The construction and application of an atomistic J-integral via Hardy estimates of continuum fields

In this work we apply a Lagrangian kernel-based estimator of continuum fields to atomic data in order to estimate the J-integral for the analysis of cracks and dislocations. We show that this method has the properties of: consistency between the energy, stress and deformation fields; path independence of the contour integrals of the Eshelby stress; and excellent correlation with linear elastic fracture mechanics theory for appropriately constructed simulations. We discuss the appropriate reference configuration and reference energy for this type of analysis. Lastly, we use canonical examples to demonstrate that the proposed method is a direct and rational approach for estimating the configurational forces on atomic defects.     

A phenomenological and extended continuum approach for modelling non-equilibrium flows

This paper presents a new technique that combines Grad’s 13-moment equations (G13) with a phenomenological approach to rarefied gas flows. This combination and the proposed solution technique capture some important non-equilibrium phenomena that appear in the early continuum-transition flow regime. In contrast to the fully coupled 13-moment equation set, a significant advantage of the present solution technique is that it does not require extra boundary conditions explicitly; Grad’s equations for viscous stress and heat flux are used as constitutive relations for the conservation equations instead of being solved as equations of transport. The relative computational cost of this novel technique is low in comparison to other methods, such as fully coupled solutions involving many moments or discrete methods. In this study, the proposed numerical procedure is tested on a planar Couette flow case, and the results are compared to predictions obtained from the direct simulation Monte Carlo method. This test case highlights the presence of normal viscous stresses and tangential heat fluxes that arise from non-equilibrium phenomena, which cannot be captured by the Navier–Stokes–Fourier constitutive equations or phenomenological modifications.      

Experimental and Numerical Study of Paperboard Interface Properties

Laminated paperboard is widely used in packaging products. Interface delamination plays a crucial role in converting paperboard to a carton through the creasing and folding process. Thus, the aim of this study is to experimentally and numerically investigate the interface fracture behavior in pure crack opening mode (mode I) and sliding mode (mode II). Four experimental tests have been evaluated and compared to numerical simulation, namely, the z-directional tensile test (ZDT), double-notch shear test (DNS), double-cantilever beam test (DCB) and end-notched flexure test (ENF). It was shown that, for the paperboard specimens tested, the ZDT test was sufficient to fully characterize the mode I crack growth response. However, the DNS and ENF tests were required to determine the maximum shear stress and the fracture toughness of pure mode II, respectively. Further mixed-mode investigation would enable the analysis of paperboard delamination behavior during the creasing and folding process.     

Anisotropic finite elastoplasticity with nonlinear kinematic and isotropic hardening and application to sheet metal forming

The paper discusses the derivation and the numerical implementation of a finite strain material model for plastic anisotropy and nonlinear kinematic and isotropic hardening. The model is derived from a thermodynamic framework and is based on the multiplicative split of the deformation gradient in the context of hyperelasticity. The kinematic hardening component represents a continuum extension of the classical rheological model of Armstrong–Frederick kinematic hardening. Introducing the so-called structure tensors as additional tensor-valued arguments, plastic anisotropy can be modelled by representing the yield surface and the plastic flow rule as functions of the structure tensors. The evolution equations are integrated by a new form of the exponential map that preserves plastic incompressibility and uses the spectral decomposition to evaluate the exponential tensor functions in closed form. Finally, the applicability of the model is demonstrated by means of simulations of several deep drawing processes and comparisons with experiments.