关于牛顿力学的力和拉格朗日力学的力——————理论力学札记之九

讨论了牛顿力学和拉格朗日力学中的力. 在牛顿力学中着重讨论了主动力, 约束和理想约束 力. 在拉格朗日力学中着重讨论了广义力的两种分解方法.     

Multiscale mechanics

正Multiscale mechanics is about multi-scale correlation and strong coupling between scales, which widely exists in engineering applications with a broad range of spatial and temporal scales. The averaging method and the perturbation method have been employed in the past to deal with weak coupling problems. For strong coupling problems, the methods based on small parameter expansion are no longer applicable. Fluid turbulence and solid failure are two typical cases in nonlinear mechanics [1–3].     

Extreme mechanics

With the development of cutting-edge sciences and new technologies, we have to consider the size, the density, the hardness, the stiffness and other properties of engineering materials and structures beyond the conventional ranges, as well as their mechanical behavior in extreme environments, such as ultra-conventional temperature, speed, physical and chemical fields, and severe weather, and more effective theories and methods of mechanics are required. This paper first gives the fundamental definition and the scientific connotation of extreme mechanics, then reviews the studies of extreme mechanics from three aspects: the extreme properties, the extreme loads, and the discipline development, as well as major engineering and scientific challenges. The characteristics of extreme mechanics and major challenges in the aspects of mechanical theory,computational methods and experimental techniques are discussed. Prospectivei developments of extreme mechanics are suggested.     

Nonlinear crack mechanics

S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 30, No. 11, pp. 3–9, November, 1994.     

Solid mechanics 2008

Solid Mechanics 2008

Solid mechanics 2008     

Geometric continuum mechanics

Geometric Continuum Mechanics ( GCM) is a new formulation of Continuum Mechanics ( CM) based on the requirement of Geometric Naturality ( GN). According to GN, in introducing basic notions, governing principles and constitutive relations, the sole geometric entities of space-time to be involved are the metric field and the motion along the trajectory. The additional requirement that the theory should be applicable to bodies of any dimensionality, leads to the formulation of the Geometric Paradigm ( GP) stating that push-pull transformations are the natural comparison tools for material fields. This basic rule implies that rates of material tensors are Lie-derivatives and not derivatives by parallel transport. The impact of the GP on the present state of affairs in CM is decisive in resolving questions still debated in literature and in clarifying theoretical and computational issues. As a consequence, the notion of Material Frame Indifference ( MFI) is corrected to the new Constitutive Frame Invariance ( CFI) and reasons are adduced for the rejection of chain decompositions of finite elasto-plastic strains. Geometrically consistent notions of Rate Elasticity ( RE) and Rate Elasto-Visco-Plasticity ( REVP) are formulated and consistent relevant computational methods are designed.     

骨质疏松与力学

简述了骨质疏松症在世界的发病状况，从骨的结构谈骨质疏松症的特征．介绍了荷载对骨量和骨强度的影响及应力松弛在接骨板中的应用．     

Multipolar continuum mechanics

A general theory of multipolar displacement and velocity fields with corresponding multipolar body and surface forces and multipolar stresses is developed using an energy principle, an entropy production inequality and invariance conditions under superposed rigid body motions. Constitutive equations for the multipolar stresses are discussed and explicit results are given for an elastic medium. Work in a previous paper by the present authors (1964) is shown to be a special case of that given here.