Multifield theories in mechanics of solids

Mariano, Paolo Maria

doi:10.1016/s0065-2156(02)80102-8

Cited by 160 publications

(152 citation statements)

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“…Theorem 7 extends to complex bodies a companion result for simple elastic bodies in [31]. The extended Hamilton-Eshelby tensor P has been introduced in [38] (see also [12]) with reference to smooth minimizers. Here the configurational balance involving P is extended to irregular minimizers.…”

Section: Irregular Minimizers: Horizontal Variationsmentioning

confidence: 91%

Ground states in complex bodies

Mariano

Modica

2008

ESAIM: COCV

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Abstract.A unified framework for analyzing the existence of ground states in wide classes of elastic complex bodies is presented here. The approach makes use of classical semicontinuity results, Sobolev mappings and Cartesian currents. Weak diffeomorphisms are used to represent macroscopic deformations. Sobolev maps and Cartesian currents describe the inner substructure of the material elements. Balance equations for irregular minimizers are derived. A contribution to the debate about the role of the balance of configurational actions follows. After describing a list of possible applications of the general results collected here, a concrete discussion of the existence of ground states in thermodynamically stable quasicrystals is presented at the end.

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Section: Irregular Minimizers: Horizontal Variationsmentioning

confidence: 91%

Ground states in complex bodies

Mariano

Modica

2008

ESAIM: COCV

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“…1. According with the material 100 multifield theory [3, 6,11], β can be thought as a substructural 101 morphological descriptor.…”

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confidence: 99%

“…2b). Thus, the overall strain ε can be 131 The momentum balance equations arising from the micro-141 morphic material theory, see Mariano [11], are given by: …”

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confidence: 99%

Computational modeling of high performance steel fiber reinforced concrete using a micromorphic approach

2013

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The HPFRC composite model takes into account the impor-23 tant effects produced by concrete fracture. A procedure for 24 simulating quasi-brittle fracture is introduced into the model 25 and is described in the paper. The present numerical method-26 ology is assessed by simulating a selected set of experimental 27 tests which proves its viability and accuracy to capture a num-28 ber of mechanical phenomenon interacting at the macro-and 29 mesoscale and leading to failure of HPFRC composites.

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“…The techniques introduced here will be, indeed, further developed in [14] to tackle the analysis of more sophisticated and physically more plausible energies arising within multifield theories of complex bodies (see [28]), for which smooth embedding in Euclidean spaces is not available.…”

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confidence: 99%

“…Therefore, the choice of one specific isometry has to be considered as a sort of additional constitutive assumption on the model (cp. with [28]). Hence, the intrinsic approach developed here frees the problem of establishing the lower semicontinuity property from this drawback.…”

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confidence: 99%