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Constitutive equation

About: Constitutive equation is a(n) research topic. Over the lifetime, 24995 publication(s) have been published within this topic receiving 665195 citation(s). The topic is also known as: Constitutive Equation of Materials.

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01 Jan 1969
Abstract: 1. Vectors and Tensors. 2. Strain and Deformation. 3. General Principles. 4. Constitutive Equations. 5. Fluid Mechanics. 6. Linearized Theory of Elasticity. Appendix I: Tensors. Appendix II: Orthogonal Curvilinear.

3,606 citations

Journal ArticleDOI
J. N. Reddy1
Abstract: A higher-order shear deformation theory of laminated composite plates is developed. The theory contains the same dependent unknowns as in the first-order shear deformation theory of Whitney and Pagano (1970), but accounts for parabolic distribution of the transverse shear strains through the thickness of the plate. Exact closed-form solutions of symmetric cross-ply laminates are obtained and the results are compared with three-dimensional elasticity solutions and first-order shear deformation theory solutions. The present theory predicts the deflections and stresses more accurately when compared to the first-order theory.

3,215 citations

Journal ArticleDOI
Abstract: In this paper we develop a new constitutive law for the description of the (passive) mechanical response of arterial tissue. The artery is modeled as a thick-walled nonlinearly elastic circular cylindrical tube consisting of two layers corresponding to the media and adventitia (the solid mechanically relevant layers in healthy tissue). Each layer is treated as a fiber-reinforced material with the fibers corresponding to the collagenous component of the material and symmetrically disposed with respect to the cylinder axis. The resulting constitutive law is orthotropic in each layer. Fiber orientations obtained from a statistical analysis of histological sections from each arterial layer are used. A specific form of the law, which requires only three material parameters for each layer, is used to study the response of an artery under combined axial extension, inflation and torsion. The characteristic and very important residual stress in an artery in vitro is accounted for by assuming that the natural (unstressed and unstrained) configuration of the material corresponds to an open sector of a tube, which is then closed by an initial bending to form a load-free, but stressed, circular cylindrical configuration prior to application of the extension, inflation and torsion. The effect of residual stress on the stress distribution through the deformed arterial wall in the physiological state is examined. The model is fitted to available data on arteries and its predictions are assessed for the considered combined loadings. It is explained how the new model is designed to avoid certain mechanical, mathematical and computational deficiencies evident in currently available phenomenological models. A critical review of these models is provided by way of background to the development of the new model.

2,617 citations

15 Jun 1989
Abstract: 1) What is rheology? historical perspective the importance of non-linearity solids and liquids rheology is a difficult subject components of rheological research. 2) Viscosity practical ranges of variables which affect viscosity the shear-dependent viscosity of non-Newtonian liquids viscometers for measuring shear viscosity. 3) Linear viscoelasticity the meaning and consequences of linearity the Kelvin and Maxwell models the relaxation spectrum oscillatory shear relationships between functions of linear viscoelasticity methods of measurement. 4) Normal stresses the nature and origin of normal stresses typical behaviour of N 1 and N 2 observable consequences of N 1 and N 2 methods of measuring N 1 and N 2 relationships between viscometric functions and linear viscoelastic functions. 5) extensional viscosity importance of extensional flow theoretical considerations experimental methods experimental results some demonstrations of high extensional viscosity behaviour. 6) Rheology of polymeric liquids general behaviour effect of temperature on polymer rheology effect of molecular weight on polymer rheology effect of concentration on the rheology of polymer solutions polymer gels liquid crystal polymers. molecular theories the method of reduced variables empirical relations between rheological functions practical applications. 7) Rheology of suspensions the viscosity of suspensions of solid particles in Newtonian liquids the colloidal contribution to viscosity viscoelastic properties of suspensions suspensions of deformable particles the interaction of suspended particles with polymer molecules also present in the continuous phase computer simulation studies of suspension rheology. 8. Theoretical rheology basic principles of continuum mechanics successful applications of the formulation principles some general constitutive equations constitutive equations for restricted classes of flows simple constitutive equations of the Oldroyd/Maxwell type solution of flow problems.

2,568 citations

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