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Theory of repeated superposition of large deformations: Elastic and viscoelastic bodies. (English) Zbl 0918.73026
Summary: We discuss the basic constitutive relations and boundary value problems of the theory of repeatedly superimposed large deformations of elastic and viscoelastic materials. We then concentrate on two-dimensional problems of nucleation and deformation of circular or elliptical holes in the finite strain formulation. The cases are examined when cavity sharp is known either initially or in the final state, or (for a viscoelastic material) at some intermediate moment. The correction for nonlinear effects is found to be of the order of 30% at the points of maximal stress concentration.

MSC:
74B20 Nonlinear elasticity
74D10 Nonlinear constitutive equations for materials with memory
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