'Thought Provoking' Request: UnOptimal ContinuumMechanics Terminology?

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A) I understand that an 'Ideal Fluid' Describe Behavior of Matter in Phase States of liquid/gas and sometimes Bulk-Solid:
-continually deform under applied shear stress or external force
-usually zero shear modulus
-behavior can further be specified by Constitutive Material model for that fluid, e.g. viscoelasticity

B) I understand that 'Ideal Solid' Describe Behavior of Matter in Phase States of Solid and sometimes Liquid:
-usually NON-zero shear modulus
-behavior can further be specified by Constitutive Material model for that solid, e.g. elasticity, plasticity, viscoelasticity
-solid-continua and structure elements

C) Historically, I understand the term Solid describes both phase state & matter behavior, whereas Fluid describes matter behavior for variety phase states

Assuming a just perfect enough world, and you would be the one to update the first term in Solid-Mechanics/Dynamics, then what more rigorous term would you update it with?

Would there even be a more general term instead of solid, as in the same spirit as fluid term? Any suggestions?-------------------------------------------------------------------------------------------------------------
PS, by the way term solid is also used when describing e.g. cylinder that is not hollow, but again solid refers to phase state of matter. Is there more rigorous term than 'solid or un-hollow' to describe object that is not hollow?

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Do not intend to change terminology instead want thoughts. Please be patient with this question it's something that's been nagging at my brain for awhile. Thanks