Continuum mechanics

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

Elastic deformations of tip and sample during atomic force microscope measurements

Abstract: Two established models, based on continuum mechanics, are discussed to describe the elastic deformation of the tip and the sample in the atomic force microscope. We present arguments why the elastic deformation of a surface is more rigorously described by Sneddon mechanics rather than by the habitually used Hertzian mechanics. The results presented here show that elastic deformations are an important issue for measurements with the atomic force microscope. We demonstrate how elastic deformations impose limits to the capability of the atomic force microscope to image at true atomic resolution and how elastic deformations can be used to measure local elastic properties of a sample. Against the commonly accepted assumption of a ‘‘rigid’’ tip, we show that the elastic deformation of the tip can become a significant factor, when imaging hard samples. With few exceptions, the atomic force microscope has not been operated at true atomic resolution so far and more complex contrast mechanisms, with multiple atom interaction, must be considered.

1 – Unified Cyclic Viscoplastic Constitutive Equations: Development, Capabilities, and Thermodynamic Framework

Abstract: This chapter focuses on the metallic materials which are developed with the objective of the inelastic analysis of structural components. They are based on the concepts of continuum mechanics, where a particular representative volume element of material can be considered as submitted to a macroscopically uniform stress, neglecting the microstress microstrain inhomogeneities at the microscale. The application domains are limited to the quasistatic deformation of metallic materials (strain rate between 10 -10 and 10 -1 ), especially under cyclic loading conditions. The constitutive equations are written in their small strain form. Also, high-temperature conditions will be considered, as well as loading under varying temperatures. Unified viscoplastic constitutive equations means the nonseparation of the plastic (rate-independent) and creep (rate-dependent) parts of the inelastic strain. Moreover, the viscoplastic equations are based on a general framework consistent both with classical plasticity (elastic domain, yield surface, loading/unloading condition) and with thermoviscoplasticity without an elastic domain. Then rate-independent conditions will be obtained consistently as a limit case of the general viscoplastic scheme.

A continuum theory of thermoelectric bodies and effective properties of thermoelectric composites

Abstract: We develop a continuum theory for thermoelectric bodies following the framework of continuum mechanics and conforming to general principles of thermodynamics. For steady states, the governing equations for local fields are intrinsically nonlinear. However, under conditions of small variations of electrochemical potential, temperature and their gradients, the governing equations may be reduced to a linear elliptic system, which can be conveniently solved to determine behaviors of thermoelectric bodies. The linear theory is further applied to predict effective properties of thermoelectric composites. In particular, explicit formula of effective properties are obtained for simple microstructures of laminates and periodic E-inclusions, which implies useful design principles for engineering thermoelectric composites.