Mindlin’s Micro-structural and Gradient Elasticity Theories and Their Thermodynamics
Mindlin’s Micro-structural and Gradient Elasticity Theories and Their Thermodynamics
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DOI：
10.1007/s10659-016-9572-7
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发表时间：
2016-02
影响因子：
2
通讯作者：
C. Broese;C. Tsakmakis;D. Beskos
中科院分区：
文献类型：
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作者：
C. Broese;C. Tsakmakis;D. Beskos
当假定微变形是经典位移梯度的函数时，Mindlin的微结构弹性材料的极限出现了特殊的梯度弹性模型。在这种情况下，连续体内部点的唯一独立的运动自由度是经典的，由位移场反映出来。目前的工作解决了一类梯度弹性模型，包括那些Mindlin，在一个连续体理论的背景下，没有双重力的平衡定律，没有部分应力是不确定的。这是通过使用一个非常规的热力学框架来完成的。所得模型被重新表述为具有非经典体和非经典惯性力的经典连续体。新的解释提出了适当的边界条件的定义，其方式不同于处理这一问题的参考文献中通常采用的方式。通过具有微刚度和微惯量的梯度弹性杆轴向运动的数值算例，说明了上述模型的性能。
Particular gradient elasticity models arise as limits of Mindlin’s micro-structured elastic materials, when the micro-deformation is assumed to be a function of the classical displacement gradient. In this case, the only independent kinematical degrees of freedom in the internal points of the continuum are the classical ones, reflected by the displacement field. The present work addresses a class of gradient elasticity models, including those of Mindlin, in the context of a continuum theory without balance laws of double-forces and without parts of stresses being left indeterminate. This is accomplished by using a non-conventional thermodynamic framework. The resulting models are restated as classical continua with non-classical body and non-classical inertial forces. The new interpretation suggests a definition of the appropriate boundary conditions in a different way than usually done in references addressing this subject. Numerical examples involving the axial motion of a gradient elastic bar possessing micro-stiffness and micro-inertia are studied in detail to illustrate the behavior of the above models.