Pub Date : 2025-01-30DOI: 10.1016/j.mechmat.2025.105266
Yen-Ling Chung, Kun-Lin Lee
Functionally Graded Materials (FGMs) with constant Young's modulus and Poisson's ratio but varying thermal expansion coefficients termed are the focus of this study. The objective is to evaluate the thermal stress intensity factors (TSIF) of interface cracks in under thermal loading using the Boundary Element Method (BEM). The thermal loading on , equated to body forces, is addressed by deriving a particular solution to Navier's equation through Fourier series expansion. This enables the application of BEM without necessitating kernel function modifications. Then with this particular solution integrated, the boundary conditions of the homogeneous problem are defined. Subsequently, the homogeneous solution is computed using the multi-region BEM. Finally, the complete solutions are obtained by combining both the homogeneous and particular solutions. This study evaluates the TSIFs of an edge crack in a single-layer and an interface crack in a two-layer. . under temperature loadings. The correlations between TSIF, bi-material characteristics, thermal expansion coefficient mismatch, and varying crack lengths are under investigation.
{"title":"Evaluation of thermal stress intensity factors of an interface crack in FGMs with varying thermal expansion coefficient by multi-region BEM","authors":"Yen-Ling Chung, Kun-Lin Lee","doi":"10.1016/j.mechmat.2025.105266","DOIUrl":"10.1016/j.mechmat.2025.105266","url":null,"abstract":"<div><div>Functionally Graded Materials (FGMs) with constant Young's modulus and Poisson's ratio but varying thermal expansion coefficients termed <span><math><mrow><mi>α</mi><mtext>FGM</mtext></mrow></math></span> are the focus of this study. The objective is to evaluate the thermal stress intensity factors (TSIF) of interface cracks in <span><math><mrow><mi>α</mi><mtext>FGMs</mtext></mrow></math></span> under thermal loading using the Boundary Element Method (BEM). The thermal loading on <span><math><mrow><mi>α</mi><mtext>FGM</mtext></mrow></math></span>, equated to body forces, is addressed by deriving a particular solution to Navier's equation through Fourier series expansion. This enables the application of BEM without necessitating kernel function modifications. Then with this particular solution integrated, the boundary conditions of the homogeneous problem are defined. Subsequently, the homogeneous solution is computed using the multi-region BEM. Finally, the complete solutions are obtained by combining both the homogeneous and particular solutions. This study evaluates the TSIFs of an edge crack in a single-layer <span><math><mrow><mi>α</mi><mtext>FGM</mtext></mrow></math></span> and an interface crack in a two-layer. <span><math><mrow><mi>α</mi><mtext>FGM</mtext></mrow></math></span>. under temperature loadings. The correlations between TSIF, bi-material characteristics, thermal expansion coefficient mismatch, and varying crack lengths are under investigation.</div></div>","PeriodicalId":18296,"journal":{"name":"Mechanics of Materials","volume":"203 ","pages":"Article 105266"},"PeriodicalIF":3.4,"publicationDate":"2025-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143387419","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-30DOI: 10.1016/j.mechmat.2025.105264
J.L. Dequiedt
The fragmentation of a one-dimensional expanding structure under dynamic loading conditions is analyzed, since the early work of Mott, as a competition between the activation of local defects and the inhibition of other ones by release fronts emitted when defect failure occurs. The celerity of these so-called Mott waves is computed under the assumption of immediate defect stress relaxation at failure time and it controls inhibition. However, in ductile metals, defects consist in progressively forming localized necks breaking by a process coupling plasticity and ductile failure, i.e., pore growth and coalescence. Failure is thus a non-instantaneous and dissipative process and the defect interaction problem is more complex. On the one hand, the propagation of release fronts is delayed and their celerity is a function of the effective cohesive model governing defect evolution. On the other hand, when the release fronts emitted by two neighboring defects meet as they are still opening, their subsequent evolution is driven by the interplay between the inertia of the block separating them and the evolution of the two cohesive stresses: defect unloading before complete opening occurs in some cases. The whole structure fragmentation process then involves broken, partially open (arrested necks) and inhibited defects and lead to fragment sets different from the ones predicted under the Mott assumption.
