Continuum mechanics

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

A hierarchical multi-physics model for design of high toughness steels

Abstract: In support of the computational design of high toughness steels as hierarchically structured materials, a multiscale, multiphysics methodology is developed for a `ductile fracture simulator.' At the nanometer scale, the method unites continuum mechanics with quantum physics, using first-principles calculations to predict the force-distance laws for interfacial separation with both normal and plastic sliding components. The predicted adhesion behavior is applied to the description of interfacial decohesion for both micron-scale primary inclusions governing primary void formation and submicron-scale secondary particles governing microvoid-based shear localization that accelerates primary void coalescence. Fine scale deformation is described by a `Particle Dynamics' method that extends the framework of molecular dynamics to multi-atom aggregates. This is combined with other meshfree and finite-element methods in two-level cell modeling to provide a hierarchical constitutive model for crack advance, combining conventional plasticity, microstructural damage, strain gradient effects and transformation plasticity from dispersed metastable austenite. Detailed results of a parallel experimental study of a commercial steel are used to calibrate the model at multiple scales. An initial application provides a Toughness-Strength-Adhesion diagram defining the relation among alloy strength, inclusion adhesion energy and fracture toughness as an aid to microstructural design. The analysis of this paper introduces an approach of creative steel design that can be stated as the exploration of the effective connections among the five key-components: elements selection, process design, micro/nanostructure optimization, desirable properties and industrial performance by virtue of innovations and inventions.

Continuum damage mechanics for hysteresis and fatigue of quasi-brittle materials and structures

Abstract: For a material exhibiting hysteresis such as quasi-brittle materials, it is natural to consider that hysteresis and fatigue are related to each other. One shows in the present work that damage, from the continuum damage mechanics point of view, may be seen as the link between both phenomena. One attempts, hence, to set up a unified modelling of hysteresis and damage. Numerical examples are given for concrete and validate the proposed model of internal sliding and friction coupled with damage. The problem of a proper phenomenological modelling of the micro-defects closure effect leading to a dissymmetric tension/compression response and to stiffness recovery in compression is also addressed. Cyclic and fatigue applications are in mind, and also random fatigue and seismic responses. Copyright © 2006 John Wiley & Sons, Ltd.

A first course in continuum mechanics : for physical and biological engineers and scientists

Abstract: 1. Introduction. 2. Vectors and Tensors. 3. Stress. 4. Principal Stresses and Principal Axes. 5. Analysis of Deformation. 6. Velocity Fields and Compatibility Conditions. 7. Constitutive Equations. 8. Isotropy. 9. Mechanical Properties of Real Fluids and Solids. 10. Derivation of Field Equations. 11. Field Equations and Boundary Conditions in Fluid Mechanics. 12. Some Simple Problems in Elasticity. 13. Stress, Strain, and Active Remodeling of Structures. Index.

Nonlocal vibration and buckling analysis of single and multi-layered graphene sheets using finite strip method including van der Waals effects

Abstract: Detailed studies on the nanoscale vibration and buckling characteristics of rectangular single and multi-layered graphene sheets (SLGSs and MLGSs) are carried out using semi-analytical finite strip method (FSM), based on the classical plate theory (CPT). The displacement functions of the sheets are evaluated using continuous harmonic function series which satisfy the boundary conditions in one direction and a piecewise interpolation polynomial in the other direction. Nonlocal continuum mechanics is employed to derive the differential equation of the system. The weighted residual method is employed to obtain stiffness, stability and mass matrices of the graphene sheets. The effects of van der Waals (vdW) forces which are present as bonding forces between the layers are considered in the stiffness matrix of the system. The analysis of MLGSs is much more complex due to the influence of vdW forces. The mechanical properties of the graphene sheet are assumed in two ways as orthotropic or isotropic materials. A matrix eigenvalue problem is solved to find the natural frequency and critical stress of GSs subjected to different types of in-plane loadings including uniform and non-uniform uniaxial loadings. The accuracy of the proposed model is validated by comparing the results with those reported by the available references. Furthermore, a comprehensive parametric study is performed to investigate the effects of various parameters such as boundary conditions, nonlocal parameter, aspect ratio and the type of loading on the results.