New Points of View on the Nonlocal Field Theory and Their Applications to the Fracture Mechanics(Ⅱ) Re-Discuss Nonlinear Constitutive Equations of Nonlocal Thermoelastic Bodies
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摘要: 按照理性力学的本构公理系统严格推导了非线性非局部热弹性体的本构方程,修正、补充和完善了以前的工作,所得的结果表明,非局部热弹性体的本构响应是与其物质空间的曲率及其高阶梯度相关联的,且存在满足零平均条件的反对称应力;文中给出了反对称应力与局部化残余的表达式,导出了热传递方向与温度降方向一致的结论,简要论述了局部化残余以及非局部能量守恒定律的客观性。Abstract: In this paper,nonlinear constitutive equations are deduced strictly according to the constitutive axioms of rational continuum mechanics.The existing judgements are modified and improved. The results show that the constitutive responses of nonlocal thermoelastic body are related to the curvature and higher order gradient of its material space,and there exists an antisymmetric stress whose average value in the domain occupied by thermoelastic body is equal to zero.The expressions of the antisymmetric stress and the nonlocal residuals are given.The conclusion that the directions of thermal conduction and temperature gradient are consistent is reached.In addition,the objectivity about the nonlocal residuals and the enrgy conservation law of nonlocal field is discussed briefly,and a formula for calculating the nonlocal residuals of energy changing with rigid motion of the spatial frame of reference is derived.
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