Strain Relation

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Xiao-ping Zhou - One of the best experts on this subject based on the ideXlab platform.

  • localization of deformation and stress Strain Relation for mesoscopic heterogeneous brittle rock materials under unloading
    Theoretical and Applied Fracture Mechanics, 2005
    Co-Authors: Xiao-ping Zhou
    Abstract:

    Abstract Stress redistribution induced by excavation of underground engineering and slope engineering results in the unloading zone in parts of surrounding rock masses. The mechanical behaviors of crack-weakened rock masses under unloading are different from those of crack-weakened rock masses under loading. A micromechanics-based model has been proposed for brittle rock material undergoing irreversible changes of their microscopic structures due to microcrack growth when axial stress is held constant while lateral confinement is reduced. The basic idea of the present model is to classify the constitution Relation of rock material into four stages including some of the stages of linear elasticity, pre-peak nonlinear hardening, rapid stress drop, and Strain softening, and to investigate their corresponding micromechanical damage mechanisms individually. Special attention is paid to the transition from structure rearrangements on microscale to the macroscopic inelastic Strain, to the transition from distribution damage to localization of damage and the transition from homogeneous deformation to localization of deformation. The closed-form explicit expression for the complete stress–Strain Relation of rock materials containing cracks under unloading is obtained. The results show that the complete stress–Strain Relation and the strength of rock materials under unloading depend on the crack spacing, the fracture toughness of rock materials, orientation of the cracks, the crack half-length and the crack density parameter.

  • Localization of deformation and stress–Strain Relation for mesoscopic heterogeneous brittle rock materials under unloading
    Theoretical and Applied Fracture Mechanics, 2005
    Co-Authors: Xiao-ping Zhou
    Abstract:

    Abstract Stress redistribution induced by excavation of underground engineering and slope engineering results in the unloading zone in parts of surrounding rock masses. The mechanical behaviors of crack-weakened rock masses under unloading are different from those of crack-weakened rock masses under loading. A micromechanics-based model has been proposed for brittle rock material undergoing irreversible changes of their microscopic structures due to microcrack growth when axial stress is held constant while lateral confinement is reduced. The basic idea of the present model is to classify the constitution Relation of rock material into four stages including some of the stages of linear elasticity, pre-peak nonlinear hardening, rapid stress drop, and Strain softening, and to investigate their corresponding micromechanical damage mechanisms individually. Special attention is paid to the transition from structure rearrangements on microscale to the macroscopic inelastic Strain, to the transition from distribution damage to localization of damage and the transition from homogeneous deformation to localization of deformation. The closed-form explicit expression for the complete stress–Strain Relation of rock materials containing cracks under unloading is obtained. The results show that the complete stress–Strain Relation and the strength of rock materials under unloading depend on the crack spacing, the fracture toughness of rock materials, orientation of the cracks, the crack half-length and the crack density parameter.

  • Bounds on the complete stress–Strain Relation for a crack-weakened rock mass under compressive loads
    International Journal of Solids and Structures, 2004
    Co-Authors: Xiao-ping Zhou, Yong-xing Zhang, Qiu-ling Ha
    Abstract:

    Abstract The interactions among multiple parallel sliding cracks in rock materials are examined asymptotically in an explicit and quantitative manner in order to reveal fully their so-called shielding and magnification effects on the complete stress–Strain Relation. Based on the micromechanical framework and the asymptotic analysis, analytical upper and lower bounds are proposed for the complete stress–Strain Relation for rock masses containing multiple rows of echelon cracks. The present model studies further influence of both the interaction among crack rows and mutual collinear interaction on the constitutive Relation and strength for a crack-weakened rock mass. The closed-form explicit expression for the complete stress–Strain Relation of rock masses containing echelon cracks subjected to compressive loads is obtained. The complete stress–Strain Relation includes the stages of linear elasticity, nonlinear hardening, Strain softening. The results show that the complete stress–Strain Relation and the strength of a crack-weakened rock mass depend on the crack interface friction coefficient, the sliding crack spacing, the fracture toughness of rock materials, orientation of cracks, the crack half-length and the crack density parameter.

