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.
- Continuous dependence
- Dirichlet boundary conditions
- Lagrange identities arguments
- Linearised elastodynamics
- Quasi-static approximation
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