2013
DOI: 10.1016/j.ijsolstr.2013.08.016
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Mindlin second-gradient elastic properties from dilute two-phase Cauchy-elastic composites Part II: Higher-order constitutive properties and application cases

Abstract: Starting from a Cauchy elastic composite with a dilute suspension of randomly distributed inclusions and characterized at first-order by a certain discrepancy tensor (see part I of the present article), it is shown that the equivalent second-gradient Mindlin elastic solid: (i.) is positive definite only when the discrepancy tensor is negative defined; (ii.) the non-local material symmetries are the same of the discrepancy tensor, and (iii.) the nonlocal effective behaviour is affected by the shape of the RVE, … Show more

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Cited by 47 publications
(30 citation statements)
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“…showing that only the first three eigenvectors have non-null components in both the strain and the curvature, while t * [4] and t * [5] have non-null components only in the curvature, and t * [6] and t * [7] only in the strain. Note that the non-null curvature components of the vectors t * [4] and t * [5] coincide with the components of vectors q * [2] and q * [4] , respectively. The seven eigenvectors (45) are rotated of an angle θ ∈ [0, 2π] to analyze the directional properties of the energy density (for a material equivalent to a lattice with stiffness ratios, k/k = 10, k/k = 100), plotted as polar diagrams in Fig.…”
Section: The Directional Properties Of the Elastic Energy For The Sgementioning
confidence: 98%
“…showing that only the first three eigenvectors have non-null components in both the strain and the curvature, while t * [4] and t * [5] have non-null components only in the curvature, and t * [6] and t * [7] only in the strain. Note that the non-null curvature components of the vectors t * [4] and t * [5] coincide with the components of vectors q * [2] and q * [4] , respectively. The seven eigenvectors (45) are rotated of an angle θ ∈ [0, 2π] to analyze the directional properties of the energy density (for a material equivalent to a lattice with stiffness ratios, k/k = 10, k/k = 100), plotted as polar diagrams in Fig.…”
Section: The Directional Properties Of the Elastic Energy For The Sgementioning
confidence: 98%
“…The need for such generalized continuum models has also been verified through experimental (Lakes et al, 1985;Beveridge et al, 2013) and theoretical (Smishlayev and Fleck, 1995;Bigoni and Drugan, 2007;Bacca et al, 2013a;2013b;Bacigalupo, 2013) approaches.…”
Section: Introductionmentioning
confidence: 94%
“…The key for the identification procedure performed in the next Section is the imposition to the infinite lattice of a linear and a quadratic nodal displacement fields (as in [3], [4], [7], [10]), together with an 'additional field' ∆u (m,n|i) , namely,…”
Section: Second-order Displacement Boundary Conditionmentioning
confidence: 99%
“…Therefore, from Eq. (18), the elastic energy of the lattice can be expressed as U (m,n) lat (a, b * ) and therefore can be represented as the following quadratic form in a and b * U (m,n) lat (a, b * ) = 2 a · H [1] k, k, k a + 2 a · mH [2] k, k, k + nH [3] k, k, k + H [4] k, k, k b * + 2 b * · m 2 H [5] k, k, k + n 2 H [6] k, k, k + m nH [7] k, k, k + mH [8] k, k, k + +nH [9] k, k, k + H [10]…”
Section: Energy Stored Within the Lattice Structurementioning
confidence: 99%
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