  • analysis of the localization of deformation and the complete stress Strain Relation for mesoscopic heterogeneous brittle rock under dynamic uniaxial tensile loading
    International Journal of Solids and Structures, 2004
    Co-Authors: Xiao-ping Zhou
    Abstract:

    Abstract Stress redistribution induced by excavation results in the tensile zone in parts of the surrounding rock mass. It is significant to analyze the localization of deformation and damage, and to study the complete stress–Strain Relation for mesoscopic heterogeneous rock under dynamic uniaxial tensile loading. On the basis of micromechanics, the complete stress–Strain Relation including linear elasticity, nonlinear hardening, rapid stress drop and Strain softening is obtained. The behaviors of rapid stress drop and Strain softening are due to localization of deformation and damage. The constitutive model, which analyze localization of deformation and damage, is distinct from the conventional model. Theoretical predictions have shown to consistent with the experimental results.

  • Analysis of the localization of deformation and the complete stress–Strain Relation for mesoscopic heterogeneous brittle rock under dynamic uniaxial tensile loading
    International Journal of Solids and Structures, 2004
    Co-Authors: Xiao-ping Zhou
    Abstract:

    Abstract Stress redistribution induced by excavation results in the tensile zone in parts of the surrounding rock mass. It is significant to analyze the localization of deformation and damage, and to study the complete stress–Strain Relation for mesoscopic heterogeneous rock under dynamic uniaxial tensile loading. On the basis of micromechanics, the complete stress–Strain Relation including linear elasticity, nonlinear hardening, rapid stress drop and Strain softening is obtained. The behaviors of rapid stress drop and Strain softening are due to localization of deformation and damage. The constitutive model, which analyze localization of deformation and damage, is distinct from the conventional model. Theoretical predictions have shown to consistent with the experimental results.

Kenzu Abdella - One of the best experts on this subject based on the ideXlab platform.

  • inversion of three stage stress Strain Relation for stainless steel in tension and compression
    Journal of Constructional Steel Research, 2011
    Co-Authors: Kenzu Abdella, Ruqaiya Ammar Thannon, Aisha Ibrahim Mehri, Fatima Ahmed Alshaikh
    Abstract:

    Abstract Presented in this paper is a new stress–Strain Relation for stainless steel alloys that provides the stress as an explicit function of the Strain. The Relation is an approximate inversion of a recently proposed three-stage stress–Strain Relation based on a modified Ramberg–Osgood equation. The three-stage Relation is a much more accurate formulation than the previous two-stage formulations and is applicable to both tensile as well as compressive stresses. The new Relation is derived by making a rational function assumption on the fractional deviation of the actual stress–Strain curve from an idealized linear elastic behaviour. The new expression is valid over the full range of the stress well beyond the elastic region. The validity of the inverted expression is tested over a wide range of material parameters. These tests demonstrate that, the new expression results in stress–Strain curves which are both qualitatively and quantitatively in excellent agreement with the fully iterated numerical solution of the full-range stress–Strain Relation with a maximum error below 4%.

  • Inversion of three-stage stress–Strain Relation for stainless steel in tension and compression
    Journal of Constructional Steel Research, 2011
    Co-Authors: Kenzu Abdella, Ruqaiya Ammar Thannon, Aisha Ibrahim Mehri, Fatima Ahmed Alshaikh
    Abstract:

    Abstract Presented in this paper is a new stress–Strain Relation for stainless steel alloys that provides the stress as an explicit function of the Strain. The Relation is an approximate inversion of a recently proposed three-stage stress–Strain Relation based on a modified Ramberg–Osgood equation. The three-stage Relation is a much more accurate formulation than the previous two-stage formulations and is applicable to both tensile as well as compressive stresses. The new Relation is derived by making a rational function assumption on the fractional deviation of the actual stress–Strain curve from an idealized linear elastic behaviour. The new expression is valid over the full range of the stress well beyond the elastic region. The validity of the inverted expression is tested over a wide range of material parameters. These tests demonstrate that, the new expression results in stress–Strain curves which are both qualitatively and quantitatively in excellent agreement with the fully iterated numerical solution of the full-range stress–Strain Relation with a maximum error below 4%.

