• 제목/요약/키워드: stiffness tensor

검색결과 15건 처리시간 0.024초

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.

Homogenization based continuum damage mechanics model for monotonic and cyclic damage evolution in 3D composites

  • Jain, Jayesh R.;Ghosh, Somnath
    • Interaction and multiscale mechanics
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    • 제1권2호
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    • pp.279-301
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    • 2008
  • This paper develops a 3D homogenization based continuum damage mechanics (HCDM) model for fiber reinforced composites undergoing micromechanical damage under monotonic and cyclic loading. Micromechanical damage in a representative volume element (RVE) of the material occurs by fiber-matrix interfacial debonding, which is incorporated in the model through a hysteretic bilinear cohesive zone model. The proposed model expresses a damage evolution surface in the strain space in the principal damage coordinate system or PDCS. PDCS enables the model to account for the effect of non-proportional load history. The loading/unloading criterion during cyclic loading is based on the scalar product of the strain increment and the normal to the damage surface in strain space. The material constitutive law involves a fourth order orthotropic tensor with stiffness characterized as a macroscopic internal variable. Three dimensional damage in composites is accounted for through functional forms of the fourth order damage tensor in terms of components of macroscopic strain and elastic stiffness tensors. The HCDM model parameters are calibrated from homogenization of micromechanical solutions of the RVE for a few representative strain histories. The proposed model is validated by comparing results of the HCDM model with pure micromechanical analysis results followed by homogenization. Finally, the potential of HCDM model as a design tool is demonstrated through macro-micro analysis of monotonic and cyclic damage progression in composite structures.

분산 자기 회로를 이용한 베어링리스 모터의 모델링 (Modeling of a bearingless motor using distributed magnetic circuit)

  • 박창용;박수진;노명규
    • 한국정밀공학회:학술대회논문집
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    • 한국정밀공학회 2004년도 추계학술대회 논문집
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    • pp.212-216
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    • 2004
  • Bearingless motors are the rotational electric machine which utilize a common magnetic structure for rotation and magnetic suspension. Since the bearing function is combined with the motor, the shaft length can be shortened resulting in higher critical speeds. Relationship between suspension force and current of bearingless motor is clearly derived by prior research. However, relationship between displacement of rotor and suspension force is not precisely defined. In this paper, we present model of bearingless motor describing the radial force variation due to the movement of the rotor. Using a distributed magnetic circuit and maxwell stress tensor, we derived a mathematical expression for the radial force. For a slotless bearingless motor, we are able to find an analytical model presented in the form of stiffness. For a slotted motor, we can compute the stiffness by semi-analytical analysis. This model is validated by a finite-element-analysis.

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An Analytical Study on Prediction of Effective Properties n Porous and Non-Porous Piezoelectric Composites

  • Lee Jae-Kon
    • Journal of Mechanical Science and Technology
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    • 제19권11호
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    • pp.2025-2031
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    • 2005
  • Eshelby type micro mechanics model with a newly developed piezoelectric Eshelby tensor is proposed for predicting the effective electroelastic properties of the piezoelectric composite. The model is applied for piezoelectric solids containing both porosities and metal inhomogeneities. The effective electroelastic moduli of the composites such as stiffness, piezoelectric constants, and dielectric constants are predicted by the present model, which are extensively compared with the existing experimental results from the literatures. The validity of Eshelby type model for predicting the effective properties of the composite is thoroughly examined. It can be concluded from this study that a new mechanism is needed to compute correctly the dielectric constants among the effective properties of the composites.

The Effects of the FIFA 11+ and Self-Myofascial Release Complex Training on Injury, Flexibility and Muscle Stiffness of High School Football Players