{"title":"Dynamic fragmentation of expanding ductile structures: Defect opening, stress release fronts and cohesive zone interactions","authors":"J.L. Dequiedt","doi":"10.1016/j.mechmat.2025.105264","DOIUrl":"10.1016/j.mechmat.2025.105264","url":null,"abstract":"<div><div>The fragmentation of a one-dimensional expanding structure under dynamic loading conditions is analyzed, since the early work of Mott, as a competition between the activation of local defects and the inhibition of other ones by release fronts emitted when defect failure occurs. The celerity of these so-called Mott waves is computed under the assumption of immediate defect stress relaxation at failure time and it controls inhibition. However, in ductile metals, defects consist in progressively forming localized necks breaking by a process coupling plasticity and ductile failure, i.e., pore growth and coalescence. Failure is thus a non-instantaneous and dissipative process and the defect interaction problem is more complex. On the one hand, the propagation of release fronts is delayed and their celerity is a function of the effective cohesive model governing defect evolution. On the other hand, when the release fronts emitted by two neighboring defects meet as they are still opening, their subsequent evolution is driven by the interplay between the inertia of the block separating them and the evolution of the two cohesive stresses: defect unloading before complete opening occurs in some cases. The whole structure fragmentation process then involves broken, partially open (arrested necks) and inhibited defects and lead to fragment sets different from the ones predicted under the Mott assumption.</div></div>","PeriodicalId":18296,"journal":{"name":"Mechanics of Materials","volume":"203 ","pages":"Article 105264"},"PeriodicalIF":3.4,"publicationDate":"2025-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143378017","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-29DOI: 10.1016/j.mechmat.2025.105273
Taiwei Liu , Fuyou Liang
The hierarchical structure and heterogeneous composition of the myocardial tissue and the differential mechanical properties of myocardial components together make the mechanical behaviors of the left ventricle (LV) highly complex. In the present study, we developed a microstructure-based (MB) finite element model to quantify the time-varying myocardial mechanics of the LV during an entire cardiac cycle while accounting for the mechanical states of individual myocardial components. The modeling work started from building constitutive models for individual myocardial components based on their microstructure and mechanical properties, followed by combining them to form an integrated constitutive model of myocardial micro-tissue that was programmed on the discretized finite elements of the myocardium. Verification/validation studies performed at multiple scale levels demonstrated the good performances of the modeling methods. Numerical simulation for a normal LV reasonably reproduced the typical pressure-volume loop, demonstrated the spatiotemporal changes in myocardial displacement and stress over a cardiac cycle, and revealed the differential mechanical states of cardiomyocytes located in different myocardial regions. Furthermore, the model was applied to address the impact of regional replacement fibrosis. The results showed that replacement fibrosis impaired both the diastolic and the systolic functions, altered the spatial distributions of myocardial displacement and stress, and reduced the systolic cardiomyocyte stress in the fibrotic myocardial region. In summary, the study demonstrated the significance of accounting for the MB mechanical properties of myocardium when modeling the mechanical behaviors of the LV, and the model may contribute as a useful tool for addressing biomechanical problems related to cardiomyopathies.
