Deviatoric stress waves due to rheology in incompressible thermoviscoelastic solid medium with small strain, small deformation physics. (English) Zbl 1522.74056
Summary: This paper demonstrates existence of deviatoric stress waves in thermoviscoelastic (TVE) solid continua due to rheology in addition to the presence of usual deviatoric stress waves purely due to elasticity of the solid continua. The physical mechanisms that enable existence of deviatoric stress waves due to rheology in TVE solid continua are identified. Evolutions of deviatoric stress waves due to rheology are presented. Propagation, reflection, transmission, and interaction of such waves in conjunction with usual elastic stress waves are presented. The parameters controlling the rheological deviatoric stress waves and the speed of propagation of composite deviatoric stress waves due to rheology and elasticity are identified, discussed and illustrated through model problem studies. Mathematical model for the TVE solids in \(\mathbb{R}^1\) is constructed using conservation and balance laws of classical continuum mechanics in \(\mathbb{R}^3\) and the constitutive theories that are derived using entropy inequality and representation theorem. Model problems and their solutions are also presented to illustrate the validity of the concepts presented in the paper.
MSC:
| 74J10 | Bulk waves in solid mechanics |
| 74F05 | Thermal effects in solid mechanics |
| 74D05 | Linear constitutive equations for materials with memory |
| 74S05 | Finite element methods applied to problems in solid mechanics |
Keywords:
elastic wave; dynamic stiffness; relaxation time; viscoelastic polymeric medium; wave speed; space-time fnite element methodReferences:
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