Tensor as a tool in engineering analysis

Abstract. This paper underscores the potency of invariant character tensor and its derivative concepts accentuate synergy between isotropic other tensors corresponding vector operations. The equivalence covariant in a curvilinear coordinates system embedded with non-constant field partial an affine ingrained constant is interrogated. role Christofell symbols as connector vectors their derivatives variable are compared to Frenet-Seret skew-matrix connecting trihedrons (i.e. tangent, normal binormal) moving space curve derivatives. nexus geodesics also shown. structure metric Levi-Chivita skew-symmetric , rank-2 rank-3 respectively highlighted, such that usual operations dot product (or scalar or inner product) cross (vector spin/rotation operation}) now expressed through tensors. Recalling theory exterior differential form invoking Poincare's theorem we show application establishing exact total differential) calculus relation plane problem Elasticity. nature objects therefrom then copiously invoked deployed establish constitutive for materials: finite elasticity, within context hyperelasticity; composites, where there trade-off heterogeneity anisotropy homogenisation process whereby equations coefficients converted coefficients; plasticity, exhibited strain gradient shown how provide balance microscopic forces, macroscopic plastic flow laws concise mathematical equations.