{"title":"A microstructure-based finite element model of the human left ventricle for simulating the trans-scale myocardial mechanical behaviors","authors":"Taiwei Liu , Fuyou Liang","doi":"10.1016/j.mechmat.2025.105273","DOIUrl":"10.1016/j.mechmat.2025.105273","url":null,"abstract":"<div><div>The hierarchical structure and heterogeneous composition of the myocardial tissue and the differential mechanical properties of myocardial components together make the mechanical behaviors of the left ventricle (LV) highly complex. In the present study, we developed a microstructure-based (MB) finite element model to quantify the time-varying myocardial mechanics of the LV during an entire cardiac cycle while accounting for the mechanical states of individual myocardial components. The modeling work started from building constitutive models for individual myocardial components based on their microstructure and mechanical properties, followed by combining them to form an integrated constitutive model of myocardial micro-tissue that was programmed on the discretized finite elements of the myocardium. Verification/validation studies performed at multiple scale levels demonstrated the good performances of the modeling methods. Numerical simulation for a normal LV reasonably reproduced the typical pressure-volume loop, demonstrated the spatiotemporal changes in myocardial displacement and stress over a cardiac cycle, and revealed the differential mechanical states of cardiomyocytes located in different myocardial regions. Furthermore, the model was applied to address the impact of regional replacement fibrosis. The results showed that replacement fibrosis impaired both the diastolic and the systolic functions, altered the spatial distributions of myocardial displacement and stress, and reduced the systolic cardiomyocyte stress in the fibrotic myocardial region. In summary, the study demonstrated the significance of accounting for the MB mechanical properties of myocardium when modeling the mechanical behaviors of the LV, and the model may contribute as a useful tool for addressing biomechanical problems related to cardiomyopathies.</div></div>","PeriodicalId":18296,"journal":{"name":"Mechanics of Materials","volume":"203 ","pages":"Article 105273"},"PeriodicalIF":3.4,"publicationDate":"2025-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143349493","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-27DOI: 10.1016/j.mechmat.2025.105272
Molin Sun , Cheng Huang , Ming Dai
Solutions for the elastic field in a perforated structure induced by internal loadings play an essential role in a variety of branches of engineering and applied sciences including pressure vessels and mechanics of biological tissues. In this paper, we reconsider the plane deformation problem of an elastic medium containing an elliptical hole under internal pressure. In contrast to the classical solution for this problem in which the local stress field around the elliptical hole is independent of the stiffness of the surrounding medium, we present a modified closed-form solution incorporating the ratio of the internal pressure to the modulus of the medium by taking into account the directional change of the internal pressure during deformation. We show via large deformation-based finite element simulations of a hyperelastic solid with a pressurized elliptical hole that the modified solution is indeed more accurate than the classical counterpart in predicting the local elastic field and is capable of capturing, to some extent, the nonlinear elastic response of the perforated solid to the internal pressure. In particular, we attain a stiffness-dependent stress intensity factor at the tips of the hole when it tends to a slender crack. Numerical examples are also presented to illustrate the detailed differences between the modified and classical solutions relative to the aspect ratio of the elliptical hole.
{"title":"Stress concentration around a pressurized elliptical hole in a soft elastic solid: Modified results and nonlinear effects","authors":"Molin Sun , Cheng Huang , Ming Dai","doi":"10.1016/j.mechmat.2025.105272","DOIUrl":"10.1016/j.mechmat.2025.105272","url":null,"abstract":"<div><div>Solutions for the elastic field in a perforated structure induced by internal loadings play an essential role in a variety of branches of engineering and applied sciences including pressure vessels and mechanics of biological tissues. In this paper, we reconsider the plane deformation problem of an elastic medium containing an elliptical hole under internal pressure. In contrast to the classical solution for this problem in which the local stress field around the elliptical hole is independent of the stiffness of the surrounding medium, we present a modified closed-form solution incorporating the ratio of the internal pressure to the modulus of the medium by taking into account the directional change of the internal pressure during deformation. We show via large deformation-based finite element simulations of a hyperelastic solid with a pressurized elliptical hole that the modified solution is indeed more accurate than the classical counterpart in predicting the local elastic field and is capable of capturing, to some extent, the nonlinear elastic response of the perforated solid to the internal pressure. In particular, we attain a stiffness-dependent stress intensity factor at the tips of the hole when it tends to a slender crack. Numerical examples are also presented to illustrate the detailed differences between the modified and classical solutions relative to the aspect ratio of the elliptical hole.</div></div>","PeriodicalId":18296,"journal":{"name":"Mechanics of Materials","volume":"203 ","pages":"Article 105272"},"PeriodicalIF":3.4,"publicationDate":"2025-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143161115","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper introduces curvilinear fiber laminated plates into the design of phononic crystal structures, proposing a model of periodic curvilinear fiber laminated plates and establishing a framework for band gap analysis. Specifically, we compare the band gap calculation results obtained using the finite element method (FEM) with those obtained using the plane wave expansion method, verifying the accuracy of our numerical approach. Based on this, we compare the band gap characteristics of curvilinear fibers and straight fibers, finding that the inclusion of curvilinear fibers significantly enhances the low-frequency band gap performance of the structure. Furthermore, we analyze the influence of the curvilinear fiber orientation parameters, discovering that these parameters affect the band gap characteristics of the structure. By adjusting the curvilinear fiber orientation parameters, it is possible to tailor the band gap properties to meet specific engineering requirements, greatly enhancing the design flexibility of the structure. Finally, we investigate the propagation of waves in various directions within the periodic curvilinear fiber laminated plates. Studies indicate that wave propagation in curvilinear fiber laminated plates exhibits more complex phenomena compared to straight fiber laminated plates. The patterns of wave energy flow also validate the effectiveness of the band gap.
