Abe Askari

Damage and Failure Analysis based on Peridynamics - Theory and Applications ∗

In this paper we give an overview over a recent non-local formulation of continuum mechanics called the Peridynamic theory in contrast to related non-local theories in the literature. The Peridynamic approach is fundamentally different as it avoids using any spatial derivatives which arise naturally when formulating balance laws in the classical, local theory. Motivated by molecular dynamics the differential operator in the equation of motion is replaced with an integral operator which can be applied to both continuous and discontinuous fields. By comparing the elastic energy density associated with homogeneous deformations in Peridynamics to the corresponding energy in classical elasticity we show how the connection to experimentally measurable material properties such as the Young’s modulus and the Poisson ratio can be established. This is done by expressing the elastic energy in Peridynamics as a function of the invariants of the strain tensor, a rigorously approach not previously published. The paper concludes with an example of a crack turning in a 3D isotropic material, illustrating the strength of the Peridynamic formulation in problems where the crack path is not known in advance.

Peridynamics for analysis of failure in advanced composite materials

Peridynamics has been recently introduced as a way to simulate the initiation and propagation of multiple discontinuities (e.g. cracks). It is an alternative to classical continuum damage mechanics and fracture mechanics and is based on a nonlocal rewriting of the equilibrium equation. This new technique is particularly promising in the case of composite materials, in which very complex mechanisms of degradation must be described. We present here some fundamental aspects of peridynamics models for composite materials, and especially laminates. We also propose an approach to couple peridynamics domains with classical continuum mechanics (which relies on the concept of contact forces) by the use of a recently introduced coupling technique: the morphing technique, that appears to be a very versatile and powerful tool for coupling local to nonlocal descriptions.

Cyclic hygrothermal aging of aircraft lightning protections: phenomenological overview.

The recent transition to full composite fuselages is a major breakthrough in aeronautical design. To ensure satisfactory lightning protection, the electrical properties of the primary composite structure need to be improved and a design solution lies on bonding a metallic shnet to the fuselage. An important issue is the prediction of the aging behavior of this top layer when exposed to severe aging conditions representative of ight environment. Multiple aging mechanisms a ect this top layer made of thermoset resin and metallic shnet with complex geometry and a rst modeling strategy is a necessary starting point to better understand its evolution. This paper describes the overall phenomenology and the di erent mechanisms that can be expected in such a structure.

Dispersive Wave Propagation in the Nonlocal Peridynamic Theory

Peridynamics is a nonlocal formulation of continuum mechanics that is oriented toward deformations including discontinuities, especially fractures. However already the linear elastic problem is considerably more complex than the corresponding local problem governed by the NAVIER equations. For example, the presence of long-range forces leads to the dispersion of elastic waves. The amount of dispersion is governed by the peridynamic horizon, a length-scale that naturally appears in in the equation of motion. Another example is the emergence and propagation of discontinuities that can be observed by studying the RIEMANN problem. In this presentation we show how FOURIER transformations can be used to find a representation of the solution of the general inhomogeneous initial value problem for the 3D linear bond-based peridynamic formulation. Several examples illustrate this approach and show the importance of the peridynamic horizon. Finally we demonstrate how the nonlinear dispersion relation can be used to capture experimentally measure dispersion relations.Copyright

Experimental investigation of cyclic hygrothermal aging of aircraft lightning protection

This work provides an experimental investigation of the cyclic hygrothermal aging of a hybrid composites. We aimed to propose a general framework in the view to further optimize polymer-based composites. It reports experimental data and relevant observations collected during an aging campaign (up to 2000 cycles) where anhydride-cured epoxy samples as well as composites samples are exposed to environmental conditions. The data gathered during the whole campaign reveals that (1) the polymer displays a non-classical sorption behavior (2) the volume change is correlated to the mass uptake (3) the elastic modulus is correlated to the glass transition temperature. Matrix and interface degradation of the hybrid composite is monitored by means of microstructural observations.