Finite Deformations of an Elastic Cylinder During Indentation

Abstract

The problem about the indentation of the rigid spherical stamp into the cylindrical specimen was considered. The material of the specimen was assumed to be weakly compressible. The formulation of the problem was performed for the case of finite deformations. The method of construction of the constitutive relations in terms of logarithmic strain tensor for elastic media and the variant of the algorithm to take into account the variation of the contact zone were proposed. The expansion of Hencky tensor and its time derivative into the series in powers of Cauchy strain tensor were used to calculate correctly the components of these tensors. Within the indentation problem, we used the model of nonlinear elastic material which provides the best agreement between numerical solution and experimental data among other used types of constitutive relations including various elastic and hypoelastic models.