Interface Stiffness Research Articles

Measurement of coating–substrate interface stiffness using a constructed ultrasonic echo phase derivative spectrum

Measurement of coating–substrate interface stiffness can indirectly characterize interface bonding quality. This paper proposes a noval quantitative inversion coating–substrate interface stiffness method based on the multi-resonance frequencies of a constructed ultrasonic echo phase derivative spectrum (UEPDS). The theoretical relationship between UEPDS resonance frequencies and interface stiffness is derived. The detection frequency and high-sensitivity interface stiffness range are optimized based on the sensitivity analyzed. Numerical simulation and experiment are implemented on a 0.48 mm aluminum layer/carbon steel substrate specimen to prove the validity of the proposed ultrasonic method. The simulation results show that the maximal relative error between the inversion and the preset interface stiffnesses is reduced from 23% to 8% compared with the traditional ultrasonic reflection coefficient amplitude spectrum-based (URCAS-based) method. The experiment results indicate that the UEPDS-based inversion interface stiffnesses have the same trend as the nominal contact pressures between the coating–substrate interface.

An interlaminar fatigue damage model based on property degradation of carbon fiber-reinforced polymer composites

Interface delamination is a significant damage mechanism in fiber-reinforced polymer (FRP) laminated composites caused by interlaminar normal and shear stresses. This is due to the low interlaminar properties including interface stiffness and strength that continuously degrade to cause fatigue crack nucleation and growth. In this respect, an interlaminar fatigue damage model is proposed to accurately address the reliability aspect of the FRP composite materials and structures. The model considers a damage process that consists of two stages: (1) fatigue damage evolution due to interlaminar properties degradation to the onset of crack nucleation. A cyclic cohesive zone model with a bilinear softening behavior is introduced along with the fatigue life model to capture the mean stress effect of the interface. This is followed by (2) the crack nucleation process leading to the physical separation/debonding of the interface material point, as governed by the cycle-dependent fracture energy dissipation. The mechanical prediction of the interlaminar fatigue damage process is illustrated through finite element simulation of a mixed-mode flexural test of a carbon fiber-reinforced polymer (CFRP) composite beam subjected to fatigue loading. The results indicate that the interlaminar normal and shear crack opening displacement increases exponentially with the larger number of load cycles. In addition, the high-stress gradient is limited to the interface crack front zone with the normal and shear stress peaks at 69.2 and 16.5 % of the respective interlaminar strength. Moreover, controlled interlaminar crack growth is initially foreseen at 7.0 × 10-6 mm/cycle, followed by an abrupt crack “jump” at 287,000 load cycles.

3D finite element performance-based study of RC interface stiffness

Although the importance of concrete-reinforcement interaction for reinforced concrete mechanics is well recognized, its intrinsic complexity needs in-depth meso-scales investigation. The contact zone between concrete and reinforcement was investigated in this study using RC ties that were short enough not to crack. The rib-scale simulation was carried out using a three-dimensional finite element technique using a simplified rib shape in the reinforcing bar. The contact between the concrete and steel was modeled using a friction cohesive zone model. An analysis was conducted to explore the impact of various contact zone parameters, suggesting numerical attributes for both normal and tangential stiffness while considering diverse rebar diameters. Concrete strain distribution and propagation of smeared splitting cracks in prisms were investigated. Additionally, a relationship between the interface's normal stiffness and rebar diameter was established through an exponential equation: Knn=2,53∙1016∙D−7,5[MN/m3]. The stiffness parameters proposed were utilized to forecast the steel strain profiles of RC ties at various load levels.

