Výpočtové modelovaní kompozitu s hyperelastickou matricí vyztuženém vlákny při zahrnutí ohybové tuhosti vláken

Computational modelling of fibre-reinforced hyperelastic solids with fibre bending stiffness

abstrakt

en

In the paper, the hyperelastic material reinforced by steel fibres is considered. Conventional anisotropic constitutive models include the reinforcing effect of tension stiffness of fibres, but neglect their bending stiffness. We, however, consider the case when the size, material properties and structure of fibres do not allow to assume their perfect flexibility. An appropriate strain energy function is proposed following the approach of Spencer and Soldatos (A.J.M. Spencer, K.P. Soldatos: Finite deformations of fibre-reinforced elastic solid withfibre bending stiffness. Int. J. Nonlinear Mech., 42 (2007)). It takes hyperelasticity and anisotropy of the material, including bending stiffness of fibres, into account. The constitutive model employs curvature of fibres and is based on the constrained Cosserat theory. It means that strain energy includes couple stresses and derivatives of rotation in addition to common stresses and strains. Due to the constrained theory, rotations are not independent variables but derived from displacements. This approach leads to second derivatives of displacements occurring in finite element formulations. To ensure continuity of the derivatives in nodes of the mesh Hermite polynomial elements are employed and a new finite element code is proposed.

In the paper, the hyperelastic material reinforced by steel fibres is considered. Conventional anisotropic constitutive models include the reinforcing effect of tension stiffness of fibres, but neglect their bending stiffness. We, however, consider the case when the size, material properties and structure of fibres do not allow to assume their perfect flexibility. An appropriate strain energy function is proposed following the approach of Spencer and Soldatos (A.J.M. Spencer, K.P. Soldatos: Finite deformations of fibre-reinforced elastic solid withfibre bending stiffness. Int. J. Nonlinear Mech., 42 (2007)). It takes hyperelasticity and anisotropy of the material, including bending stiffness of fibres, into account. The constitutive model employs curvature of fibres and is based on the constrained Cosserat theory. It means that strain energy includes couple stresses and derivatives of rotation in addition to common stresses and strains. Due to the constrained theory, rotations are not independent variables but derived from displacements. This approach leads to second derivatives of displacements occurring in finite element formulations. To ensure continuity of the derivatives in nodes of the mesh Hermite polynomial elements are employed and a new finite element code is proposed.

In the paper, the hyperelastic material reinforced by steel fibres is considered. Conventional anisotropic constitutive models include the reinforcing effect of tension stiffness of fibres, but neglect their bending stiffness. We, however, consider the case when the size, material properties and structure of fibres do not allow to assume their perfect flexibility. An appropriate strain energy function is proposed following the approach of Spencer and Soldatos (A.J.M. Spencer, K.P. Soldatos: Finite deformations of fibre-reinforced elastic solid withfibre bending stiffness. Int. J. Nonlinear Mech., 42 (2007)). It takes hyperelasticity and anisotropy of the material, including bending stiffness of fibres, into account. The constitutive model employs curvature of fibres and is based on the constrained Cosserat theory. It means that strain energy includes couple stresses and derivatives of rotation in addition to common stresses and strains. Due to the constrained theory, rotations are not independent variables but derived from displacements. This approach leads to second derivatives of displacements occurring in finite element formulations. To ensure continuity of the derivatives in nodes of the mesh Hermite polynomial elements are employed and a new finite element code is proposed.

hyperelasticity, anisotropy, fibre composite, Cosserat continuum, finite element method

hyperelasticity, anisotropy, fibre composite, Cosserat continuum, finite element method

01.07.2013

Brno

978-80-214-4739-4

61–61

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