  • Choi, Young-In;Choi, Houng-Sik;Kim, Tack-Hoon;Choi, Kyu-Hwan;Kim, Gyoung-Mo;Roh, Jung-Suk
    • The Journal of Korean Physical Therapy
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    • 제34권1호
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    • pp.38-44
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    • 2022
  • Purpose: The purpose of this study was to investigate the effects of complex training on injury, flexibility, and muscle stiffness in high school male football players. Methods: A total of 60 football players were included in the study and were divided into three groups viz. the complex training group (CTG), 11+ training group (11+TG), and traditional training group (TTG). Injuries were recorded based on the prospective investigation method after starting the study, and the flexibility and muscle stiffness of the subjects were evaluated. Results: The research results showed that the injury rate per match was significantly lower in the CTG and 11+TG than the TTG. In the CTG, the flexibility of the hamstrings significantly increased and the stiffness of the rectus femoris (RF), biceps femoris (BF), and tensor fascia latae (TFL) muscles significantly decreased (p<0.05). In the 11+TG, the stiffness of the RF significantly decreased (p<0.05). In the TTG, the flexibility of the hamstrings significantly increased (p<0.05). Hamstring flexibility showed a significantly higher increase in the CTG and TTG compared to the 11+TG (p<0.05). Also, the stiffness of the RF and TFL muscles showed a significantly higher decrease in the CTG compared to the 11+TG and TTG (p<0.05). The stiffness of the BF muscles too showed a more significant decrease in the CTG compared to the TTG (p<0.05). Conclusion: The complex training method of the Fédération International de Football Association (FIFA) 11+ and self-myofascial release (SMFR) as a warm-up program, prevent injuries, enhance flexibility, and lower muscle stiffness of football players in high school. Thus, it is necessary to ensure the widespread use of the complex training program by instructors and players under the supervision of the Korea Football Association (KFA), given its reliability in preventing injuries and improving the performance of football players.

나노박막의 표면응력에 의한 평형상태에 대한 연구 (A study of surface stress effects on equilibrium states of thin nanofilm)

  • 김원배;조맹효
    • 한국전산구조공학회:학술대회논문집
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    • 한국전산구조공학회 2009년도 정기 학술대회
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    • pp.34-37
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    • 2009
  • 본 논문에서는 원자적 계산(atomistic calculation)을 이용한 나노박막의 평형상태(self-equilibrium state)에 대한 해석기법을 제시한다. 두께가 얇은 나노박막은 표면 응력(surface stress)에 의한 영향으로 원자간 거리가 벌크상태의 거리보다 작아진다. 두께가 얇은 나노박막에서의 원자 사이의 거리는 표면 응력과 탄성계수들의 표현식으로 계산이 가능하며, 본 논문에서는 {100}, {111}, {110} 표면을 가지는 나노박막의 평형상태의 해석을 위한 해석적 방법을 제시한다. 원자 사이의 거리를 계산하기 위해서는 보다 정확한 표면 응력의 계산방법이 필요하다. 본 연구에서는 나노박막의 평형상태에 대한 해석을 위해 surface relaxation model을 제시하고, 이 모델을 이용하여 표면응력(surface stress)과 표면강성계수(surface stiffness tensor)와 같은 surface parameter의 계산을 수행한다. 본 논문에서 제시된 surface relaxation model을 검증하기 위하여 분자동역학 전산모사(molecular dynamics simulation)의 수치 결과를 제시하고, 본 연구에서 계산한 equilibrium strain과 비교 검증한다.

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A damage model formulation: unilateral effect and RC structures analysis

  • Pituba, Jose J.C.
    • Computers and Concrete
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    • 제15권5호
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    • pp.709-733
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    • 2015
  • This work deals with a damage model formulation taking into account the unilateral effect of the mechanical behaviour of brittle materials such as concrete. The material is assumed as an initial elastic isotropic medium presenting anisotropy, permanent strains and bimodularity induced by damage evolution. Two damage tensors governing the stiffness in tension or compression regimes are introduced. A new damage tensor in tension regimes is proposed in order to model the diffuse damage originated in prevails compression regimes. Accordingly with micromechanical theory, the constitutive model is validate when dealing with unilateral effect of brittle materials, Finally, the proposed model is applied in the analyses of reinforced concrete framed structures submitted to reversal loading. The numerical results have shown the good performance of the modelling and its potentialities to simulate practical problems in structural engineering.