Effects of Freeze-Thaw Cycles on Interfacial Shear Transfer Characteristics in Section Steel Reinforced Concrete Composite Structures with Stud Connectors

This study examines how freeze-thaw cycles influence the shear transfer characteristics at the interface of section steel with stud connectors and concrete. Push out tests were performed on fourteen section steel reinforced concrete composite structures with stud connectors (SRCSC) and two without them. The analysis focused on examining the impact of variables such as the number of freeze-thaw cycles, the diameter of studs, and the arrangement of studs on the interfacial shear capacity of the SRCSCs. Experimental results showed that with an increase in the number of freeze-thaw cycles, the damage morphology of the SRCSCs transitions from stud shearing to concrete splitting. Concurrently, the interfacial shear capacity and shear stiffness of SRCSCs diminish. Large-diameter studs could effectively improve the interfacial shear properties of SRCSCs. Additionally, SRCSCs with studs positioned in the web demonstrate enhanced interfacial shear transfer capabilities compared to those with studs located in the flange. The proposed method for the residual interfacial shear capacity of the SRCSCs after freeze-thaw cycles was based on experimental data analysis. Results from this calculation method were consistent with the experimental observations.

Physical and 3D numerical modelling of reinforcements pullout test

This paper reports results of laboratory and 3D numerical modeled pull-out tests with steel ladders and polymeric strip reinforcements. These types of reinforcement are commonly used in reinforced soil walls constructed with concrete facing elements. Laboratory pull-out tests are required to determine accurate and realistic pull-out strength values considering the interaction of specific reinforcement and backfill materials under different confining pressures (i.e., trying to simulate the different reinforcement layer arrangements and load conditions in actual reinforced soil walls). International design Codes for reinforced soil walls provide default values for pull-out strength. However, in many cases, default values are too conservative and/or are not strictly specified for particular reinforcement types. Pull-out tests can be difficult and expensive to perform, thus not being common nor worth for the vast majority of reinforced soil wall projects. Consequently, calibrated numerical models can be useful to predict pull-out response under site-specific conditions, and provide further understanding of the mechanisms involved in the soil-reinforcement interaction. Details of the numerical approach, including relevant aspects of the soil-reinforcement interfaces, are described. Examples of calibrated numerical predictions for pull-out loads, displacements, and soil-dilatancy effects are presented. The influence of reinforcement, soil and interface stiffnesses is shown. Numerical results provide useful insight for future modelling works of the complex interaction between type-specific backfill materials and reinforcement element, relevant for investigation and/or practical design of reinforced soil walls.

Abstract 1505: Unraveling diepafitaxis: Investigating ECM stiffness and microarchitecture in tumor spheroid migration

Abstract Background: Metastasis, accounting for up to 90% of cancer-related deaths, remains one of the least understood aspects of cancer progression. Recent research has shifted focus from solely biological hallmarks to the physical characteristics of cancer, such as the stiffness and microarchitecture of the extracellular matrix (ECM), which play pivotal roles in metastatic advancement. We previously introduced the concept of 'diepafitaxis' to describe a unique mechanism driving the interface-mediated tropism of tumor spheroids at matrix-surface boundaries. This phenomenon suggests that cancer cells preferentially migrate along a 2D 'interfacial' track formed by heterogeneous 3D ECM structures, facilitating invasion and dispersion. However, the exact mechanisms by which interfacial components, stiffness, and structural attributes influence cell movement remain debated. To investigate this, we have developed a microfluidic chip with a precisely controlled stiffness of the hydrogel matrix-matrix interface (MMI), aiming to shed light on specific diepafitatic behaviors. Method: We developed a polydimethylsiloxane (PDMS)-based microfluidic chip using a traditional photolithographic process. This chip features three channels, with the center channel designed to precisely control various MMI stiffness combinations: stiff vs soft (t-o), stiff vs stiff (t-t) and soft vs soft (o-o). MDA-MB-231 breast cancer spheroids (BCS), representing an in vitro tumor model, were embedded in the top gel. We observed the dynamic behavior of these cancer spheroids over a 24-h period using differential interference contrast (DIC) microscopy. Result: The study revealed that BCS exhibited more pronounced dispersion in a soft homogeneous ECM compared to a stiff ECM in 3D environments. Interestingly, when BCS were near an MMI, a stiffer MMI (t-t) significantly enhanced BCS invasiveness and single-cell migration, more so than t-o, and notably more than o-o. We previously described this phenomenon as '2.5D migration,' where cells migrate in a ventral 2D manner within a sandwiched 3D gel structure. This diepafitatic behavior was further analyzed for its response to gravitational effects and the influence of chemotaxis, induced by introducing VEGF on one side of the microfluidic channel. Conclusion: Conclusively, our study demonstrates that the stiffness and structure of the ECM, particularly at MMI, significantly influence the invasive behavior and migration patterns of BCS, underscoring the critical role of mechanical microenvironments in cancer metastasis. Citation Format: Hsiang-Pei Chen, Ya-Chu Tsai, Ting-Yuan Tu. Unraveling diepafitaxis: Investigating ECM stiffness and microarchitecture in tumor spheroid migration [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2024; Part 1 (Regular Abstracts); 2024 Apr 5-10; San Diego, CA. Philadelphia (PA): AACR; Cancer Res 2024;84(6_Suppl):Abstract nr 1505.

