• 제목/요약/키워드: Isotropic strain

검색결과 239건 처리시간 0.029초

Constitutive equations for polymer mole and rubbers: Lessons from the $20^{th}$ century

  • Wagner, Manfred H.
    • Korea-Australia Rheology Journal
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    • 제11권4호
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    • pp.293-304
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    • 1999
  • Refinements of classical theories for entangled or crosslinked polymeric systems have led to incommensurable models for rubber networks and polymer melts, contrary to experimental evidence, which suggests a great deal of similarity. Uniaxial elongation and compression data of linear and branched polymer melts as well as of crosslinked rubbers were analyzed with respect to their nonlinear strain measure. This was found to be the result of two contributions: (1) affine orientation of network strands, and (2) isotropic strand extension. Network strand extension is caused by an increasing restriction of lateral movement of polymer chains due to deformation, and is modelled by a molecular stress function which in the tube concept of Doi and Edwards is the inverse of the relative tube diameter. Up to moderate strains, $f^2$ is found to be linear in the average stretch for melts as well as for rubbers, which corresponds to a constant tube volume. At large strains, rubbers show maximum extensibility, while melts show maximum molecular tension. This maximum value of the molecular stress function governs the ultimate magnitude of the strain-hardening effect of linear and long-chain branched polymer melts in extensional flows.

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균일한 두께분포를 위한 신장/블로 공정을 이용한 초소성 성형 공정설계 해석 (Analysis of Superplastic Forming Process Design Using a Combined Stretch/Blow Process for Uniform Thickness Distribution)

  • Hong, S.S.;Lee, J.S.;Kin, Y.H.
    • 한국정밀공학회지
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    • 제11권1호
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    • pp.129-137
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    • 1994
  • A rigid-viscoplastic finite element method has been used for modeling superplastic stretch/blow process design to improve thickness distribution. Punch velocity-time relationship of the stretch forming and pressure-time cycle of the blow forming for a given strain rate are calculated. A superplastic material is assumed to be isotropic and a plane-strain line element based on membrane approximation is employed for the formulation. The effects of the width, corner radius and height of the punch during stretch forming are examined for the final thickness distribution, and the process design to improve thickness distribution can be established.

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Buckling of plates including effect of shear deformations: a hyperelastic formulation

  • Musa, Idris A.
    • Structural Engineering and Mechanics
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    • 제57권6호
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    • pp.1107-1124
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    • 2016
  • Consistent finite strain Plate constitutive relations are derived based on a hyperelastic formulation for an isotropic material. Plate equilibrium equations under finite strain are derived following a static kinematic approach. Three Euler angles and four shear angles, based on Timoshenko beam theory, represent the kinematics of the deformations in the plate cross section. The Green deformation tensor has been expressed in term of a deformation tensor associated with the deformation and stretches of an embedded plate element. Buckling formulation includes the in-plane axial deformation prior to buckling and transverse as well as in-plane shear deformations. Numerical results for a simply supported thick plate under uni-axial compression force are presented.

증분 변형 이론을 이용한 반무한체에 접합된 두 탄성층의 좌굴 해석 (Buckling Analysis of Two Elastic Layers Bonded to a Semi-Infinite Substrate Using Incremental Deformation Theory)

  • 정경문;범현규
    • 대한기계학회:학술대회논문집
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    • 대한기계학회 2000년도 춘계학술대회논문집A
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    • pp.369-374
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    • 2000
  • The buckling of two elastic layers bonded to a semi-infinite substrate under a transverse compressive plane strain is investigated. Incremental deformation theory is employed to describe the buckling behavior of both two isotropic layers and the semi-infinite substrate. The problem is converted to an eigenvalue-eigenvector case, from which the critical buckling strain and the wavelength of the buckled shape are obtained. The results are presented on the effects of the layer geometries and material properties on the buckling behavior.

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응력경로에 따른 단일항복면구성모델의 토질매개변수 특성 (Parameters Characteristics of Single Work Hardening Model Dependent on the Stress Path)

  • 김찬기
    • 한국농공학회지
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    • 제38권2호
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    • pp.133-144
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    • 1996
  • To get accurate results, the realistic stress-strain relationships of soils are dependent on a number of factors such as soil types, density, stress levels and stress path. Such attempts are continuously being made by the developement of analytical models for soils incorporating all such factors. Isotropic compression-expansion test and a series of drained conventional triaxial tests with several stress path for Baekma river sand were performed to investigate parameters characteristics of Lade's single work hardening model dependant on the stress path. Using the computer program based on the regression analysis, the values of parameters for the model were determined. In conclusion, the parameters of Lade's model are little influenced by the stress paths. Though yield criterion parameters ( h, ${\alpha}$a) are much influenced by stress level and stress path, the parameters don't have influence on stress-strain behavior.

