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Stress-induced phase transformations of an isotropic incompressible elastic body subject to a triaxial stress state
No full textThe present paper concerns the stable multiphase isochoric deformations for an isotropic elastic body subject to a surface traction of uniform Piola stress with two equal principal forces which are opposite to the third. To model the occurrence of such deformations, we consider a strain energy density function which depends on the first principal invariant of deformation through a non-convex function and which has an added linear dependence on the second invariant. We establish existence conditions for equilibrium multiphase deformations which give restrictions on the morphology of the connecting phases as well as on the orientation of the flat interfaces between the phases. Finally, by considering a special, but representative, form for the non-convex strain energy function, we show that there exists a "critical" value of the external load which allows for the emergence of stable coexistent deformation fields
Phase transformations in isotropic elastic materials induced by shear stress states
No full textIn this paper we study the stable two-phase deformations for an incompressible isotropic elastic body subjected to a homogeneous distribution of dead load tractions on the boundary with two opposite principal forces, whereas the third one is arbitrary. By considering a stored energy function with a nonconvex (rank-one) dependence on the first invariant of strain and an added linear dependence on the second invariant, we determine values of the boundary tractions which support stable two-phase deformations and discuss some kinematical properties of such solutions
Solidi Elastici Incomprimibili con Energia non Convessa Soggetti a Stati di Sforzo Elementari I. Il Problema del Taglio
No full textPhase Transitions, Hysteresis and Bifurcation for Generalized Mooney-Rivlin Elastic Bodies
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