The Nonlinear Theory of Elastic Shells with Phase Transitions

Eremeyev, Victor A.; Pietraszkiewicz, Wojciech

doi:10.1023/b:elas.0000026106.09385.8c

Cited by 108 publications

(126 citation statements)

References 33 publications

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“…[40]) and in general in elasticity theory (see [43][44][45][46][47][48]). On the other hand, beam theory, and especially generalized beam theory, is particularly interesting nowadays in view of applications to lattice systems [49,50,31], and in this context pantographic structures are naturally leading to the problem of large deformations of the fibers (see for instance [51][52][53][54][55][56][57]).…”

Section: Discussionmentioning

confidence: 99%

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Large deformations of 1D microstructured systems modeled as generalized Timoshenko beams

Battista

Corte

Isola

et al. 2018

Z. Angew. Math. Phys.

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In the present paper we study a natural nonlinear generalization of Timoshenko beam model and show that it can describe the homogenized deformation energy of a 1D continuum with a simple microstructure. We prove the well-posedness of the corresponding variational problem in case of a generic end load, discuss some regularity issues and evaluate the critical load. Moreover, we generalize the model so as to include an additional rotational spring in the microstructure. Finally, some numerical simulations are presented and discussed.

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Section: Discussionmentioning

confidence: 99%

“…except at the points s such that G * (φ(s)) is not differentiable. We already showed that, in caseF < 1, θ solves the equations (44) in the whole interval [0, 1].…”

Section: Euler-lagrange Equationsmentioning

confidence: 99%

Large deformations of 1D microstructured systems modeled as generalized Timoshenko beams

Battista

Corte

Isola

et al. 2018

Z. Angew. Math. Phys.

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“…For instance, quasi-static or dynamic non-material interfaces are able to model the martensitic type phase transitions in solids such as shape memory alloys (see, e.g., [136][137][138]), where one can find solutions of mono-dimensional problems. Motivated by experimental observations of phase transitions in thin-walled structures (see, e.g., [139][140][141]), the behavior of thin-walled structural elements made of materials undergoing phase transitions within the nonlinear shell theory was considered in [142][143][144][145]. Unlike to three-dimensional models of elasticity and plasticity of solids with phase interfacial zones (e.g., [146][147][148]), the bi-dimensional models based on the shell and plate theory are supplying a powerful tool for decreasing the computational effort needed to design complex thin structures undergoing phase transitions.…”

Section: Localization Problems In Solids and Structuresmentioning

confidence: 99%

On the contribution of Angelo Luongo to Mechanics: in honor of his 60th birthday

Piccardo

D’Annibale

Zulli

2014

Continuum Mech. Thermodyn.

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This paper intends to summarize the scientific production of Angelo Luongo on the occasion of his Sixtieth Birthday, focusing on his main contributions in the field of Mechanics. The task will not be easy because of the breadth of his scientific production, only apparently attributable to a restricted number of keywords. In fact, even when the work seems purely algorithmic, speculation on the physical and mechanical aspects of the problem is always present, providing new interpretations and innovative openings to a careful reader. Similarly, also the works, which apparently seem to be high-level applications, always reserve methodological aspects that are not negligible. The editorial choice to divide his papers through a small number of keywords is certainly simplistic, but offers the possibility to better highlight all the connections among his variegated production. The most original contributions of Angelo Luongo in the context of perturbation methods, linear and nonlinear dynamics and control, elastic buckling and structural analysis, bifurcation and stability of non-conservative systems, are discussed in detail. Finally, the Angelo Luongo's central role in the creation and development of activities of the international research center M&MoCS is pointed out.

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“…The two-dimensional (2D) local laws of shell thermomechanics can be derived by direct and exact through-the-thickness integration of global 3D balances of forces, moments, energy and the entropy inequality, see [6][7][8]. After appropriate transformations the resulting 2D local Lagrangian laws in M \C become…”

Section: Basic Relationsmentioning

confidence: 99%

“…The non-linear equilibrium conditions of elastic shells undergoing PT of martensitic type were formulated in [6][7][8] within the dynamically and kinematically exact theory of shells presented in [9][10][11]. In this shell theory the translation vector u and rotation tensor Q fields are the only independent variables.…”

Section: Introductionmentioning

confidence: 99%

On the bending and tension of thermoelastic shells undergoing phase transitions

Eremeyev

Pietraszkiewicz

2009

Proc Appl Math and Mech

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FederationApplying the general non-linear theory of shells undergoing phase transitions, we derive the balance equations along the singular surface curve modelling the phase interface in the shell. From the integral forms of balance laws of linear momentum, angular momentum, and energy as well as the entropy inequality we obtain the local static balance equations along the curvilinear phase interface. We also derive the thermodynamic condition allowing one to determine the interface position on the deformed shell midsurface. The theoretical model is illustrated by the example of thin circular cylindrical shell made of two-phase material subjected to tensile forces and bending couples at the shell boundary. The elastic solution reveals the existence of the hysteresis loop whose size depends upon values of several loading parameters.

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The Nonlinear Theory of Elastic Shells with Phase Transitions

Cited by 108 publications

References 33 publications

Large deformations of 1D microstructured systems modeled as generalized Timoshenko beams

Large deformations of 1D microstructured systems modeled as generalized Timoshenko beams

On the contribution of Angelo Luongo to Mechanics: in honor of his 60th birthday

On the bending and tension of thermoelastic shells undergoing phase transitions

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