Speaker
Description
This contribution examines the unification of tensor and matrix approaches in continuum mechanics, with a particular emphasis on their relationships and the potential for smooth interchange between the two frameworks. While tensor algebra provides a coordinate-independent framework, matrix algebra offers a computationally accessible representation. The tensor and matrix representations are both powerful tools for describing physical phenomena; however, their distinct notations often lead to confusion. By examining the connections between these two approaches, the presentation demonstrate how tensor operations, such as contraction, inner product and linear transformation, translate directly into matrix operations, and vice versa. This unification allows for a more rationalized and efficient treatment of continuum problems, fostering clearer insights into the underlying physics while enhancing computational efficiency. By clarifying the relationship between these approaches, this work aims to enhance both theoretical understanding and computational mechanics.