{"title":"Numerical simulation of band gap characteristics for periodically arranged curvilinear fiber laminated plates","authors":"Houan Ma , Zixu Xia , Yu Cong , Shuitao Gu , Liqun Xiao","doi":"10.1016/j.mechmat.2025.105265","DOIUrl":"10.1016/j.mechmat.2025.105265","url":null,"abstract":"<div><div>This paper introduces curvilinear fiber laminated plates into the design of phononic crystal structures, proposing a model of periodic curvilinear fiber laminated plates and establishing a framework for band gap analysis. Specifically, we compare the band gap calculation results obtained using the finite element method (FEM) with those obtained using the plane wave expansion method, verifying the accuracy of our numerical approach. Based on this, we compare the band gap characteristics of curvilinear fibers and straight fibers, finding that the inclusion of curvilinear fibers significantly enhances the low-frequency band gap performance of the structure. Furthermore, we analyze the influence of the curvilinear fiber orientation parameters, discovering that these parameters affect the band gap characteristics of the structure. By adjusting the curvilinear fiber orientation parameters, it is possible to tailor the band gap properties to meet specific engineering requirements, greatly enhancing the design flexibility of the structure. Finally, we investigate the propagation of waves in various directions within the periodic curvilinear fiber laminated plates. Studies indicate that wave propagation in curvilinear fiber laminated plates exhibits more complex phenomena compared to straight fiber laminated plates. The patterns of wave energy flow also validate the effectiveness of the band gap.</div></div>","PeriodicalId":18296,"journal":{"name":"Mechanics of Materials","volume":"203 ","pages":"Article 105265"},"PeriodicalIF":3.4,"publicationDate":"2025-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143161112","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-25DOI: 10.1016/j.mechmat.2025.105258
Alexander Dyck , Johannes Gisy , Frederik Hille , Stefan Wagner , Astrid Pundt , Thomas Böhlke
For the usage of intercalating material systems to store and convert energy of renewable sources, their phase stabilities need to be engineered to adjust to the desired operation conditions. This can, e.g., be achieved by miniaturization, leading to constraints that modify the systems thermodynamics. The experimental investigation of such systems is cumbersome, as experiments on nano-sized systems are time intensive. Numerical simulations based on chemo-mechanically coupled continuum models can serve as a tool helping to understand these systems and to study different effects of miniaturization. In this work we present a phase-field model for the example of open, constrained metal hydrogen thin film systems, that allows the prediction of the hydrogen intercalation and hydride formation. The model relies on a free energy density consisting of chemical, mechanical and interfacial parts. The first two contributions are based on measurements of the thermodynamics of open Niobium–Hydrogen thin films, that are chosen as a model. The interfacial contribution of Cahn–Hilliard-type introduces a phase-field description for both phases. To study the systems behavior a numerical implementation in the commercial Finite Element solver ABAQUS is presented. Numerical results are presented and compared to previously obtained experimental results on the open systems thermodynamics. We show, that the model is capable of reproducing experimentally observed behavior of thin films especially regarding the coexistence of - and hydride-phase in thermodynamic equilibrium, where the equilibrium concentrations in both phases drastically differ from bulk values, and gradients in concentration and stresses result due to the interfacial constraint conditions.
