Abstract

A computational methodology is presented for modeling the non-linear mechanical behavior of composite structures made of FRP (Fiber-Reinforced Polymers) laminates. The model is based on the appropriate combination of the constitutive models of compounding materials, considered to behave as isolated continua, together with additional “closure equations” that characterize the micro-mechanics of the composite from a morphological point of view. To this end, any appropriate constitutive model may be selected for each phase. Each component is modeled separately and the global response is obtained by assembling all contributions taking into account the interactions between components in a general phenomenological way. To model the behavior of a single uni-directional (UD) composite laminated, a Serial-Parallel continuum approach has been developed assuming that components behave as parallel materials in the fibers alignment direction and as serial materials in orthogonal directions. Taking into account the internal morphology of the composite material, it is devised a strategy for decoupling and coupling component phases. This methodology [Rastellini 2006], named "compounding of behavior", allows to take into consideration local non linear phenomenon in the compounding materials, like damage, plasticity, etc. in a coupled manner. It is based on the proper management of homogenous constitutive models, already available for each component. In this way, it is used all developments achieved in constitutive modeling for plain materials, what makes possible the transference of this technology to composites. A laminated theory complemented with the proposed UD model is employed to describe the mechanical behavior of multi-directional laminates. A specific solution strategy for the general non linear case is proposed. It provides quick local and global convergences, what makes the model suitable for large scale structures. The model brings answers on the non-linear behavior of composites, where classical micro-mechanics formulas are restricted to their linear elastic part. The methodology is validated through several numerical analyses and contrasted against experimental data and benchmark tests.

Abstract

The understanding of the mechanics of atomistic systems greatly benefits from continuum mechanics. One appealing approach aims at deductively constructing continuum theories starting from models of the interatomic interactions. This viewpoint has become extremely popular with the quasicontinuum method. The application of these ideas to carbon nanotubes presents a peculiarity with respect to usual crystalline materials: their structure relies on a two-dimensional curved lattice. This renders the cornerstone of crystal elasticity, the Cauchy–Born rule, insufficient to describe the effect of curvature. We discuss the application of a theory which corrects this deficiency to the mechanics of carbon nanotubes (CNTs). We review recent developments of this theory, which include the study of the convergence characteristics of the proposed continuum models to the parent atomistic models, as well as large scale simulations based on this theory. The latter have unveiled the complex nonlinear elastic response of thick multiwalled carbon nanotubes (MWCNTs), with an anomalous elastic regime following an almost absent harmonic range.

Abstract

This paper shows that the stress field in the classical theory of continuum mechanics may be taken to be a covector-valued differential two-form. The balance laws and other fundamental laws of continuum mechanics may be neatly rewritten in terms of this geometric stress. A geometrically attractive and covariant derivation of the balance laws from the principle of energy balance in terms of this stress is presented.

Abstract

We revisit the derivation of the microscopic stress, linking the statistical mechanics of particle systems and continuum mechanics. The starting point in our geometric derivation is the Doyle-Ericksen formula, which states that the Cauchy stress tensor is the derivative of the free-energy with respect to the ambient metric tensor and which follows from a covariance argument. Thus, our approach to define the microscopic stress tensor does not rely on the statement of balance of linear momentum as in the classical Irving-Kirkwood-Noll approach. Nevertheless, the resulting stress tensor satisfies balance of linear and angular momentum. Furthermore, our approach removes the ambiguity in the definition of the microscopic stress in the presence of multibody interactions by naturally suggesting a canonical and physically motivated force decomposition into pairwise terms, a key ingredient in this theory. As a result, our approach provides objective expressions to compute a microscopic stress for a system in equilibrium and for force-fields expanded into multibody interactions of arbitrarily high order. We illustrate the proposed methodology with molecular dynamics simulations of a fibrous protein using a force-field involving up to 5-body interactions.

Abstract

Abstract