A thermomechanical theory for a porous anisotropic elastic solid with inclusions

1984 ◽  
Vol 87 (1) ◽  
pp. 11-33 ◽  
Author(s):  
Stephen L. Passman ◽  
Romesh C. Batra
Keyword(s):  
Elastic Solid ◽  
Thermomechanical Theory ◽  
Anisotropic Elastic

Simulation of the Film Blowing Process Using a Continuum Model for Crystallization in Polymers

2000 ◽  
Author(s):  
I. J. Rao
Keyword(s):  
Viscoelastic Fluid ◽  
Crystalline Phase ◽  
Elastic Solid ◽  
Second Law Of Thermodynamics ◽  
Maxwell Model ◽  
Polymer Processing ◽  
Solid Polymer ◽  
Crystalline Solid ◽  
Film Blowing ◽  
Anisotropic Elastic

Abstract In this paper we simulate the film blowing process using a model developed to study crystallization in polymers (see Rao (1999), Rao and Rajagopal (2000b)). The framework was developed to generate mathematical models in a consistent manner that are capable of simulating the crystallization process in polymers. During crystallization the polymer transitions from a fluid like state to a solid like state. This transformation usually takes place while the polymer undergoes simultaneous cooling and deformation, as in film blowing. Specific models are generated by choosing forms for the internal energy, entropy and the rate of dissipation. The second law of thermodynamics along with the assumption of maximization of dissipation is used to determine constitutive forms for the stress tensor and the rate of crystallization. The polymer melt is modeled as a rate type viscoelastic fluid and the crystalline solid polymer is modeled as an anisotropic elastic solid. The mixture region, where in the material transitions from a melt to a semi-crystalline solid, is modeled as a mixture of a viscoelastic fluid and an elastic solid. The anisotropy of the crystalline phase and consequently that of the final solid depends on the deformation in the melt during crystallization, a fact that has been known for a long time and has been exploited in polymer processing. The film blowing process is simulated using a generalized Maxwell model for the melt and an anisotropic elastic solid for the crystalline phase. The results of the simulation agree qualitatively with experimental observations and the methodology described provides a framework in which the film blowing problem can be analyzed.

Finite strains in an anisotropic elastic continuum

1950 ◽  
Vol 202 (1070) ◽  
pp. 345-358 ◽  
Keyword(s):  
Equations Of State ◽  
Elastic Solid ◽  
Finite Strains ◽  
Free Energy Function ◽  
Elastic Solids ◽  
Elastic Continuum ◽  
Invariance Properties ◽  
Anisotropic Elastic ◽  
Necessary And Sufficient ◽  
Thermodynamic Restrictions

The discussion in a previous paper (Oldroyd 1950), on the invariance properties required of the equations of state of a homogeneous continuum, is extended by taking into account thermodynamic restrictions on the form of the equations, in the case of an elastic solid deformed from an unstressed equilibrium configuration. The general form of the finite strainstress-temperature relations, expressed in terms of a free-energy function, is deduced without assuming that the material is isotropic. The results of other authors based on the assumption of isotropy are shown to follow as particular cases. The equations of state are derived by considering quasi-static changes in an elastic solid continuum; the results then apply to non-ideally elastic solids in equilibrium, or subjected to quasi-static changes only, and to ideally elastic solids in general motion. A necessary and sufficient compatibility condition for the finite strains at different points of a continuum is also derived. As a simple illustration of the derivation and use of equations of state involving anisotropic physical constants, the torsion of an anisotropic cylinder is discussed briefly.

On the existence of type-6 transonic states in linear elastic media of cubic symmetry

1987 ◽  
Vol 411 (1840) ◽  
pp. 251-263 ◽  
Keyword(s):  
Wave Propagation ◽  
Surface Wave ◽  
Elastic Solid ◽  
Mechanics Of Solids ◽  
Elastic Media ◽  
Slowness Surface ◽  
Cubic Symmetry ◽  
Linear Elastic ◽  
Surface Wave Propagation ◽  
Anisotropic Elastic

Crucial to the understanding of surface-wave propagation in an anisotropic elastic solid is the notion of transonic states, which are defined by sets of parallel tangents to a centred section of the slowness surface. This study points out the previously unrecognized fact that first transonic states of type 6 (tangency at three distinct points on the outer slowness branch S 1 ) indeed exist and are the rule, rather than the exception, in so-called C 3 cubic media (satisfying the inequalities c 12 + c 44 > c 11 - c 44 > 0); simple numerical analysis is used to predict orientations of slowness sections in which type-6 states occur for 21 of the 25 C 3 cubic media studied previously by Chadwick & Smith (In Mechanics of solids , pp. 47-100 (1982)). Limiting waves and the composite exceptional limiting wave associated with such type-6 states are discussed.

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