  • Inversion of a three-stage full-range stress-Strain Relation for stainless steel alloys
    2010
    Co-Authors: Kenzu Abdella, Ruqaiya Ammar Thannon, Aisha Ibrahim Mehri, Fatima Ahmed Alshaik
    Abstract:

    Presented in this paper is a new stress-Strain Relation for stainless steel alloys that provides the stress as an explicit function of the Strain. The Relation is an approximate inversion of a recently proposed three-stage stress-Strain Relation based on a modified Ramberg-Osgood equation. The new Relation is derived by making a rational function assumption on the fractional deviation of the actual stress-Strain curve from an idealized linear elastic behaviour. The new expression is valid over the fullrange of the stress well beyond the elastic region. The validity of the inverted expression is tested over a wide range of material parameters. These tests demonstrate that, the new expression results in stress-Strain curves which are both qualitatively and quantitatively in excellent agreement with experimental results and the fully iterated numerical solution of the full-range stresss-train Relation.

  • inversion of a full range stress Strain Relation for stainless steel alloys
    International Journal of Non-linear Mechanics, 2006
    Co-Authors: Kenzu Abdella
    Abstract:

    Abstract This paper presents an approximate inversion of the stress–Strain Relation for stainless steel alloys. Using currently available stress–Strain Relations based on a modified Ramberg–Osgood equation, a new expression for the stress σ as an explicit function of the total Strain e is obtained. The new expression is valid over the full-range of the stress well beyond the 0.2 % proof stress σ 0.2 , defined as the stress level corresponding to the plastic Strain value of 0.2 % . The validity of the inverted expression is tested over a wide range of material parameters. The tests show that the new expression results in stress–Strain curves which are both qualitatively and quantitatively consistent with the fully iterated numerical solution of the full-range stress–Strain Relation.

  • Inversion of a full-range stress–Strain Relation for stainless steel alloys
    International Journal of Non-linear Mechanics, 2006
    Co-Authors: Kenzu Abdella
    Abstract:

    Abstract This paper presents an approximate inversion of the stress–Strain Relation for stainless steel alloys. Using currently available stress–Strain Relations based on a modified Ramberg–Osgood equation, a new expression for the stress σ as an explicit function of the total Strain e is obtained. The new expression is valid over the full-range of the stress well beyond the 0.2 % proof stress σ 0.2 , defined as the stress level corresponding to the plastic Strain value of 0.2 % . The validity of the inverted expression is tested over a wide range of material parameters. The tests show that the new expression results in stress–Strain curves which are both qualitatively and quantitatively consistent with the fully iterated numerical solution of the full-range stress–Strain Relation.

Panayotis E. Karayannacos - One of the best experts on this subject based on the ideXlab platform.

  • a structural basis for the aortic stress Strain Relation in uniaxial tension
    Journal of Biomechanics, 2006
    Co-Authors: Dimitrios P. Sokolis, Harisios Boudoulas, Emmanuel M Kefaloyannis, Mirsini Kouloukoussa, Evangelos Marinos, Panayotis E. Karayannacos
    Abstract:

    Abstract A constitutive law that includes three analytical expressions was recently proposed to approximate the low, physiologic, and high-stress parts of the aortic stress–Strain Relation in uniaxial tension, consistent with the biphasic nature of the aortic wall under passive conditions. This consistency, and the fact that previous phenomenological uniaxial laws have only indirectly been related to vessel wall structure, motivates the investigation of the structural basis underlying the newly proposed three-part constitutive law. For this purpose, longitudinally oriented aortic strips were fixed in Karnovsky's solution, while subjected to various pre-selected levels of uniaxial tensile stress. Light microscopy examination disclosed that the elastic lamellae gradually unfolded at low and were almost straight at physiologic and high stresses, while collagen fibers reoriented in the longitudinal axis at low, started uncoiling at physiologic, and straightened massively at high stresses. In the circumferential sections, the elastic lamellae and the circumferentially distributed collagen bundles remained wavy at all levels of longitudinally applied stress. These microstructural changes suggest that elastin becomes load-bearing at low, and collagen at physiologic but mostly at high stresses, so that the first and third parts of the constitutive law are in turn due to the presence of elastin and collagen alone, and the second due to both elastin and collagen. The structural basis of this constitutive law allows physically significant interpretation of its parameters, offering insight into how the aortic microstructure determines the macromechanical response.

