New Points of View on the Nonlocal Field Theory and Their Applications to the Fracture Mechanics(Ⅲ)——Re-Discuss the Linear Theory of Nonlocal Elasticity
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摘要: 证明了在线性非局部弹性力学中能量平衡方程是动量平衡方程的首次积分,论证了在非局部场论中局部化体力残余恒为零。详细推导了线性非局部弹性理论的本构方程,得到了反对称应力存在的新结果。Abstract: In this paper, it is proven that the balance equation of energy is the first integral of the balance equation of momentum in the linear theory of nonlocal elasticity. In other words, the balance equation of energy is not an independent one. It is also proven that the residual of nonlocal body force identically equals zero. This makes the transform formula of the nonlocal residual of energy much simpler. The linear nonlocal constitutive equations of elastic bodies are deduced in details, and a new formula to calculate the antisymmetric stress is given.
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[1] Eringen C.Vistas of nonlocal continuum physics[J].Int J Engrg Sci,1992,30(14):1551. [2] 黄再兴.关于非局部场论的几个新观点及其在断裂力学中的应用(Ⅱ)——重论非线性非局部热弹性本构方程[J].应用数学和力学,1999,20(7):713～720. [3] Friedman,Katz M.A representation theorem for additive functionals[J].Arch Rational Mech Anal,1966,21(1):49. -
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