Effect of the experimental parameters on the ice-asphalt adhesion strength and corresponding theoretical model based on the energy-balanced principle

Ice adhesion behavior plays a crucial role in assessing ice-phobic materials. However, the variation of ice-adhesion strength across different laboratories is attributed to the neglect of ice/substrate characteristics. In this work, ice-adhesion strength under different geometric parameters of ice/substrate on asphalt surfaces was examined through an optimized methodology. Additionally, a theoretical model was developed based on the energy balance principle to analyze the influence of various parameters on ice-adhesion strength and to make predictions. The results suggested that the ice-adhesion strength was positively correlated with the substrate thickness and negatively correlated with both the asphalt thickness and the ice diameter. The detachment process of the ice-asphalt interface was divided into two regions, the non-linear mechanical response region, and the linear damage region. The slope of the linear damage region can be defined as the interfacial stiffness of the ice-asphalt system, which was the main reason leading to the change in ice adhesion strength. The increase in ice-adhesion strength was observed as the interfacial stiffness increased. Moreover, the theoretical model of ice-adhesion strength illustrated the effect of ice/substrate geometric characteristics on ice-adhesion strength and was verified by the experiments. This study may provide some new references and a theoretical basis for further research on ice adhesion behavior in different laboratories.

Investigation on shear behavior of the interface between engineered cementitious composites and normal-strength concrete

Engineering cementitious composites (ECC), possessing excellent mechanical properties for good durability, can be applied to repair and strengthen reinforced concrete structures. In the present study, the interface shear behavior between ECC and normal-strength concrete was studied. Thirty bonded joint specimens were fabricated and subjected to push-out direct-shear tests. The construction methods of ECC mixture (precast and cast-in-place), ECC strength, and interface bonding methods (i.e., Epoxy resin, UHPC, cast-in-place ECC, cast-in-place ECC with chiseling, and bolts) were investigated. The results indicated that interface bonding methods have a significant influence on the failure modes and interface shear strength between ECC and existing concrete. There were three failure modes: interface debonding, interface debonding converted to concrete fracture, and concrete matrix destruction failure. Epoxy resin bonded specimens exhibited the highest shear strength, and cast-in-place ECC bonded specimens showed the lowest shear strength. Moreover, the shear performance of the ECC and the normal-strength concrete interface was analyzed in terms of interfacial shear strength and shear stiffness, bond-slip curve, and shear transfer mechanism. Finally, an analytical model for estimating the interfacial shear strength considering the interfacial bonding methods was established, with its predictions having high accuracy.

Damage recovery in composite laminates through deep learning from acoustic scattering of guided waves

We propose an innovative deep learning (DL) regression strategy combined with guided wave modes to address inverse acoustic scattering problems effectively. This approach allows for accurate recovery of heterogeneous defect fields at the interfaces of composite laminates. The neural network (NN) model’s training process employs stochastic Gaussian fields as output, which are linked to the interfacial defect fields of the physical problem. Our method assumes prior knowledge of the material geometrical properties of the constituent layers. To model the interfaces, we utilize the Quasi-Static Approximation, a technique generating position-dependent interfacial stiffness matrices containing uncoupled normal and tangential springs. We validate our approach by assessing its performance in handling noisy input data and reduced models, as well as accounting model errors at the composite interface. The obtained results show that the proposed method has a remarkable generalization capability, allowing it to recover diverse defect field profiles with accuracy. Moreover, it exhibits robustness concerning noisy data and model errors. Lastly, thanks to the guided wave modes approach, the presented methodology not only maintains its capability to recover heterogeneous defect fields potentially in real-time but also extends the range of inspection to encompass a significantly larger structural area.

