Continuum mechanics

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

Evidence for size-dependent mechanical properties from simulations of nanoscopic polymeric structures

Abstract: Discontinuous molecular dynamics simulations of a model polymer have been conducted to investigate the glass transition of ultrathin films and the mechanical properties of nanoscopic structures. Continuum mechanics models have been applied to interpret simulation data and extract apparent Young’s Moduli. Consistent with experiments, the results of simulations indicate that the glass transition temperature of thin films can be higher or lower than that of the bulk, depending on the nature of polymer–substrate interactions. Simulations also indicate that the mechanical properties of nanoscopic structures can be considerably different from those of the bulk. An analysis of molecular strain distributions in nanostructures undergoing a deformation indicate that significant stress relaxation occurs at air–polymer interfaces. A comparison of these distributions to the results of continuum, finite-element calculations reveal pronounced differences between the continuum and molecular approaches.

Superfluid mechanics for a high density of vortex lines

Abstract: There are two well known theories to describe the motion and thermodynamics of superfluids when a large number of quantized vortex lines are present and when the phenomena under study are on scales large compared with the vortex line spacing. These works have been criticised on the grounds that their governing equations for the smoothly varying, spatially averaged, fields do not satisfy the accepted invariance principles basic to modern continuum mechanics. This paper demonstrates one way in which such theories can arise from a properly invariant continuum approach and indicates the presence of hitherto unconsidered terms that bring them closer to the generally accepted microscopic picture. The resulting theory has applications both to rotating helium II in the laboratory, and to rotating neutron stars (pulsars).

Nucleation of spherical shell-like interfaces by second gradient theory: Numerical simulations

Abstract: The theory of second gradient fluids (which are able to exert shear stresses also in equilibrium conditions) allows us: (i) to describe both the thermodynamical and the mechanical behavior of systems in which an interface is present; (ii) to express the surface tension and the radius of microscopic bubbles in terms of a functional of the chemical potential; (iii) to predict the existence of a (minimal) nucleation radius for bubbles. Moreover, the above theory supplies a 3D-continuum model which is endowed with sufficient structure to allow the construction of a 2D-shell-like continuum representing a consistent approximate 2D-model for the interface between phases. In this paper we use numerical simulations in the framework of second gradient theory to obtain explicit relationships for the surface quantities typical of 2D-models. In particular, for some of the most general two-parameter equations of state, it is possible to obtain the curves describing the relationship between the surface tension, the thickness, the surface mass density and the radius of the spherical interfaces between fluid phases of the same substance. These results allow us to predict the (minimal) nucleation radii for this class of equations of state.

On the geometrical material structure of anelasticity

Abstract: G-structures are the geometric backbone of the theory of material uniformity in continuum mechanics. Within this geometric framework, anelasticity is seen as a result of evolving distributions of inhomogeneity reflected as material nonintegrability. Constitutive principles governing thetime evolution of the G-structure underlying the finite-strain theory of anelasticity (e.g., plasticity) are proposed. The material Eshelby stress tensor is shown to be thedriving force behind this evolution. This should allow for a thermodynamically admissible formulation of anelasticity viewed as a G-structure evolution.

From A to (BK)Z in Constitutive Relations

Abstract: The K‐BKZ constitutive model is now 25 years old. The article reviews the connections of the model and its variants with continuum mechanics, molecular theory, and experiment. An application of this type of model to computation is mentioned.