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As a model for the energy of a brittle elastic body we consider an integral functional consisting of two parts: a volume one (the usual linearly elastic energy) which is quadratic in the strain, and a surface part, which is concentrated along the fractures (i.e. on the discontinuities of the displacement function) and whose density depends on the jump part of the strain. We study the problem of the lower semicontinuous envelope of such a functional under the assumptions that the surface energy density...
Given a Borel function ψ defined on a bounded open set Ω
with Lipschitz boundary and ,
we prove an explicit representation formula for the L1 lower
semicontinuous envelope of Mumford-Shah type functionals
with the obstacle constraint
The displacement field caused by the classic earthquake mechanism model consisting of a slip along the fault is extended to the case when besides the slip, also an opening occurs caused by tensional forces. The tensor matrix describing the moment tensor does not necessarily have a nil trace. The direct problem is solved finding the radiation pattern for and waves. A method to solve the inverse problem of the determination of the four parameters describing the source is presented and tested on...
The framework for shape and topology sensitivity analysis in geometrical domains with cracks is established for elastic bodies in two spatial dimensions. The equilibrium problem for the elastic body with cracks is considered. Inequality type boundary conditions are prescribed at the crack faces providing a non-penetration between the crack faces. Modelling of such problems in two spatial dimensions is presented with all necessary details for further applications in shape optimization in structural...
Stimuli-responsive polymers result in
on-demand regulation of properties and functioning of various
nanoscale systems. In particular, they allow stimuli-responsive
control of flow rates through membranes and nanofluidic devices
with submicron channel sizes. They also allow regulation of drug
release from nanoparticles and nanofibers in response to
temperature or pH variation in the surrounding medium. In the
present work two relevant mathematical models are introduced to
address precipitation-driven...
Si considera un corpo indefinito in deformazione piana con una fessura semiinfinita al cui apice è localizzata una zona plastica. Se i carichi crescono monotonamente in forma quasi statica, si determina la velocità di avanzamento dell'apice della fessura. Il risultato è esteso, sotto opportune ipotesi, a variazioni di carico cicliche. Ciò permette di trovare una relazione fra l'incremento di lunghezza della fessura e l'oscillazione del fattore di concentrazione degli sforzi, giustificando così la...
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