The influence of thermal expansion of carbon-carbon composite materials on the stability of their tribological parameters

The influence of thermal expansion of disk specimens made of carbon-carbon composite materials on the stability of their tribological characteristics in a friction pair with a ceramic ring counterbody is studied theoretically and experimentally. The temperature characteristics of composites with two different structures — fibrous and fabric — are studied. The experimental dependences of the load change on time during frictional heating are compared with the calculation model obtained by methods of contact interaction mechanics. A relation is established between changes in interface stiffness and the dependence of the coefficient of thermal expansion on temperature for the materials under study. Uneven wear of the fabric composite is revealed at the initial stage with destruction of fabric layers and tearing out of structural components. Keywords:carbon-carbon composite material, contact interaction, friction, temperature, frictional heating, coefficient of thermal expansion, wear ivan.yu.tsukanov@gmail.com, lyubicheva@mail.ru, bukovskiy.pavel@gmail.com

Sp-Carbon-Conjugated Organic Polymer as Multifunctional Interfacial Layers for Ultra-Long Dendrite-Free Lithium Metal Batteries.

Fatal issues in lithium metal anodes (LMA), such as detrimental lithium dendrites growth and fragile solid-electrolyte interphase (SEI) during the Li plating/stripping process, often hinder the practical application of Li metal batteries (LMBs). Herein, cobalt-coordinated sp-carbon-conjugated organic polymer (Co-spc-COP) is constructed as the protective layer for regulating the interface stability of LMA. The unique synergistic beneficial effect of organic functional groups (C≡C linkage, C=N units and aromatic rings) and Co sites not only regulate the Li+ coordination environment and rearrange Li+ concentration to facilitate its transport by optimizing the electronic density, enhancing the compatibility with electrolyte interface and supplying "external magnetic driving strategy", but also strengthens the interfacial stiffness with high Young's modulus to better withstand the mechanical stress. These beneficial effects and relative underlying working mode and mechanism of uniform Li plating and rapid Li+ migration on the Co-spc-COP are also revealed by various in situ/ex situ experimental technologies and theory calculation. The Co-spc-COP-based cell delivers an extraordinary lifespan of 6600 h and ultrahigh capacity retention of 78.3 % (111.9 mAh g-1) after 1000 cycles at 1 C. This demonstrated synergistic strategy in Co-coordinated organic polymer may gain new insights to regulate the uniform and non-dendritic deposition/dissolution behaviors for highly stable LMBs.

Sp‐Carbon‐Conjugated Organic Polymer as Multifunctional Interfacial Layers for Ultra‐Long Dendrite‐Free Lithium Metal Batteries

AbstractFatal issues in lithium metal anodes (LMA), such as detrimental lithium dendrites growth and fragile solid‐electrolyte interphase (SEI) during the Li plating/stripping process, often hinder the practical application of Li metal batteries (LMBs). Herein, cobalt‐coordinated sp‐carbon‐conjugated organic polymer (Co‐spc‐COP) is constructed as the protective layer for regulating the interface stability of LMA. The unique synergistic beneficial effect of organic functional groups (C≡C linkage, C=N units and aromatic rings) and Co sites not only regulate the Li+ coordination environment and rearrange Li+ concentration to facilitate its transport by optimizing the electronic density, enhancing the compatibility with electrolyte interface and supplying “external magnetic driving strategy”, but also strengthens the interfacial stiffness with high Young's modulus to better withstand the mechanical stress. These beneficial effects and relative underlying working mode and mechanism of uniform Li plating and rapid Li+ migration on the Co‐spc‐COP are also revealed by various in situ/ex situ experimental technologies and theory calculation. The Co‐spc‐COP‐based cell delivers an extraordinary lifespan of 6600 h and ultrahigh capacity retention of 78.3 % (111.9 mAh g−1) after 1000 cycles at 1 C. This demonstrated synergistic strategy in Co‐coordinated organic polymer may gain new insights to regulate the uniform and non‐dendritic deposition/dissolution behaviors for highly stable LMBs.

