Continuum mechanics

About: Continuum mechanics is a research topic. Over the lifetime, 5042 publications have been published within this topic receiving 181027 citations.

A coupled atomistic/continuum model of defects in solids

Abstract: A method is introduced for reducing the degrees of freedom in simulations of mechanical behavior of materials without sacrificing important physics. The method essentially combines the quasicontinuum (QC) method with continuum defect models such as the discrete dislocation (DD) method. The QC formulation is used to couple a fully atomistic region to a defect-free elastic continuum. Defects existing in the elastic continuum region of the full problem of interest are treated by the DD-like methods with special boundary conditions. The full coupled problem is then solved by an Eshelby-like procedure involving superposition of the QC and DD problems, and is appropriate in both 2d and 3d. Special attention is given to dealing with dislocation defects. A procedure for the “passing” of dislocation defects from the atomistic to the continuum description in 2d problems is also presented. The overall 2d method with dislocation defects is validated by comparing the predictions of the coupled model to “exact” fully atomistic models for several equilibrium dislocation geometries and a nanoindentation problem in aluminum, and excellent agreement is obtained. The method proposed here should find application to a broad host of problems associated with the multiscale modeling of atomistic, nano- and micromechanical behavior of crystalline solids under mechanical loads.

Description of Elastic Forces in Absolute Nodal Coordinate Formulation

Abstract: The objective of this paper is to investigate the accuracy of the elastic force models that can be used in the absolute nodal coordinate finite element formulation. This study focuses on the description of the elastic forces in three-dimensional beams. The elastic forces of the absolute nodal coordinate formulation can be derived using a continuum mechanics approach. This study investigates the accuracy and usability of such an approach for a three-dimensional absolute nodal coordinate beam element. This study also presents an improvement proposal for the use of a continuum mechanics approach in deriving the expression of the elastic forces in the beam element. The improvement proposal is verified using several numerical examples that show that the proposed elastic force model of the beam element agrees with the analytical results as well as with the solutions obtained using existing finite element formulation. In the beam element under investigation, global displacements and slopes are used as the nodal coordinates, which resulted in a large number of nodal degrees of freedom. This study provides a physical interpretation of the nodal coordinates used in the absolute nodal coordinate beam element. It is shown that a beam element based on the absolute nodal coordinate formulation relaxes the assumption of a rigid cross-section and is capable of representing a distortional deformation of the cross-section. The numerical results also imply that the beam element does not suffer from the phenomenon called shear locking.

Continuum damage mechanics-based fatigue model of asphalt concrete

Abstract: A fatigue performance prediction model of asphalt concrete is developed from a uniaxial constitutive model based on the elastic-viscoelastic correspondence principle and continuum damage mechanics through mathematical simplifications. This fatigue model has a form similar to the phenomenological tensile strain-based fatigue model. Therefore, a comparison between the new model and the phenomenological model yields that the regression coefficients in the phenomenological model are functions of viscoelastic properties of the materials, loading conditions, and damage characteristics. The experimental study on two mixtures with compound loading histories demonstrates that the fatigue model maintains all of the strengths of the constitutive model such as its accuracy and abilities to account for the effects of rate of loading, stress/strain level dependency, rest between loading cycles, and mode-of-loading on fatigue life of asphalt concrete.