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首页> 外文期刊>Journal of mechanics of materials and structures >ADVANTAGES OF FORMULATING EVOLUTION EQUATIONS FOR ELASTIC-VISCOPLASTIC MATERIALS IN TERMS OF THE VELOCITY GRADIENT INSTEAD OF THE SPIN TENSOR
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ADVANTAGES OF FORMULATING EVOLUTION EQUATIONS FOR ELASTIC-VISCOPLASTIC MATERIALS IN TERMS OF THE VELOCITY GRADIENT INSTEAD OF THE SPIN TENSOR

机译：自弹张量的速度梯度公式中弹性粘弹材料演化方程的计算公式的优势

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摘要

Evolution equations for tensors that characterize elastic-viscoplastic materials are often formulated in terms of a Jaumann derivative based on the spin tensor. Typically, numerical integration algorithms for such equations split the integration operation by first calculating the response due to rate of deformation, followed by a finite rotation. Invariance under superposed rigid body motions of algorithms, incremental objectivity and strong objectivity are discussed. Specific examples of steady-state simple shear at constant rate and steady-state isochoric extension relative to a rotating coordinate system are used to analyze the robustness and accuracy of different algorithms. The results suggest that it is preferable to reformulate evolution equations in terms of the velocity gradient instead of the spin tensor, since strongly objective integration algorithms can be developed using the relative deformation gradient. Moreover, this relative deformation gradient can be calculated independently of the time dependence of the velocity gradient during a typical time step.
机译：通常使用基于自旋张量的Jaumann导数来表达表征弹性-粘塑性材料的张量的演化方程。通常，用于此类方程的数值积分算法通过首先计算由于变形率引起的响应，然后进行有限旋转来拆分积分运算。讨论了在刚体运动叠加下的不变性，增量客观性和强客观性。使用恒定速率的稳态简单剪切和相对于旋转坐标系的稳态等速扩展的特定示例来分析不同算法的鲁棒性和准确性。结果表明，最好用速度梯度代替自旋张量来重新构造演化方程，因为可以使用相对变形梯度来开发强大的目标积分算法。此外，可以在典型的时间步长内独立于速度梯度的时间依赖性来计算该相对变形梯度。

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