Analysis of stress state and crack initiation time around hard-brittle particles in nickel-based alloys by interface model

The finite element method was used to simulate the stress distribution around hard-brittle particles with different particle-matrix interface states in nickel-based alloy with different sample thicknesses under 760 ℃/357 MPa and 980 ℃/250 MPa. The cohesive interface model was used to simulate different particle-matrix interface states. The effects of particle-matrix interface states, geometric characteristics of particles, particle positions in the sample, matrix orientation, and other factors on stress distribution were summarized. Through a thorough analysis of the stress distribution surrounding the particles, the crack initiation time was calculated. The results showed that the maximum stress around the particles was greater when the interface was in completely de-bonded CD state (no binding force between particles and the matrix) compared to the completely bonded CB state (completely coherent between particle and matrix). Furthermore, when the interface was CD, the larger the aspect ratio of the particles, and the closer they were to the surface of the sample, the greater the maximum stress around the particles. When the interface stiffness was reduced (due to mismatch or damage), the stress distribution did not change significantly under high interface stiffness conditions. However, when the interface stiffness decreased to a certain extent, the maximum stress value rapidly increased. In addition, the stress concentration factor began to change when the ratio of sample thickness to particle size (ξ) was less than 5. When the interfacial bonding was weak (with low interface stiffness), the crack initiation time around particles with large aspect ratio decreased significantly with the decrease of interface stiffness. Compared with the condition of 760℃/357 MPa (the same ratio of load to yield strength at 980℃), the crack initiation time around the particle was shorter at 980℃/250 MPa, and the influence of particle geometric features was smaller.

Interface pressures and stiffnesses of different bandages studied on a Hiraï leg

Hirai et al. have developed a tool to assess the in vitro pressures of different compression devices. This tool has the advantage of being easy to use and finally inexpensive. The study of 7 bandages (Biflex 16, Urgo K2, Urgo K1, Coban 2, Biflex kit, Rosidal K and Rosidal Sys) on a Hirai leg allowed a precise analysis of the evolution of pressures and stiffnesses. Interface pressures were measured using the Picopress system and a 5 cm diameter probe. The difference between pre-stretch and stretch pressures in mmHg characterized stiffness. If the difference is greater than 10 mmHg, the bandage is considered stiff. These bandages were applied with a pressure of 45±2 mmHg at point B1. One hundred extension maneuvers were then performed. A decrease in mean pre-stretch pressures was noted more frequently for Rosidal K, Urgo K1 and Coban 2 than for the other bandages. Biflex 16 has a stiffness of less than 10 mmHg (p<0.001). Urgo K1, Urgo K2, Coban 2, Kit Biflex have very similar stiffnesses (p=ns). Rosidal K and Rosidal Sys have higher stiffness (p<0.001).

Assessing Numerical Simulation Methods for Reinforcement–Soil/Block Interactions in Geosynthetic-Reinforced Soil Structures

The purpose of this study is to assess effects of two different simulation methods (i.e., interfaces with a single spring-slider system and interfaces with double spring-slider systems) for interactions between reinforcement and the surrounding medium on the performances of geosynthetic-reinforced soil (GRS) structures when conducting numerical analyses. The fundamental difference between these two methods is the number of the spring-slider systems used to connect the nodes of structural elements simulating the geosynthetic reinforcement and the points of solid grids simulating the surrounding medium. Numerical simulation results of pull-out tests show that both methods reasonably predicted the pullout failure mode of the reinforcement embedded in the surrounding medium. However, the method using the interfaces with a single spring-slider system could not correctly predict the interface shear failure mode between the geosynthetics and surrounding medium. Further research shows that these two methods resulted in different predictions of the performance of GRS piers as compared with results of a laboratory load test. Numerical analyses show that a combination of interfaces with double spring-slider systems for reinforcement between facing blocks and interfaces with a single spring-slider system for reinforcement in soil resulted in the best performance prediction of the GRS structures as compared with the test results. This study also proposes and verifies an equivalent method for determining/converting the interface stiffness and strength parameters for these two methods.