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인장 시편 및 원자력 배관계의 반복 변형거동에 미치는 경화 모델의 영향 (Effects of Hardening Models on Cyclic Deformation Behavior of Tensile Specimen and Nuclear Piping System)

  • 전다솜;강주연;허남수;김종성;김윤재
    • 한국압력기기공학회 논문집
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    • 제13권2호
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    • pp.67-74
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    • 2017
  • Recently there have been many concerns on structural integrity of nuclear piping under seismic loadings. In terms of failure of nuclear piping due to seismic loadings, an important failure mechanism is low cycle fatigue with large cyclic displacements. To investigate the effects of seismic loading on low cycle fatigue behavior of nuclear piping, the cyclic behavior of materials and nuclear piping needs to be accurately estimated. In this paper, the non-linear finite element (FE) analyses have been carried out to evaluate the effects of three different cyclic hardening models on cyclic behavior of materials and nuclear piping, such as isotropic hardening, kinematic hardening and combined hardening.

불포화토의 등방압축 삼축시험시 변형계수에 관한 연구 (Isotropic Compression Triaxial Test of Deformation Modulus of Unsaturated soils)

  • 이종필;오세붕;김태경
    • 한국지반공학회:학술대회논문집
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    • 한국지반공학회 2009년도 춘계 학술발표회
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    • pp.132-135
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    • 2009
  • In order study, experimental stress-strain relationships were achieved for various suctions by triaxial tests. A failure envelop was occurred on a plane in p-q-$\psi$ space, since the level of matric suction is in the small range. It was found that the failure criteria could be defined uniquely by the Bishop stress and were also independent of matric suctions. At the level of small strain, deformation moduli were evaluated according to matric suctions by fitting to Ramberg-Osgood model. It was found that deformation moduli increase as matric suctions increase.

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Hellinger-Reissner 범함수를 이용한 효율적인 3절점 판 유한요소의 개발 (Development of an efficient 3-node plate bending element by using the Hellinger-Reissner functional)

  • 이윤규;최창근;이필승
    • 한국전산구조공학회:학술대회논문집
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    • 한국전산구조공학회 2011년도 정기 학술대회
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    • pp.760-763
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    • 2011
  • 본 논문의 목적은 효율적인 3절점 판 유한요소를 개발하는 것이다. Hellinger-Reissner 범함수에 근거한 혼합정식화(mixed formulation)를 사용한다. 잠김현상을 일으키는 전단변형률장을 독립적으로 분리한 후, MITC(Mixed Interpolation of Tensorial Components)방법을 이용하여 대체전단변형률장(assumed transverse shear strain field)을 구성한다. 추가적으로 회전된 반변기저벡터(contravariant base vector)로 정의된 근사전단변형률장(approximated transverse shear strain field)에 미지수(unknowns)를 도입하여 혼합정식화를 완성시키고 정적응축(static condensation)을 통해 최종 강성행렬을 구성한다. 거짓영에너지모드시험(spurious zero energy mode test), 조각시험(patch test), 등방성시험(isotropic test) 등을 실시하였으며, 4변 완전구속 정사각형 판 구조물과 60도 기울어진 단순지지 판 구조물 등 예제들을 해석하여 MITC3판 유한요소와 수렴성능을 비교하였다.

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Determination of the elastic properties in CFRP composites: comparison of different approaches based on tensile tests and ultrasonic characterization

  • Munoz, Victor;Perrin, Marianne;Pastor, Marie-Laetitia;Welemane, Helene;Cantarel, Arthur;Karama, Moussa
    • Advances in aircraft and spacecraft science
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    • 제2권3호
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    • pp.249-261
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    • 2015
  • The mechanical characterization of composite materials is nowadays a major interest due to their increasing use in the aeronautic industry. The design of most of these materials is based on their stiffness, which is mainly obtained by means of tensile tests with strain gauge measurement. For thin laminated composites, this classical method requires adequate samples with specific orientation and does not provide all the independent elastic constants. Regarding ultrasonic characterization, especially immersion technique, only one specimen is needed and the entire determination of the stiffness tensor is possible. This paper presents a study of different methods to determine the mechanical properties of transversely isotropic carbon fibre composite materials (gauge and correlation strain measurement during tensile tests, ultrasonic immersion technique). Results are compared to ISO standards and manufacturer data to evaluate the accuracy of these techniques.

Absolute effective elastic constants of composite materials

  • Bulut, Osman;Kadioglu, Necla;Ataoglu, Senol
    • Structural Engineering and Mechanics
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    • 제57권5호
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    • pp.897-920
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    • 2016
  • The objective is to determine the mechanical properties of the composites formed in two types, theoretically. The first composite includes micro-particles in a matrix while the second involves long, thin fibers. A fictitious, homogeneous, linear-elastic and isotropic single material named as effective material is considered during calculation which is based on the equality of the strain energies of the composite and effective material under the same loading conditions. The procedure is carried out with volume integrals considering a unique strain energy in a body. Particularly, the effective elastic shear modulus has been calculated exactly for small-particle composites by the same procedure in order to determine of bulk modulus thereof. Additionally, the transverse shear modulus of fiber reinforced composites has been obtained through a simple approach leading to the practical equation. The results have been compared not only with the outcomes in the literature obtained by different method but also with those of finite element analysis performed in this study.