Hemivariational Inequality Modeling of Hybrid Laminates with Unidirectional Composite Constituents

Abstract

Theoveralltensileandbendingbehaviorofunidirectionalcompositeelementswithmonotoneandnonmonotone, possibly multivalued,constitutive laws foreach constituent arestudied within a nonsmooth mechanics framework. A nondifferentiable and possibly nonconvex, caused by degradation effects, potential energy is formulated for the whole mechanical system. For the structural analysis problem the potential energy minimization problem is considered. The arising variational or hemivariational (in the case of nonmonotone laws ) inequality problems are solved by appropriate nonconvex-nonsmooth computational mechanics techniques. Parametric numerical investigations of typical composite elements are presented, which shed light into the complex behavior of the composite structural elements. On the other hand, the arising overall laws can be used as phenomenological laws for structural analysis of large-scale structures incorporating the studied composite elements. I. Introduction C OMPOSITE materials is a rapidly maturing technology with emerging applications in a wide range of industries far beyond the aerospace domain where they e rst became popular. Nowadays, composites are popular even in the civil-engineering domain and are used for the construction of light bridges, domes, space trusses, etc. Moreover, composite elements are used in structures that are susceptible to electrochemical actions or corrosion, such as underground facilities, offshore oil platforms, waterways, and harbors. 1 The basic principles involved in the design of structures made of compositematerialsarethesameasthoseofisotropicmaterialssuch as steel. The classical theories and methods of analysis can be used for the design ofcomposite structures, asfar as the constitutive relationship takes into account the material anisotropy and the strength degradation effects, which are present in the majority of composite materials. Moreover, the same basic design knowledge and technique used for other materials as, e.g., for reinforced concrete, can be applied to compositestructures.However, thereader shouldhave inmindthattheimplementationofaccuratedesignmethodsforsteel (which is the materialwith the most simple constitutive relationship used today in civil-engineering structures ) has required a century of research and experience. In this framework it is not only very important to study these new materials at the materials level, but it is also very important to know their behavior at the structural level. (Compare in this respect the combined effects in the study of beam-to-column connections in steel structures, which lead to strong nonlinearities.) Also, the phenomenological (macroscopic ) response under certain types of loading is of great importance. In unidirectional composites the e bers are aligned in one only direction, thus achieving the maximum e ber alignment and the maximum e ber content. As in principle, the strength of a composite structural element increases in proportion to increasing e ber content, this type of composite provides high strength to the direction of the e bers but very low transverse strength. Therefore it is very common to combine unidirectional composite materials in a cer