An accurate forming model for capturing the nonlinear material behaviour of multilayered binder-stabilised fabrics and predicting fibre wrinkling

Prefabricated stacks of binder-stabilised dry fabrics are used to increase reinforcement deposition rates in the manufacturing of large composite structures such as wind turbine blades. To ensure optimal part quality, accurate simulation tools may be used to avoid costly trial-and-error experiments. This paper introduces a new modelling framework for predicting wrinkle defects that arise from forming thick binder-stabilised stacks of quasi-unidirectional non-crimp fabric. In this context, quasi-unidirectional non-crimp fabrics are unidirectional rovings stabilised with a backing layer. The non-constant bending stiffness of the fabric is modelled using an asymmetric compressive modulus, while a mixed-mode cohesive formulation with user-defined damage evolution is used for modelling the initial non-constant elastic binder interface stiffness and interface degradation. The model is verified against cantilever bending tests of single fabric layers and transverse shear experiments of bindered fabric layers. Comparison with experimental results on the forming of preforms shows that the model accurately predicts wrinkle location and geometry during the forming of thick binder-stabilised preforms. The error between the wrinkle geometry predicted by the new modelling approach and the experimentally measured wrinkle geometry is reduced by 35% to 94% compared to wrinkles predicted by conventional modelling approaches. The modelling framework is freely available at https://doi.org/10.5281/zenodo.10077428.

Mechanistic investigation of grid-reinforced asphalt pavements with measured interface properties

The bond properties at layer interfaces are a required input in mechanistic asphalt pavement models. For design and analysis procedures, involving the calculation of key responses that are commonly linked to performance, perfect bond conditions are regularly assumed between layers. One emerging approach for prolonging the service life of asphalt pavements, either new or rehabilitated, is installing asphalt grid reinforcement (AGR) products between paving lifts. In these cases, the perfect bond assumption may not hold – undermining the reinforcement potential. Accordingly, the objective of this study was to investigate the effects of layer interface properties on key responses in pavements with AGR. The investigation was carried out by combining results from a full-scale construction, laboratory tests on asphalt concrete (AC) cores, and synthetic simulations. The latter were performed with a recently developed semi-analytic mechanistic code that can accept AGR products. This code can handle time- and temperature-dependent layer and interface properties, as well as moving loads. From the laboratory tests, it was found that the bond between AC lifts, with and without an AGR, is time- and temperature-dependent – best characterised by a relaxation interface stiffness function. This relaxation function was measured to be consistently larger without an AGR than with an AGR. Nonetheless, pavement simulations showed that including an AGR has no pronounced effect on strain magnitudes under high-speed/low-temperature conditions, can lessen horizontal strain magnitudes at the reinforced interface and at the AC bottom (mainly under slow-speed/high-temperature conditions, and depending on the installation depth of the AGR), and has no pronounced effect on deflections regardless of the loading speed and temperature level. It is concluded that even if laboratory measurements display a reduced interface stiffness when including an AGR, the reduction may not have any practical implication on key pavement responses, and the reinforcement potential is not necessarily undermined. The modelling and experimental approaches outlined and utilised in this study offer a rational tool for analysing this matter/question on a case-by-case basis.

