Continuum mechanics

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

Peridynamic Analysis of Impact Damage in Composite Laminates

Abstract: The traditional methods for analyzing deformation in structures attempt to solve the partial differential equations of the classical theory of continuum mechanics. Yet these equations, because they require the partial derivatives of displacement to be known throughout the region modeled, are in some ways unsuitable for the modeling of discontinuities caused by damage, in which these derivatives fail to exist. As a means of avoiding this limitation, the peridynamic model of solid mechanics has been developed for applications involving discontinuities. The objective of this method is to treat crack and fracture as just another type of deformation, rather than as pathology that requires special mathematical treatment. The peridynamic theory is based on integral equations so there is no problem in applying the equations across discontinuities. The peridynamic method has been applied successfully to damage and failure analysis in composites. It predicts in detail the delamination and matrix damage process in c...

Mechanics of micromorphic materials

Abstract: In several previous papers [1, 2, 3], we presented some properly invariant nonlinear continuum theories of micro-elastic solids and micro-fluids in which the first stress moments, micro-stress averages and inertial spin play important roles. In the present paper we extend some of these ideas in the formulation of continuum mechanics of micromorphic materials in which the local micro-structure and intrinsic motions of the material are important. While it employs some simple statistical averages, the theory presented is not based on molecular theories and statistical mechanics but on a continuum theory. The foundation of the theory is consistent with the known principles of mechanics and a properly invariant theory of constitutive equations. It is believed that the theory has great promise in explaining many new phenomena hitherto unknown or treated partly through statistical mechanical approach in desperation. To name a few, the theory is capable of explaining the phenomenon of surface tension, couple stress, inertial spin, distributed vortices and micro-anisotropy in oriented materials, and it provides a firm foundation for the theory of polar materials. All of the classical theories of solids and fluids are included in the theory of micromorphic materials. Nevertheless, the ultimate success of the theory will have to be judged on the future outcome of rational experiments.

A molecular-statistical basis for the Gent constitutive model of rubber elasticity

Abstract: Molecular constitutive models for rubber based on non-Gaussian statistics generally involve the inverse Langevin function. Such models are widely used since they successfully capture the typical strain-hardening at large strains. Limiting chain extensibility constitutive models have also been developed on using phenomenological continuum mechanics approaches. One such model, the Gent model for incompressible isotropic hyperelastic materials, is particularly simple. The strain-energy density in the Gent model depends only on the first invariant I 1 of the Cauchy–Green strain tensor, is a simple logarithmic function of I 1 and involves just two material parameters, the shear modulus μ and a parameter J m which measures a limiting value for I 1−3 reflecting limiting chain extensibility. In this note, we show that the Gent phenomenological model is a very accurate approximation to a molecular based stretch averaged full-network model involving the inverse Langevin function. It is shown that the Gent model is closely related to that obtained by using a Pade approximant for this function. The constants μ and J m in the Gent model are given in terms of microscopic properties. Since the Gent model is remarkably simple, and since analytic closed-form solutions to several benchmark boundary-value problems have been obtained recently on using this model, it is thus an attractive alternative to the comparatively complicated molecular models for incompressible rubber involving the inverse Langevin function.

The Foundations of Classical Mechanics in the Light of Recent Advances in Continuum Mechanics

Abstract: It is a widespread belief even today that classical mechanics is a dead subject, that its foundations were made clear long ago, and that all that remains to be done is to solve special problems. This is not so. It is true that the mechanics of systems of a finite number of mass points has been on a sufficiently rigorous basis since Newton. Many textbooks on theoretical mechanics dismiss continuous bodies with the remark that they can be regarded as the limiting case of a particle system with an increasing number of particles. They cannot. The erroneous belief that they can had the unfortunate effect that no serious attempt was made for a long period to put classical continuum mechanics on a rigorous axiomatic basis. Only the recent advances in the theory of materials other than perfect fluids and linearly elastic solids have revived the interest in the foundations of classical mechanics. A clarification of these foundations is of importance also for the following reason. It is known that continuous matter is really made up of elementary particles. The basic laws governing the elementary particles are those of quantum mechanics. The science that provides the link between these basic laws and the laws describing the behavior of gross matter is statistical mechanics.