{"title":"Hydride formation in open thin film metal hydrogen systems: Cahn–Hilliard-type phase-field simulations coupled to elasto-plastic deformations","authors":"Alexander Dyck , Johannes Gisy , Frederik Hille , Stefan Wagner , Astrid Pundt , Thomas Böhlke","doi":"10.1016/j.mechmat.2025.105258","DOIUrl":"10.1016/j.mechmat.2025.105258","url":null,"abstract":"<div><div>For the usage of intercalating material systems to store and convert energy of renewable sources, their phase stabilities need to be engineered to adjust to the desired operation conditions. This can, e.g., be achieved by miniaturization, leading to constraints that modify the systems thermodynamics. The experimental investigation of such systems is cumbersome, as experiments on nano-sized systems are time intensive. Numerical simulations based on chemo-mechanically coupled continuum models can serve as a tool helping to understand these systems and to study different effects of miniaturization. In this work we present a phase-field model for the example of open, constrained metal hydrogen thin film systems, that allows the prediction of the hydrogen intercalation and hydride formation. The model relies on a free energy density consisting of chemical, mechanical and interfacial parts. The first two contributions are based on measurements of the thermodynamics of open Niobium–Hydrogen thin films, that are chosen as a model. The interfacial contribution of Cahn–Hilliard-type introduces a phase-field description for both phases. To study the systems behavior a numerical implementation in the commercial Finite Element solver ABAQUS is presented. Numerical results are presented and compared to previously obtained experimental results on the open systems thermodynamics. We show, that the model is capable of reproducing experimentally observed behavior of thin films especially regarding the coexistence of <span><math><mi>α</mi></math></span>- and hydride-phase in thermodynamic equilibrium, where the equilibrium concentrations in both phases drastically differ from bulk values, and gradients in concentration and stresses result due to the interfacial constraint conditions.</div></div>","PeriodicalId":18296,"journal":{"name":"Mechanics of Materials","volume":"203 ","pages":"Article 105258"},"PeriodicalIF":3.4,"publicationDate":"2025-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143161118","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-24DOI: 10.1016/j.mechmat.2025.105269
Xiaotian Mao, Fulin Shang
Polymers exhibit complex mechanical behaviors during curing process, ranging from viscous liquids to elastic solids, which are linked to the dynamic processes of the highly flexible polymer chains. However, these physical insights have not been fully integrated into the development of continuum model of viscoelasticity. Based on chain statistical mechanics, a molecular-derived constitutive model is developed to provide molecular picture that underlies the viscoelasticity of soft polymers during cure. The polymer network is assumed to comprise the entangled chain and crosslinked strands. At first, the stress evolution of a single entangled chain is derived from its dynamic process based on polymer dynamics. Then the effect of curing reaction on the dynamic process is analyzed by statistically describing the evolution of the network structure during cure. Finally, the stress constitutive equation of the whole network is derived based on the affine deformation assumption. The underlying molecular meanings of viscoelastic measurements such as the temperature shift factor, the cure shift factor and the relaxation spectrum, are demonstrated by the proposed model. Further, the connection between viscoelastic measurements and molecular dynamics as well as the physical foundation of the constitutive form is discussed.
{"title":"A molecular-derived constitutive model of viscoelasticity based on chain statistical mechanics of polymers during cure","authors":"Xiaotian Mao, Fulin Shang","doi":"10.1016/j.mechmat.2025.105269","DOIUrl":"10.1016/j.mechmat.2025.105269","url":null,"abstract":"<div><div>Polymers exhibit complex mechanical behaviors during curing process, ranging from viscous liquids to elastic solids, which are linked to the dynamic processes of the highly flexible polymer chains. However, these physical insights have not been fully integrated into the development of continuum model of viscoelasticity. Based on chain statistical mechanics, a molecular-derived constitutive model is developed to provide molecular picture that underlies the viscoelasticity of soft polymers during cure. The polymer network is assumed to comprise the entangled chain and crosslinked strands. At first, the stress evolution of a single entangled chain is derived from its dynamic process based on polymer dynamics. Then the effect of curing reaction on the dynamic process is analyzed by statistically describing the evolution of the network structure during cure. Finally, the stress constitutive equation of the whole network is derived based on the affine deformation assumption. The underlying molecular meanings of viscoelastic measurements such as the temperature shift factor, the cure shift factor and the relaxation spectrum, are demonstrated by the proposed model. Further, the connection between viscoelastic measurements and molecular dynamics as well as the physical foundation of the constitutive form is discussed.</div></div>","PeriodicalId":18296,"journal":{"name":"Mechanics of Materials","volume":"203 ","pages":"Article 105269"},"PeriodicalIF":3.4,"publicationDate":"2025-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143160602","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-23DOI: 10.1016/j.mechmat.2025.105271