  • A structural basis for the aortic stress–Strain Relation in uniaxial tension
    Journal of Biomechanics, 2005
    Co-Authors: Dimitrios P. Sokolis, Harisios Boudoulas, Emmanuel M Kefaloyannis, Mirsini Kouloukoussa, Evangelos Marinos, Panayotis E. Karayannacos
    Abstract:

    Abstract A constitutive law that includes three analytical expressions was recently proposed to approximate the low, physiologic, and high-stress parts of the aortic stress–Strain Relation in uniaxial tension, consistent with the biphasic nature of the aortic wall under passive conditions. This consistency, and the fact that previous phenomenological uniaxial laws have only indirectly been related to vessel wall structure, motivates the investigation of the structural basis underlying the newly proposed three-part constitutive law. For this purpose, longitudinally oriented aortic strips were fixed in Karnovsky's solution, while subjected to various pre-selected levels of uniaxial tensile stress. Light microscopy examination disclosed that the elastic lamellae gradually unfolded at low and were almost straight at physiologic and high stresses, while collagen fibers reoriented in the longitudinal axis at low, started uncoiling at physiologic, and straightened massively at high stresses. In the circumferential sections, the elastic lamellae and the circumferentially distributed collagen bundles remained wavy at all levels of longitudinally applied stress. These microstructural changes suggest that elastin becomes load-bearing at low, and collagen at physiologic but mostly at high stresses, so that the first and third parts of the constitutive law are in turn due to the presence of elastin and collagen alone, and the second due to both elastin and collagen. The structural basis of this constitutive law allows physically significant interpretation of its parameters, offering insight into how the aortic microstructure determines the macromechanical response.

  • Assessment of the aortic stress-Strain Relation in uniaxial tension
    Journal of Biomechanics, 2002
    Co-Authors: Dimitrios P. Sokolis, Harisios Boudoulas, Panayotis E. Karayannacos
    Abstract:

    The passive elastic characteristics of the abdominal aorta were investigated in two experimental animal models, aiming at assessing the stress–Strain Relation of the aortic wall. Twenty porcine and 15 rabbit healthy abdominal aortas were subjected to uniaxial stress–Strain analysis, performed on a tensile-testing device, while immersed in a physiologic saline bath at body temperature. Measured parameters included original length, width and thickness, as well as axial force and extension. Based on these data, Kirchhoff stress and Green–St.Venant Strain were computed and one-dimensional constitutive equations were defined, comprising of a power function and two exponential ones, in turn, for the low, physiologic and high-stress regions. The stress–Strain curves were plotted as elastic modulus versus stress, displaying nonlinear part I and linear parts II and III. These were regressed, yielding parameters k, q (part I), a, b (part II) and c, d (part III). A detailed comparison of these constitutive parameters was undertaken between the two species, demonstrating variations in d (p

  • assessment of the aortic stress Strain Relation in uniaxial tension
    Journal of Biomechanics, 2002
    Co-Authors: Dimitrios P. Sokolis, Harisios Boudoulas, Panayotis E. Karayannacos
    Abstract:

    The passive elastic characteristics of the abdominal aorta were investigated in two experimental animal models, aiming at assessing the stress–Strain Relation of the aortic wall. Twenty porcine and 15 rabbit healthy abdominal aortas were subjected to uniaxial stress–Strain analysis, performed on a tensile-testing device, while immersed in a physiologic saline bath at body temperature. Measured parameters included original length, width and thickness, as well as axial force and extension. Based on these data, Kirchhoff stress and Green–St.Venant Strain were computed and one-dimensional constitutive equations were defined, comprising of a power function and two exponential ones, in turn, for the low, physiologic and high-stress regions. The stress–Strain curves were plotted as elastic modulus versus stress, displaying nonlinear part I and linear parts II and III. These were regressed, yielding parameters k, q (part I), a, b (part II) and c, d (part III). A detailed comparison of these constitutive parameters was undertaken between the two species, demonstrating variations in d (p<0.05). No statistical differences were found in parameters a, b, c, k and q, implying that the two aortas were equally stiff under low and physiologic stresses, whereas the porcine aorta was stiffer at higher stresses. In conclusion, a bi-exponential in addition to a power law was established, relating stress and Strain in the aorta, which is advantageous in comparison with previous constitutive equations. Under passive conditions, the nonlinear nature of this constitutive law may account for the low, part I, physiologic, part II, and high-stress, part III of the stress–Strain Relationship, supporting the concept of the aortic wall as a biphasic material.