인발-와인딩에 의한 불포화수지 섬유강화 중공봉의 기계적 거동해석 (Analysis of Mechanical Behavior for a Pultruded-Wound Hollow Rod of Unsaturated Polyester Resin(UP) with Glass Fibers)

  • 김조권;린예
    • Composites Research
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    • 제14권6호
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    • pp.16-23
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    • 2001
  • 인발 와인딩에 의한 섬유강화 복합재료 중공 봉의 기계적 거동해석을 수행하였다. 이 목적의 수행을 위해 새롭게 제작된 와인더를 전통적 인발 시스템에 부탁하여 시편을 제작하였다. 또한 인발-와인딩된 시편을 제작할 수 있는 새로운 공법을 개발하였다. 이 연구를 위해 유한요소 해석 프로그램 POSTII를 확장 개발하였다. 비선형유한요소 수식화에는 2차 피올라-키르히호프 응력 텐서와 그린 변형률 텐서에 기초한 업데이트된 라그란지언 표현법이 사용되었다. 복합재료 중공봉의 유한요소 모델링을 위해 8절점 응축쉘요소를 사용하였다. 파손평가를 위해 모든 유한요소의 각 단층에서의 평균응력을 최대음력 판정법에 대입하였다. 수치해석 예로서 불포화 섬유강화 복합재료 중공 봉의 기계적 거동을 초기 하중상태에서 최종 붕괴가지 조사하였다. 파손에 따른 강성저하와 응력제하를 고려한 유한요소해석 결과는 극만 하중과 파손 및 변형에서 실험치와 잘 일치하였다.

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초음파공명분광법에 의한 Zr-2.5Nb 압력관 재료의 고온 이방성 탄성계수 측정 (Measurement of High Temperature Anisotropic Elastic Constants of Zr-2.5Nb Pressure Tube Materials by Resonant Ultrasound Spectroscopy)

  • 정용무;김성수;김영석
    • 비파괴검사학회지
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    • 제22권2호
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    • pp.140-148
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    • 2002
  • 중수로 압력관으로 사용되는 Zr-2.5Nb 재료의 고온 이방성 탄성계수를 고온 초음파공명분광법(RUS)로 측정하였다. 소형 가열로 내에 알루미나 waveguide와 광대역 초음파 센서를 사용하여 초음파에너지를 시편에 가하고 시편의 공명주파수를 측정하였다. 압력관의 축 방향, 반경 방향, 원주 방향에 일치하도록 장방형 시편을 가공하였으며 각 방향에 대한 탄성계수 텐서 9개의 값을 상온${\sim}500^{\circ}C$ 온도 구간에서 측정하였다. 탄생계수 텐서, $c_{ij}$는 모두 온도가 증가함에 따라 점진적으로 감소하며 원주 방향의 탄성계수가 축 방향 및 반경 방향의 탄성계수보다 높았다. 이것은 Young's modulus나 shear modulus의 경우에도 일치하였으며 축 방향과 반경 방향의 경우 큰 차이를 나타내지 않았다. 축 방향 및 반경 방향의 비틀림 탄생계수가 $150^{\circ}C$ 부근에서 서로 교차하였으며 이는 단결정 지르코늄의 $c_{44}$$c_{66}$의 교차 현상과 일치하였다.

이바노브-율리신 항복조건을 이용한 4절점 비선형 준적합 쉘요소 (A nonlinear Co-rotational Quasi-Conforming 4-node Shell Element Using Ivanov-Ilyushin Yield Criteria)

  • 파노트 송삭 프라민;김기두
    • 한국강구조학회 논문집
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    • 제20권3호
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    • pp.409-419
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    • 2008
  • 율리신-이바노브 항복 조건을 이용하여 4절점 순수변위 준적합 쉘요소의 정식화를 제안하였다. 기하강성 행렬은 그린 변형률 텐서를 이용하여 휨변형률 및 전단변형률도 기하강성행렬에 고려되었다. 그 결과 접선강성행렬의 해석적인 적분으로 비선형 해석시 매우 효율적으로 계산이 되고 있다. 이 정식은 변형률 경화의 이바노브-유리신 항복조건을 이용하여 재료 비선형 해석시에도 쉽게 적분이 된다. 즉 두께 방향의 적층 적분을 하지 않는 율리신-이바노브의 정식은 대규모의 쉘 구조에도 계산상 아주 적합하다. 검증된 수치 예제에서 만족스러운 결과를 보여주고 있다.