Tensor values of the second order in theory of elasticity

Abstract

The paper is devoted to basic concepts and quantities that are used in theory of elasticity. All these quantities are tensor quantities of various orders – scalars as tensors of zero order, vectors as tensors of the first order and tensors of the second order, named usually tensors. Tensors of higher orders are defined and also used in theory of elasticity. Main interest of the paper is focused on tensors of the second order, since this category comprises some basic quantities used in theory of elasticity. These are mainly a stress tensor, strain tensor and tensor of quadratic moments of area. Physical meaning and geometric notion of scalars and vectors is comparatively easy, in case of tensors of the second order it is somewhat more difficult and it is usually not mentioned in textbooks and publications. The authors attempt in their paper to demonstrate a clear geometric notion and physical meaning of tensor quantities of the second order on examples of stress tensor, strain tensor and namely tensor of quadratic moment of area.