt;2 mm)). The combination with the highest germination rate was T10 (MHR-M4/F5) at 89%. In addition, the pathogenicity of the combined strains was evaluated, showing a direct correlation with mortality and mycosis development in the coffee berry borer in treatments T1 (PMR-M12/P19), T10 (MHR-M4/F5), and T11 (MMR-M15/P19), reaching 100% mortality at 72 h with grade 4 mycosis. Regarding mycelial growth, treatments T1 (PMR-M12/P19), T4 (MMR-M1/P19), and T12 (GOR-M18/P19) reached the highest percentages, between 85.8% and 83.10% at 240 h. This study demonstrates the feasibility of using native strains of B. peruviensis and Metarhizium sp. as a biocontrol strategy against the coffee berry borer in the Amazon department, presenting them as an alternative to traditional chemical methods.

A Study of {10-12} Twinning Activity Associated with Stress State in Mg-3Al-1Zn Alloy during Compression

An eight-sided prism sample, obtained from a hot-rolled AZ31 magnesium alloy sheet, was compressed at room temperature along the transverse direction to investigate the influence of local strain on twinning behavior using electron backscatter diffraction (EBSD) measurements, hardness distribution, and metallographic observations. The octagonal surface of the sample was divided into distinct regions based on hardness distribution and metallographic observations. Combined analysis of the Schmid factor (SF) and the strain compatibility factor (m’) was employed to study twin variant selection. Basal on SF ratio distribution, the Schmid factor criterion, can predict over 75% of observed twin variants in regions A and D (normal stress samples). In contrast, 64% of twin variant selection behavior in region C (shear stress sample) can be effectively explained using a pure shear model. Twin variants with high strain compatibility factors may prefer activation to reduce stress concentration. The strain compatibility factor is more appropriate than the Schmid factor for analyzing the effect of local strain on the selection behavior of twin variants.

Behavior and design of eccentrically compressed hybrid steel and GFRP reinforced concrete columns at elevated temperature

AbstractThis study presents analytical model for the analysis of hybrid (steel and fiber reinforced polymers (FRP)) reinforced concrete (RC) columns at elevated temperature under eccentric compressive loads. The bending moment resistance of the (RC) columns at elevated temperature is formulated based on force equilibrium and strain compatibility of the concrete column section under combined bending moment and axial force. Deterioration the mechanical properties of concrete, steel, and FRP bars due to the rise of temperature has been taken into account using equations proposed by previous studies. Validating the suggested model was carried out by comparing the analytical results with corresponding experimental and numerical results in terms of axial load‐lateral displacement relationships, axial load‐bending resistance interaction diagrams, and failure modes. Validation results have shown the accuracy of the suggested analytical model. A parametric study has also been conducted using the proposed analytical model to investigate the effect of some parameters on the axial load‐bending resistance interaction diagrams of hybrid steel and FRP‐RC columns under elevated temperature. These parameters include the effect of higher temperature values, the effect of reinforcement material, and the effect of reinforcement configuration. Parametric study results have revealed some interesting conclusions that may be implemented in the design of hybrid RC columns at fire.

Maximum permissible safe length of integral abutment bridges supported by steel H-piles

The absence of a defined allowable pile ductility in integral abutment bridges (IABs) creates a critical gap in determining the maximum safe bridge length. This paper introduces a design aid procedure to assist bridge engineers in establishing the length limits of jointless bridges. Numerical and analytical approaches were used in formulating the design aid procedure. A total of 66 finite difference models were established to obtain pile equivalent cantilever length considering various design parameters (soil stiffness, pile size, pile orientation, axial compressive load, and lateral displacement magnitude). The analytical approach incorporates a strain compatibility and equilibrium model to generate moment-curvature diagrams and load-deflection curves for standard HP sections commonly used in IABs construction. The validity of the developed design aid procedure was examined and tested with available experimental and numerical results. Lateral buckling displacement capacity of HP sections ranged from 50 to 100 mm (2–4 in.). Based on these displacement capacities, length limits for IABs were established and compared with existing studies. The maximum length limits for steel integral bridges fall within the range of 162–320 m (530–1050 ft), while concrete integral bridges have limits ranging from 210 to 390 m (680–1285 ft). These limits depend on factors such as pile size, soil stiffness, and climate conditions.

