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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: In this paper, the authors present a numerical formulation aimed at modeling the nonlinear response of elastic materials using large deformation continuum mechanics in 3D. This finite element formulation is based on the Eulerian description of motion and the transport of the deformation gradient.
Abstract: SUMMARY
We present a numerical formulation aimed at modeling the nonlinear response of elastic materials using large deformation continuum mechanics in three dimensions. This finite element formulation is based on the Eulerian description of motion and the transport of the deformation gradient. When modeling a nearly incompressible solid, the transport of the deformation gradient is decomposed into its isochoric part and the Jacobian determinant as independent fields. A homogeneous isotropic hyperelastic solid is assumed and B-splines-based finite elements are used for the spatial discretization. A variational multiscale residual-based approach is employed to stabilize the transport equations. The performance of the scheme is explored for both compressible and nearly incompressible applications. The numerical results are in good agreement with theory illustrating the viability of the computational scheme. Copyright © 2011 John Wiley & Sons, Ltd.
48 citations
TL;DR: In this article, a methodology is devised to utilize the statistical mechanical entropy of an isolated, constrained atomistic system to define constitutive response functions for the dissipative driving force and energetic fields in continuum thermomechanics.
Abstract: A methodology is devised to utilize the statistical mechanical entropy of an isolated, constrained atomistic system to define constitutive response functions for the dissipative driving-force and energetic fields in continuum thermomechanics A thermodynamic model of dislocation mechanics is discussed as an example Primary outcomes are constitutive relations for the back-stress tensor and the Cauchy stress tensor in terms of the elastic distortion, mass density, polar dislocation density, and the scalar statistical density
48 citations
01 Jan 1968
TL;DR: In this article, it was shown that the Cosserat continuum and the theory of elasticity with microstructure can be interpreted as analytical models describing the dynamic behavior of a composite material.
Abstract: It is shown that the Cosserat continuum and the theory of elasticity with micro-structure can be interpreted as analytical models describing the dynamic behavior of a composite material. The nonclassical material constants are simply functions of the geometry and the classical constants of the two materials constituting the composite. The study of wave propagation in a laminated composite reveals that a more complex micro-structure needs to be introduced in a continuum in order to describe adequately the dispersive character of (essentially) longitudinal waves.
48 citations
TL;DR: In this article, a mesh fragmentation technique is proposed to model cracks in quasi-brittle materials based on the use of interface solid finite elements, which can be performed integrally in the context of the continuum mechanics, and complex crack patterns can be simulated without the need of tracking algorithms.
48 citations
TL;DR: In this article, the authors proposed a general one-dimensional nonlinear magneto-thermo-mechanical coupled constitutive model for a giant magnetostrictive rod under the action of multiple physical loads, such as an external magnetic field, temperature and axial pre-stress.
Abstract: For a giant magnetostrictive rod under the action of multiple physical loads, such as an external magnetic field, temperature and axial pre-stress, this paper proposes a general one-dimensional nonlinear magneto-thermo-mechanical coupled constitutive model. This model is based on the Taylor expansion of the elastic Gibbs free energy of giant magnetostrictive material and thermodynamic relations from the perspective of macro continuum mechanics. Predictions made using this model are in good agreement with experimental data for magnetization and the magnetostrictive strain curve under the collective effect of pre-stress and temperature. Additionally, the model overcomes the drawback of the existing magneto-thermo-mechanical constitutive model that cannot accurately predict the magnetization and magnetostrictive strain curve for different temperatures and pre-stresses. Furthermore, the constitutive model does not contain an implicit function and is compact, and can thus be applied in both situations of tensile and compressive stress and to both positive and negative magnetostrictive materials, and it is thus appropriate for engineering applications. Comprehensive analysis shows that the model fully describes the nonlinear coupling properties of a magnetic field, magnetostrictive strain and elasticity of a magnetostrictive material subjected to stress, a magnetic field and heat.
48 citations