Continuum mechanics

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

Average balance equations, scale dependence, and energy cascade for granular materials.

Abstract: A new averaging method linking discrete to continuum variables of granular materials is developed and used to derive average balance equations. Its novelty lies in the choice of the decomposition between mean values and fluctuations of properties which takes into account the effect of gradients. Thanks to a local homogeneity hypothesis, whose validity is discussed, simplified balance equations are obtained. This original approach solves the problem of dependence of some variables on the size of the averaging domain obtained in previous approaches which can lead to huge relative errors (several hundred percentages). It also clearly separates affine and nonaffine fields in the balance equations. The resulting energy cascade picture is discussed, with a particular focus on unidirectional steady and fully developed flows for which it appears that the contact terms are dissipated locally unlike the kinetic terms which contribute to a nonlocal balance. Application of the method is demonstrated in the determination of the macroscopic properties such as volume fraction, velocity, stress, and energy of a simple shear flow, where the discrete results are generated by means of discrete particle simulation.

Thermoelastic damping in nonlocal nanobeams considering dual-phase-lagging effect:

Abstract: This paper aims to present an explicit relation for thermoelastic damping in nanobeams capturing the small-scale effects on both the continuum mechanics and heat conduction domains. To incorporate ...

A micromorphic approach to dislocation theory and its relation to several existing theories.

Abstract: : Two separate continuum dislocation theories are presented; one dealing with static incompatible, micropolar dislocations and disclinations, as encountered in initial stress problems, and the other with a dynamical theory of micromorphic solids containing continuous distributions of dislocations Relationships between several continuum dislocation theories and micromorphic mechanics are established by providing extensions and new interpretations of the micromorphic theory First both micromorphic and micropolar theories of elastic solids are summarized, and then the theories of Kroner, Fox, and Berdichevskii and Sedov are discussed in some detail within this framework In the last section, by use of micromorphic kinematics, dislocation density, strain, and microstrain tensors are introduced and constitutive equations are constructed Together with the balance laws this constitutes a complete dynamical theory The theory is intended for predictions of motions and micromotions of a solid containing dislocations undergoing elastic deformations From the micromotion, the dislocation density and first stress moments can be calculated (Author)

A review of contact algorithms

Abstract: Moving interfaces between media play an important role in technological and natural processes. The development of methods for solving problems with moving interfaces is one of the major aims of continuum mechanics. This review concentrates on parts of the numerical methods of continuum mechanics named contact algorithms that serve to track and calculate moving interfaces such as contact, phase change, and moving free boundaries.