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Continuum mechanics
About: Continuum mechanics is a research topic. Over the lifetime, 5042 publications have been published within this topic receiving 181027 citations.
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TL;DR: A framework that adapts local and non-local continuum models to simulate static fracture problems and develops an adaptive coupling technique based on the morphing method to restrict the non- local model adaptively during the evolution of the fracture.
Abstract: We introduce a framework that adapts local and non-local continuum models to simulate static fracture problems. Non-local models based on the peridynamic theory are promising for the simulation of fracture, as they allow discontinuities in the displacement field. However, they remain computationally expensive. As an alternative, we develop an adaptive coupling technique based on the morphing method to restrict the non-local model adaptively during the evolution of the fracture. The rest of the structure is described by local continuum mechanics. We conduct all simulations in three dimensions, using the relevant discretization scheme in each domain, i.e., the discontinuous Galerkin finite element method in the peridynamic domain and the continuous finite element method in the local continuum mechanics domain.
59 citations
TL;DR: In this paper, a phenomenological constitutive equation is proposed to represent coupled pressure-dependent plastic yield and nonlinear viscous flow deformation components for modeling and classifying mass-movement processes.
Abstract: A phenomenological constitutive equation can serve as a basis for modeling and classifying mass-movement processes. The equation is derived using the principles of continuum mechanics and several simplifying assumptions about mass-movement behavior. These assumptions represent idealizations of field behavior, but they appear highly justifiable in light of the geomorphological insight that can be gained through modeling application of a mathematically tractable constitutive equation. The equation represents coupled pressure-dependent plastic yield and nonlinear viscous flow deformation components. The plastic yield component is a generalization of the Coulomb criterion to three-dimensional stress states, and the effect of pore-water pressures is accounted for by treating normal stresses as effective stresses. The nonlinear viscous flow component is a dimensionally homogeneous form of a three-dimensional power-law equation. Straightforward laboratory and field experiments can be used to estimate all plastic...
59 citations
01 Jan 2005
TL;DR: In this paper, the authors compared three formulations for a flexible spatial beam element for dynamic analysis: a finite element method (FEM) formulation, an absolute nodal coordinate (ANC) formulation with a continuum mechanics approach and an ANC formulation with an elastic line concept where the shear locking of the asymmetric bending mode is suppressed by the application of the Hellinger-Reissner principle.
Abstract: Three formulations for a flexible spatial beam element for dynamic analysis are compared: a finite element method (FEM) formulation, an absolute nodal coordinate (ANC) formulation with a continuum mechanics approach and an ANC formulation with an elastic line concept where the shear locking of the asymmetric bending mode is suppressed by the application of the Hellinger–Reissner principle. The comparison is made by means of an eigenfrequency analysis on two stylized problems. It is shown that the ANC continuum approach yields too large torsional and flexural rigidity and that shear locking suppresses the asymmetric bending mode. The presented ANC formulation with the elastic line concept resolves most of these problems.Copyright © 2005 by ASME
59 citations
TL;DR: In this article, the authors applied continuum mechanics and discrete modeling to investigate numerically rotary drill cutting experimental results on four marbles and found that the predictions of the continuum model are in full accordance with measured forces during drilling.
59 citations
TL;DR: In this article, the authors extend the theory of dimensional regularization to pre-fractal media with lower and upper cut-offs, in which D is also the order of fractional integrals employed to state global balance laws.
Abstract: This paper further continues the recently begun extension of continuum mechanics and thermodynamics to fractal porous media which are specified by a mass (or spatial) fractal dimension D, a surface fractal dimension d, and a resolution lengthscale R. The focus is on pre-fractal media (i.e., those with lower and upper cut-offs) through a theory based on dimensional regularization, in which D is also the order of fractional integrals employed to state global balance laws. In effect, the global forms of governing equations may be cast in forms involving conventional (integer-order) integrals, while the local forms are expressed through partial differential equations with derivatives of integer order but containing coefficients involving D, d and R. Here we first generalize the principles of virtual work, virtual displacement and virtual stresses, which in turn allow us to extend the minimum energy theorems of elasticity theory. Next, we generalize the extremum principles of elasto-plastic and rigid-plastic bodies. In all the cases, the derived relations depend explicitly on D, d and R, and, upon setting D = 3 and d = 2, they reduce to conventional forms of governing equations for continuous media with Euclidean geometries.
59 citations