Continuous data dependence estimates are employed to rigorously derive conditions that validate the quasi-static approximation for the initial homogeneous boundary value problem in the theory of small elastic deformations superposed upon large elastic deformations. This theory imposes no sign-definite assumptions on the linearised elastic moduli and in consequence the requisite estimates are established using methods principally motivated by known Lagrange identity arguments.

中文翻译：

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线性弹性动力学初边值问题中的准静态逼近

连续数据依赖估计用于严格导出条件，该条件验证了将小弹性变形理论叠加在大弹性变形上的初始齐次边界值问题的准静态逼近。该理论没有对线性化的弹性模量施加任何符号确定的假设，因此，必要的估计是使用主要由已知的拉格朗日恒等式引力的方法建立的。