Natural Frequency Response of FG-CNT Coupled Curved Beams in Thermal Conditions

This study investigates the sensitivity of dynamic properties in coupled curved beams reinforced with carbon nanotubes (CNTs) to thermal variations. Temperature-dependent (TD) mechanical properties are considered for poly methyl methacrylate (PMMA) to be strengthened with single-walled CNTs (SWCNTs), employing the basic rule of mixture to define the equivalent mechanical properties of nanocomposites. The governing equations of motion are derived using a first-order shear deformation theory (FSDT) and Hamilton’s principle, accounting for elastic interfaces modeled using elastic springs. A meshfree solution method based on a generalized differential quadrature (GDQ) approach is employed to discretize the eigenvalue problem and to obtain the frequency response of the structure. The proposed numerical procedure’s accuracy is verified against predictions in the literature for homogeneous structural cases under a fixed environmental temperature. The systematic investigation assesses the impact of various geometric and material properties, including curvature, boundary conditions, interfacial stiffness, and CNT distribution patterns, on the vibrational behavior.

Study on multi-cluster fracturing simulation of deep reservoir based on cohesive element modeling

With the depletion of conventional reservoir development, reservoir fracturing under deep high geo-stress and high geo-stress difference conditions is receiving increasing attention. Deep reservoirs typically require multi-cluster fracturing to achieve efficient reservoir transformation and development. In this paper, considering the relevant geological parameters of a certain reservoir in the southwest, three-dimensional multi-cluster reservoir fracturing models were established based on cohesive element modeling. Then, the propagation law of artificial fractures in reservoirs under the influence of the different number of fracturing clusters, injection displacement, and Young’s modulus in different regions of the 60 m fracturing well section is analyzed, and the quantitative law of parameters such as fracture length, maximum fracture width, injection point fracture width, fracture area, and tensile failure ratio during multi-cluster fracturing construction, as well as the propagation law of fracture morphology are revealed. The simulation results show that using multi-cluster fracturing can significantly improve the effectiveness of reservoir reconstruction, but as the number of fracturing clusters increases, it is also easy to form some small opening artificial fractures. These small opening artificial fractures may not be conducive to the transportation of proppants and fluids. During single cluster fracturing, the interface stiffness and rock Young’s modulus have a significant impact on the propagation of artificial fractures in the reservoir. As the number of fracturing clusters increases, the competition between artificial main fractures expands significantly, which may reduce the impact of interface stiffness and rock Young’s modulus. The fluid injection rate has a significant impact on reservoir fracturing, and in the same area, using high displacement injection can significantly increase the volume of reservoir reconstruction. This study can provide some reference for multi-cluster fracturing construction in deep reservoirs.

Nonlocal interfaces accounting for progressive damage within continuum-kinematics-inspired peridynamics

In this work, we present a modeling approach to nonlocal material interfaces in the framework of continuum-kinematics-inspired peridynamics. The nonlocal model accounts for progressive damage within a finite-thickness interface, as opposed to the more common practice of abrupt bond breakage across a zero-thickness interface. Our approach is based on an overlap of the constituents within the interface. Interfacial bonds between initially overlapping partner points are governed by a constitutive law reminiscent of a traction-separation-law. The governing equations for continuum-kinematics-inspired peridynamics in the presence of an interface are derived using a rate-variational principle. The damage formulation is established using the classical concept of internal variables. Following the notion of a standard dissipative material, thermodynamic consistency of the constitutive laws and the evolution of the internal variables is ensured. The latter results in a straightforward evaluation of a damage function. We give details about the computational implementation comprising a peridynamic discretization and a Newton–Raphson scheme. A sound approach to approximate the interface normal during deformation is presented, which allows to penalize material penetration across the interface. The proposed model is explored in a series of numerical examples, i.e., classical peeling and shearing tests, for a variety of damage functions. A key feature of our interface model are the nonlocal characteristics that are assumed to play a role especially at small scales. We, first, observe that an increasing thickness of the nonlocal interface leads to stronger interfacial bonding and less damage. Second, an increase in horizon size results in stiffer material behavior. When studying the wrinkling and delamination behavior of a compressed bilayer, it is found that an increase in interface stiffness leads to a smaller wrinkling wavelength. Moreover, delamination due to progressive damage of interfacial bonds in the post-wrinkling regime is observed, which, to the best of our knowledge, has not been studied in a nonlocal model before.