Finite element analysis of concrete‐encased columns reinforced with multiple steel sections

SummaryConcrete‐encased columns reinforced with one built‐up steel core are widely used as mega columns in high‐rise buildings. Due to the enormous size of the steel core, multiple steel segments have to be welded and spliced on‐site, which might inflict detrimental impacts on the integrity and ductility of the columns. To solve this practical issue, one method using multiple steel sections to replace one gigantic built‐up section is proposed. However, whether those columns reinforced with individual steel sections could have the same capacity as the ones reinforced with one steel core and whether the current design method relying on strain compatibility is still applicable to design such columns remain unknown. In this study, one column specimen reinforced with multiple steel sections is tested and the test results are utilized to calibrate finite element models. Afterward, finite element (FE) analysis is performed on concrete‐encased columns reinforced with multiple steel sections to numerically examine the load capacity of those columns. Based on the numerical analysis, a design method based on modified strain distribution is proposed. Numerical results indicate that concrete‐encased columns reinforced with multiple steel sections exhibit similar performance compared with the one reinforced with one steel core, showing great potential to be applied as mega columns in high‐rise buildings.

P-M INTERACTION DIAGRAMS FOR REINFORCED CONCRETE WALLS RETROFITTED WITH EXTERNALLY BONDED CARBON-FIBER REINFORCED POLYMER

This research develops analytical axial load-bending moment (P-M) interaction diagrams for reinforced concrete (RC) walls retrofitted with carbon fiber reinforced polymer (CFRP). A 12-inch thick, 1-foot strip of RC wall section is considered with varying reinforcement ratios, varying axial compressive loading, and varying number of CFRP layers. The CFRP material is treated as externally bonded onto the tension face of the RC wall to investigate its impact on the flexural capacity of the section. Each P-M interaction diagram was generated considering a discretized compression zone and by satisfying principles of static equilibrium and strain compatibility. An elastic-plastic steel stress-strain relationship is used for Grade 60 reinforcement; a uniaxial nonlinear compressive stress-strain relationship is used for concrete; and a linear stress-strain relationship is used for CFRP in tension. The failure modes considered are steel yielding, concrete crushing, and CFRP debonding. The computed P-M interaction diagrams are normalized for their general use in the retrofit of existing RC walls using CFRP. Results show that as the axial compressive force on the RC wall increases, the less effective CFRP is. CFRP is more effective in sections with beam-like behavior, where the reinforcement ratio tends to be the smallest.

Auxotrophy-Independent Plasmid Shuttle Vectors for Applications in Diverse Yeasts

Plasmid shuttle vectors are a common tool used to study yeast physiology. The majority of yeast plasmids have been optimized for Saccharomyces cerevisiae lab strain compatibility, relying on auxotrophic complementation as their selective property. We sought to construct a series of plasmid shuttle vectors to extend functionality beyond strains with auxotrophic requirements, and test compatibility across a diverse panel of yeasts. We constructed 18 plasmids which were successfully maintained by yeasts from several genera. From a panel of 24 yeast strains, these plasmids were maintained by 18 yeasts, spanning 11 species within the genera Lachancea, Metschnikowia, Pichia, Saccharomyces, and Torulaspora. Additionally, an integrated gene expression reporter was assayed for functional compatibility with the 18 strains. Plasmid-derived gene expression was observed for 13 strains, spanning five species within the Saccharomyces genus, in addition to Torulaspora delbrueckii. These results indicate that this plasmid series is broadly useful for advancements and applications within academia, biotechnology, and the food and fermentation industries for research utilizing diverse Saccharomyces and non-Saccharomyces yeasts.