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In this chapter, we present certain mathematical and continuum mechanics principles that are relevant to constitutive modeling and boundary value analysis. One of the most important topics is the concept of tensors. Tensors are quantities that obey coordinate transformation rules. Examples of tensors include certain scalars (mass, area, and volume), vectors (displacements and forces) and certain quantities encountered in continuum mechanics (stresses and strains).
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References
Butkov, E. (1968). Mathematical Physics. Addison-Wesley, Reading, MA, 735 pages.
Mase, G.E. (1970). Continuum Mechanics. Schaum’s Outline Series. McGraw Hill, New York, 221 pages.
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Anandarajah, A. (2010). Mathematical Foundations. In: Computational Methods in Elasticity and Plasticity. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-6379-6_2
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DOI: https://doi.org/10.1007/978-1-4419-6379-6_2
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