Bharath Antarvedi Goda, Mattia Bacca
Cutting mechanics in soft solids present a complex challenge due to the intricate behavior of soft ductile materials as they undergo crack nucleation and propagation. Recent research has explored the relationship between the cutting force needed to continuously cut a soft material and the radius of the wire (blade). A typical simplifying assumption is that of material incompressibility, albeit no material in nature is really incompressible. In this study, we relax this assumption and examine how material (in)compressibility influences the correlation between cutting forces and material properties like toughness and modulus. The ratio , where and are the shear and bulk moduli, indicates the material's degree of compressibility, where incompressible materials have , and larger provide higher volumetric compressibility. We observe that the cutting forces are controlled by the ratio between the cutting wire radius and the elasto-cohesive length of the material (proportional to the critical crack opening displacement at crack propagation under uniaxial tension), where is the toughness of the material. Following previous observations, we have two cutting regimes: (i) high (small wire), and (ii) low (large wire). Regime (i) is dominated by frictional dissipation, while regime (ii) is dominated by adhesive debonding and/or the wear resistance of the material. In the large radius regime (ii), our theoretical findings reveal that incompressible materials require larger forces (e.g., requiring half force compared to incompressible, ), while in the small radius regime (i) we observe the opposite trend. Notably, the transition wire radius between regimes (i) and (ii) also depend on compressibility, and is larger for compressible materials. Thus, material compressibility favors friction-domination for a given wire radius.
{"title":"Cutting mechanics of soft compressible solids – Force-radius scaling versus bulk modulus","authors":"Bharath Antarvedi Goda, Mattia Bacca","doi":"10.1016/j.mechmat.2025.105271","DOIUrl":"10.1016/j.mechmat.2025.105271","url":null,"abstract":"<div><div>Cutting mechanics in soft solids present a complex challenge due to the intricate behavior of soft ductile materials as they undergo crack nucleation and propagation. Recent research has explored the relationship between the cutting force needed to continuously cut a soft material and the radius of the wire (blade). A typical simplifying assumption is that of material incompressibility, albeit no material in nature is really incompressible. In this study, we relax this assumption and examine how material (in)compressibility influences the correlation between cutting forces and material properties like toughness and modulus. The ratio <span><math><mrow><mi>μ</mi><mo>/</mo><mi>K</mi></mrow></math></span>, where <span><math><mrow><mi>μ</mi></mrow></math></span> and <span><math><mrow><mi>K</mi></mrow></math></span> are the shear and bulk moduli, indicates the material's degree of compressibility, where incompressible materials have <span><math><mrow><mi>μ</mi><mo>/</mo><mi>K</mi><mo>=</mo><mn>0</mn></mrow></math></span>, and larger <span><math><mrow><mi>μ</mi><mo>/</mo><mi>K</mi></mrow></math></span> provide higher volumetric compressibility. We observe that the cutting forces are controlled by the ratio between the cutting wire radius <span><math><mrow><msub><mi>R</mi><mi>w</mi></msub></mrow></math></span> and the elasto-cohesive length <span><math><mrow><msub><mi>L</mi><mi>e</mi></msub><mo>=</mo><mi>Γ</mi><mo>/</mo><mi>μ</mi></mrow></math></span> of the material (proportional to the critical crack opening displacement at crack propagation under uniaxial tension), where <span><math><mrow><mi>Γ</mi></mrow></math></span> is the toughness of the material. Following previous observations, we have two cutting regimes: (i) high <span><math><mrow><msub><mi>L</mi><mi>e</mi></msub><mo>/</mo><msub><mi>R</mi><mi>w</mi></msub></mrow></math></span> (small wire), and (ii) low <span><math><mrow><msub><mi>L</mi><mi>e</mi></msub><mo>/</mo><msub><mi>R</mi><mi>w</mi></msub></mrow></math></span> (large wire). Regime (i) is dominated by frictional dissipation, while regime (ii) is dominated by adhesive debonding and/or the wear resistance of the material. In the large radius regime (ii), our theoretical findings reveal that incompressible materials require larger forces (<em>e.g.