Residually Stressed Fiber Reinforced Solids: A Spectral Approach

Materials

Jose Merodio¹  MohdHalim Bin Mohd Shariff² 

[1] Department of Continuum Mechanics and Structures, Escuela de Ingenieros de Caminos, Universidad Politecnica de Madrid, 28040 Madrid, Spain;Department of Mathematics, Khalifa University of Science and Technology, Abu Dhabi 127788, UAE;

关键词: nonlinear elasticity;    constitutive model;    residual stress;    preferred direction;    spectral formulations;    physical invariants;   

DOI  :  10.3390/ma13184076

来源: DOAJ

【 摘 要 】

We use a spectral approach to model residually stressed elastic solids that can be applied to carbon fiber reinforced solids with a preferred direction; since the spectral formulation is more general than the classical-invariant formulation, it facilitates the search for an adequate constitutive equation for these solids. The constitutive equation is governed by spectral invariants, where each of them has a direct meaning, and are functions of the preferred direction, the residual stress tensor and the right stretch tensor. Invariants that have a transparent interpretation are useful in assisting the construction of a stringent experiment to seek a specific form of strain energy function. A separable nonlinear (finite strain) strain energy function containing single-variable functions is postulated and the associated infinitesimal strain energy function is straightforwardly obtained from its finite strain counterpart. We prove that only 11 invariants are independent. Some illustrative boundary value calculations are given. The proposed strain energy function can be simply transformed to admit the mechanical influence of compressed fibers to be partially or fully excluded.

【 授权许可】

Unknown