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Yes, indeed. Sometimes tensile modulus is different from flexural modulus, especially for composites. But tensile modulus and elastic modulus and Young's modulus are equivalent terms.
The elastic modulus, also called Young's modulus, is identical to the tensile modulus. It relates stress to strain when loaded in tension.
Young's modulus
1. Young's modulus of elasticity, E, also called elastic modulus in tension 2. Flexural modulus, usually the same as the elastic modulus for uniform isotropic materials 3. Shear modulus, also known as modulus of rigidity, G ; G = E/2/(1 + u) for isotropic materials, where u = poisson ratio 4. Dynamic modulus 5. Storage modulus 6. Bulk modulus The first three are most commonly used; the last three are for more specialized use
Young's Modulus (modulus of elasticity) describes the stress-strain behavior of a material under monotonic loading. The dynamic modulus of elasticity describes the same behavior under cyclic or vibratory loading.