Dimitrios P. Sokolis - One of the best experts on this subject based on the ideXlab platform.

  • a structural basis for the aortic stress Strain Relation in uniaxial tension
    Journal of Biomechanics, 2006
    Co-Authors: Dimitrios P. Sokolis, Harisios Boudoulas, Emmanuel M Kefaloyannis, Mirsini Kouloukoussa, Evangelos Marinos, Panayotis E. Karayannacos
    Abstract:

    Abstract A constitutive law that includes three analytical expressions was recently proposed to approximate the low, physiologic, and high-stress parts of the aortic stress–Strain Relation in uniaxial tension, consistent with the biphasic nature of the aortic wall under passive conditions. This consistency, and the fact that previous phenomenological uniaxial laws have only indirectly been related to vessel wall structure, motivates the investigation of the structural basis underlying the newly proposed three-part constitutive law. For this purpose, longitudinally oriented aortic strips were fixed in Karnovsky's solution, while subjected to various pre-selected levels of uniaxial tensile stress. Light microscopy examination disclosed that the elastic lamellae gradually unfolded at low and were almost straight at physiologic and high stresses, while collagen fibers reoriented in the longitudinal axis at low, started uncoiling at physiologic, and straightened massively at high stresses. In the circumferential sections, the elastic lamellae and the circumferentially distributed collagen bundles remained wavy at all levels of longitudinally applied stress. These microstructural changes suggest that elastin becomes load-bearing at low, and collagen at physiologic but mostly at high stresses, so that the first and third parts of the constitutive law are in turn due to the presence of elastin and collagen alone, and the second due to both elastin and collagen. The structural basis of this constitutive law allows physically significant interpretation of its parameters, offering insight into how the aortic microstructure determines the macromechanical response.

  • A structural basis for the aortic stress–Strain Relation in uniaxial tension
    Journal of Biomechanics, 2005
    Co-Authors: Dimitrios P. Sokolis, Harisios Boudoulas, Emmanuel M Kefaloyannis, Mirsini Kouloukoussa, Evangelos Marinos, Panayotis E. Karayannacos
    Abstract:

    Abstract A constitutive law that includes three analytical expressions was recently proposed to approximate the low, physiologic, and high-stress parts of the aortic stress–Strain Relation in uniaxial tension, consistent with the biphasic nature of the aortic wall under passive conditions. This consistency, and the fact that previous phenomenological uniaxial laws have only indirectly been related to vessel wall structure, motivates the investigation of the structural basis underlying the newly proposed three-part constitutive law. For this purpose, longitudinally oriented aortic strips were fixed in Karnovsky's solution, while subjected to various pre-selected levels of uniaxial tensile stress. Light microscopy examination disclosed that the elastic lamellae gradually unfolded at low and were almost straight at physiologic and high stresses, while collagen fibers reoriented in the longitudinal axis at low, started uncoiling at physiologic, and straightened massively at high stresses. In the circumferential sections, the elastic lamellae and the circumferentially distributed collagen bundles remained wavy at all levels of longitudinally applied stress. These microstructural changes suggest that elastin becomes load-bearing at low, and collagen at physiologic but mostly at high stresses, so that the first and third parts of the constitutive law are in turn due to the presence of elastin and collagen alone, and the second due to both elastin and collagen. The structural basis of this constitutive law allows physically significant interpretation of its parameters, offering insight into how the aortic microstructure determines the macromechanical response.