</em>, <span><math><mrow><mi>K</mi><mo>=</mo><mi>μ</mi></mrow></math></span> requiring half force compared to incompressible, <span><math><mrow><mi>K</mi><mo>≫</mo><mi>μ</mi></mrow></math></span>), while in the small radius regime (i) we observe the opposite trend. Notably, the transition wire radius between regimes (i) and (ii) also depend on compressibility, and is larger for compressible materials. Thus, material compressibility favors friction-domination for a given wire radius.</div></div>","PeriodicalId":18296,"journal":{"name":"Mechanics of Materials","volume":"203 ","pages":"Article 105271"},"PeriodicalIF":3.4,"publicationDate":"2025-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143299416","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-22DOI: 10.1016/j.mechmat.2025.105261
Zhenyu Fan , Duo Li , Xianqi Lei , Yujie Wei
Crosslinked polymeric films are widely used as a bonding component in flexible electronic devices. The ultra-thin polymeric materials are often transversely isotropic and visco-hyperelastic in response to a wide range of strains. The mechanical properties of such adhesives are a crucial part of the design process and device reliability evaluation. In this paper, we perform systematic investigation by characterizing the mechanical behavior of a typical group of optically clear adhesives (OCAs). By including the influence of pendant chains on the mechanical behaviors of OCAs under different loading conditions, we propose a network-based constitutive model for those OCAs, where a hyperelastic response originates from the crosslinked and entanglement networks and a viscous effect comes from free chains and pendant chains. The model is applied to predict the mechanical response of four commercially available 3M OCAs. Results show that our model can predict the mechanical response of OCAs well. We expect the experiment observation and the developed modelling may help in understanding the mechanical behavior of a wide range of polymeric adhesives for engineering practice.
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Pub Date : 2025-01-21DOI: 10.1016/j.mechmat.2025.105268
Xiao Tian, Pengfei Ying, Yong Xia
This study expands on the layered structure model established in part Ⅰ to predict the fracture behavior of polymer-metal-polymer film (PMPF). To capture the fracture behavior of PMPF, the all-boundary cohesive zone model (ABCZM) is adopted, which involves inserting cohesive elements between all continuum element boundaries in potential fracture areas. This allows for the evaluation of the damage behavior of components by FE simulation. To enable the ABCZM in shell assembly, a specific shell cohesive element is introduced. Fracture parameters are identified through the double-edge notched tension, and the fracture response of PMPF is predicted under circular notched tension with different radii. The convergence of the mesh size in ABCZM is discussed, and it is found that a similar fracture behavior of PMPF can be achieved by satisfying a specific relation between the mesh size and fracture parameters. Furthermore, the fracture behavior of the punch test of PMPF is investigated and analyzed through ABCZM, demonstrating its progressiveness in predicting potential cracking paths of PMPF in engineering scenarios.
{"title":"Modeling the large deformation and fracture of polymer-metal-polymer film composites – Part Ⅱ: Fracture behaviors","authors":"Xiao Tian, Pengfei Ying, Yong Xia","doi":"10.1016/j.mechmat.2025.105268","DOIUrl":"10.1016/j.mechmat.2025.105268","url":null,"abstract":"<div><div>This study expands on the layered structure model established in part Ⅰ to predict the fracture behavior of polymer-metal-polymer film (PMPF). To capture the fracture behavior of PMPF, the all-boundary cohesive zone model (ABCZM) is adopted, which involves inserting cohesive elements between all continuum element boundaries in potential fracture areas. This allows for the evaluation of the damage behavior of components by FE simulation. To enable the ABCZM in shell assembly, a specific shell cohesive element is introduced. Fracture parameters are identified through the double-edge notched tension, and the fracture response of PMPF is predicted under circular notched tension with different radii. The convergence of the mesh size in ABCZM is discussed, and it is found that a similar fracture behavior of PMPF can be achieved by satisfying a specific relation between the mesh size and fracture parameters. Furthermore, the fracture behavior of the punch test of PMPF is investigated and analyzed through ABCZM, demonstrating its progressiveness in predicting potential cracking paths of PMPF in engineering scenarios.</div></div>","PeriodicalId":18296,"journal":{"name":"Mechanics of Materials","volume":"203 ","pages":"Article 105268"},"PeriodicalIF":3.4,"publicationDate":"2025-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143161113","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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