Continuum mechanics

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

A Linear Beam Finite Element Based on the Absolute Nodal Coordinate Formulation

Abstract: In this paper, a new two-dimensional shear deformable beam element based on the absolute nodal coordinate formulation is proposed. The nonlinear elastic forces of the beam element are obtained using a continuum mechanics approach, without employing a local element coordinate system. In this study, linear polynomials are used to interpolate both the transverse and longitudinal components of the displacement. This is different from other absolute nodal-coordinate-based beam elements where cubic polynomials are used in the longitudinal direction. The use of linear interpolation polynomials leads to the phenomenon known as shear locking. This defect is avoided through the adoption of selective integration within the numerical integration method. The proposed element is verified using several numerical examples. The results of the proposed element are compared to analytical solutions and the results for an existing shear deformable beam element. It is shown that by using the proposed element, accurate linear and nonlinear static deformations, as well as realistic dynamic behavior including the capturing of the centrifugal stiffening effect, can be achieved with a smaller computational effort than by using existing shear deformable two-dimensional beam elements.

Continuum Mechanics Aspects of Geodynamics and Rock Fracture Mechanics : Proceedings of the NATO Advanced Study Institute held in Reykjavik, Iceland, 11-20 August, 1974

Abstract: Aspects of earthquake energy.- Construction of earth models.- The Fe2O theory of planetary cores.- Principles of fracture mechanics.- Fracture problems in a nonhomogeneous medium.- Dynamics, of fracture propagation.- Nonlocal elasticity and waves.- On the problem of crack tip in nonlocal elasticity.- Statistical problems in the theory of elasticity.- Internal stresses in crystals and in the earth.- The elements of non-linear continuum mechanics.- Anisotropic elastic and plastic materials.- Symmetric micromorphic continuum: Wave propagation, point source solutions and some applications to earthquake processes.- Surface deformation in Iceland and crustal stress over a mantle plume.- Fault displacement and ground tilt during small earthquakes.

Micromechanical modeling for behavior of cementitious granular materials

Abstract: Crack damage is commonly observed in cementitious granular materials. Previous analytical models based on continuum mechanics have limitations in analyzing localized damages at a microscale level. In this paper, a micromechanics approach is adopted that considers a contract law for the interparticle behavior of two particles connected by a binder. The model is based on the premises that the interparticle binder initially contains microcracks. As a result of external loading, these microcracks propagate and grow. Thus, binders are weakened and fail. Theory of fracture mechanics is employed to model the propagation and growth of the microcracks. The contact law is then incorporated in the analysis for the overall damage behavior of material using a discrete element method. Using this model, the stress-strain behaviors under uniaxial and biaxial conditions were simulated. A reasonable agreement is found between the predictions and experimental results.

Nonlinear Elasticity: Strain-energy Functions with Multiple Local Minima: Modeling Phase Transformations Using Finite Thermo-elasticity

Abstract: This chapter provides a brief introduction to the following basic ideas pertaining to thermoelastic phase transitions: the lattice theory of martensite, phase boundaries, energy minimization, Weierstrass-Erdmann corner conditions, phase equilibrium, nonequilibrium processes, hysteresis, the notion of driving force, dynamic phase transitions, nonuniqueness, kinetic law, nucleation condition, and microstructure. Introduction This chapter provides an introduction to some basic ideas associated with the modeling of solid-solid phase transitions within the continuum theory of finite thermoelasticity. No attempt is made to be complete, either in terms of our selection of topics or in the depth of coverage. Our goal is simply to give the reader a flavor for some selected ideas. This subject requires an intimate mix of continuum and lattice theories, and in order to describe it satisfactorily one has to draw on tools from crystallography, lattice dynamics, thermodynamics, continuum mechanics and functional analysis. This provides for a remarkably rich subject which in turn has prompted analyses from various distinct points of view. The free-energy function has multiple local minima, each minimum being identified with a distinct phase, and each phase being characterized by its own lattice Crystallography plays a key role in characterizing the lattice structure and material symmetry, and restricts deformations through geometric compatibility. The thermodynamics of irreversible processes provides the framework for describing evolutionary processes. Lattice dynamics describes the mechanism by which the material transforms from one phase to the other. And eventually all of this needs to be described at the continuum scale.