  • Assessment of the aortic stress-Strain Relation in uniaxial tension
    Journal of Biomechanics, 2002
    Co-Authors: Dimitrios P. Sokolis, Harisios Boudoulas, Panayotis E. Karayannacos
    Abstract:

    The passive elastic characteristics of the abdominal aorta were investigated in two experimental animal models, aiming at assessing the stress–Strain Relation of the aortic wall. Twenty porcine and 15 rabbit healthy abdominal aortas were subjected to uniaxial stress–Strain analysis, performed on a tensile-testing device, while immersed in a physiologic saline bath at body temperature. Measured parameters included original length, width and thickness, as well as axial force and extension. Based on these data, Kirchhoff stress and Green–St.Venant Strain were computed and one-dimensional constitutive equations were defined, comprising of a power function and two exponential ones, in turn, for the low, physiologic and high-stress regions. The stress–Strain curves were plotted as elastic modulus versus stress, displaying nonlinear part I and linear parts II and III. These were regressed, yielding parameters k, q (part I), a, b (part II) and c, d (part III). A detailed comparison of these constitutive parameters was undertaken between the two species, demonstrating variations in d (p

  • assessment of the aortic stress Strain Relation in uniaxial tension
    Journal of Biomechanics, 2002
    Co-Authors: Dimitrios P. Sokolis, Harisios Boudoulas, Panayotis E. Karayannacos
    Abstract:

    The passive elastic characteristics of the abdominal aorta were investigated in two experimental animal models, aiming at assessing the stress–Strain Relation of the aortic wall. Twenty porcine and 15 rabbit healthy abdominal aortas were subjected to uniaxial stress–Strain analysis, performed on a tensile-testing device, while immersed in a physiologic saline bath at body temperature. Measured parameters included original length, width and thickness, as well as axial force and extension. Based on these data, Kirchhoff stress and Green–St.Venant Strain were computed and one-dimensional constitutive equations were defined, comprising of a power function and two exponential ones, in turn, for the low, physiologic and high-stress regions. The stress–Strain curves were plotted as elastic modulus versus stress, displaying nonlinear part I and linear parts II and III. These were regressed, yielding parameters k, q (part I), a, b (part II) and c, d (part III). A detailed comparison of these constitutive parameters was undertaken between the two species, demonstrating variations in d (p<0.05). No statistical differences were found in parameters a, b, c, k and q, implying that the two aortas were equally stiff under low and physiologic stresses, whereas the porcine aorta was stiffer at higher stresses. In conclusion, a bi-exponential in addition to a power law was established, relating stress and Strain in the aorta, which is advantageous in comparison with previous constitutive equations. Under passive conditions, the nonlinear nature of this constitutive law may account for the low, part I, physiologic, part II, and high-stress, part III of the stress–Strain Relationship, supporting the concept of the aortic wall as a biphasic material.

Feng Xing - One of the best experts on this subject based on the ideXlab platform.

  • axial compressive behavior of frp confined lightweight aggregate concrete an experimental study and stress Strain Relation model
    Construction and Building Materials, 2016
    Co-Authors: Yingwu Zhou, Feng Xing
    Abstract:

    Abstract Due to its low strength and high brittleness, lightweight aggregate concrete (LWAC) can mainly be used to fabricate non-load bearing structures. Wrapping LWAC with fiber-reinforced polymer (FRP) can effectively improve its mechanical properties, thereby allowing to realize a structural lightweight design. This study therefore aimed to investigate the effect of a FRP confinement on the mechanical properties of LWAC. Three types of coarse aggregate material, i.e., class 600 shale ceramsite, class 800 shale ceramsite and hollow sealed thin-wall steel balls, were selected to design the LWAC and compared in the experiments. After wrapping with three layers of FRP, the strengths of LWACs prepared from the three different materials were improved by a factor of 2.6, 2.1 and 5.4, respectively, whereas their ultimate deformations were improved by a factor of 33.4, 8.5 and 31.2, respectively. Meanwhile, the strength and stress-Strain Relation for the FRP-confined LWAC were obtained through axial compression tests. Models for the ultimate strength, the ultimate Strain and the stress-Strain Relation of FRP-confined LWAC were successfully established, and a comparative analysis revealed that the predictions made using these models are very accurate. A numerical analysis of these models further showed that, for LWAC and normal concrete with the same strength and FRP confinement, the mechanical behavior was different and found to heavily depend on the FRP confinement aspect properties and the types of the light-weight aggregate.