Inertia

About: Inertia is a research topic. Over the lifetime, 12006 publications have been published within this topic receiving 164291 citations.

The Continuum Mechanics of Coherent Two-Phase Elastic Solids with Mass Transport

Abstract: We develop a theory for the dynamics of an interface in a two-phase elastic solid with kinetics driven by mass transport and stress. We consider a two-phase system consisting of bulk regions separated by a sharp interface endowed with energy and capable of supporting force. Our discussion is based on balance laws for mass and force in conjunction with a version of the second law-appropriate to a mechanical system out of equilibrium-which we use to develop a suitable constitutive theory for the interface. It is assumed that mass transport is characterized by the bulk diffusion of a single independent species; we neglect mass diffusion within the interface; limit our discussion to a continuous chemical potential and to a coherent interface; neglect the elasticity of the interface; and consider only infinitesimal deformations, neglecting inertia. We show that the field equations and free-boundary conditions can be developed in a simple manner in terms of the diffusion potential and its time derivatives, as opposed to the usual formulation in terms of concentration. Natural consequences of the thermodynamic framework are Lyapunov functions for the resulting evolution problems. This leads to a hierarchy of variational principles that should describe the equilibrium shapes of misfitting particles as well as possible microstructures that might form; these principles are applicable both in the absence and presence of an applied stress.

Effect of inertia on sheared disordered solids: critical scaling of avalanches in two and three dimensions.

Abstract: Molecular dynamics simulations with varying damping are used to examine the effects of inertia and spatial dimension on sheared disordered solids in the athermal quasistatic limit In all cases the distribution of avalanche sizes follows a power law over at least three orders of magnitude in dissipated energy or stress drop Scaling exponents are determined using finite-size scaling for systems with 10(3)-10(6) particles Three distinct universality classes are identified corresponding to overdamped and underdamped limits, as well as a crossover damping that separates the two regimes For each universality class, the exponent describing the avalanche distributions is the same in two and three dimensions The spatial extent of plastic deformation is proportional to the energy dissipated in an avalanche Both rise much more rapidly with system size in the underdamped limit where inertia is important Inertia also lowers the mean energy of configurations sampled by the system and leads to an excess of large events like that seen in earthquake distributions for individual faults The distribution of stress values during shear narrows to zero with increasing system size and may provide useful information about the size of elemental events in experimental systems For overdamped and crossover systems the stress variation scales inversely with the square root of the system size For underdamped systems the variation is determined by the size of the largest events

New insights on steady, non-linear flow in porous media

Abstract: We consider two problems of nonlinear flow in porous media: 1) a derivation of a cubic weak inertia correction of Darcy's law which is valid for any matrix anisotropy, and 2) a description of flow by the weak inertia equation for low Reynolds numbers and a Forchheimer equation for high Reynolds number laminar flow Recent homogenization studies show that the weak inertia correction to Darcy's law is not a square term in velocity, as it is in the Forchheimer equation, but instead a cubic term in velocity By imposing that the pressure loss is invariant under flow reversion, it has been shown that the weak inertia equation is valid even for anisotropic media We show, by using the homogenization technique, that the weak inertia equation is valid for any anisotropic matrix symmetry without imposing a reversed flow symmetry For the second problem, we reexamine published data We find that the description 2) applies well A spline may be applied in the crossover regime

Motor control goes beyond physics: differential effects of gravity and inertia on finger forces during manipulation of hand-held objects

Abstract: According to basic physics, the local effects induced by gravity and acceleration are identical and cannot be separated by any physical experiment. In contrast—as this study shows—people adjust the grip forces associated with gravitational and inertial forces differently. In the experiment, subjects oscillated a vertically-oriented handle loaded with five different weights (from 3.8 N to 13.8 N) at three different frequencies in the vertical plane: 1 Hz, 1.5 Hz and 2.0 Hz. Three contributions to the grip force—static, dynamic, and stato-dynamic fractions—were quantified. The static fraction reflects grip force related to holding a load statically. The stato-dynamic fraction reflects a steady change in the grip force when the same load is moved cyclically. The dynamic fraction is due to acceleration-related adjustments of the grip force during oscillation cycles. The slope of the relation between the grip force and the load force was steeper for the static fraction than for the dynamic fraction. The stato-dynamic fraction increased with the frequency and load. The slope of the dynamic grip force–load force relation decreased with frequency, and as a rule, increased with the load. Hence, when adjusting grip force to task requirements, the central controller takes into account not only the expected magnitude of the load force but also such factors as whether the force is gravitational or inertial and the contributions of the object mass and acceleration to the inertial force. As an auxiliary finding, a complex finger coordination pattern aimed at preserving the rotational equilibrium of the object during shaking movements was reported.