On a general constitutive description for the inelastic and failure behavior of fibrous laminatesPart I: Lamina theory
It is well known that a structural design with isotropic materials can be accomplished only based on a stress failure criterion. This is, however, generally not true with laminated composites. Only when the laminate is subjected to an in-plane load, the ultimate failure of the laminate can correspond to its last-ply failure, and hence a stress failure criterion may be sufficient to detect the maximum load that can be sustained by the laminate. Even in such case, the load shared by each lamina in the laminate cannot be correctly determined if the lamina instantaneous stiffness matrix is inaccurately provided, since the lamina is always statically indeterminate in the laminate. If, however, the laminate is subjected to a lateral load, its ultimate failure occurs before the last-ply failure and the only use of the stress failure criterion is no longer sufficient; an additional critical deflection or curvature condition must be employed as well. This necessitates development of an efficient constitutive relationship for laminated composites in order that the laminate strains/deflections until the ultimate failure can be accurately calculated. A general constitutive description for the thermo-mechanical response of a fibrous laminate up to the ultimate failure with applications to various fibrous laminates is presented in these two parts of papers. The constitutive relationship is obtained by combining the classical lamination theory with a recently developed bridging micromechanics model, through a layer-by-layer analysis. The present paper focuses on the lamina analysis. Attention has been given to the applicability of the constitutive theory to the fibrous laminates stacked with a wide variety of composite laminae, including multidirectional tape laminae, woven and braided fabric composites, and knitted fabric reinforced composites, which have different constituent behavior such as elasto-plasticity and elastic-visco-plasticity. The laminate analysis and the application examples will be presented in the subsequent paper.
lamina theory laminated composite constitutive relationship bridging micromechanics model textile composite metal matrix composite composite structure mechanical property