Material Inhomogeneities in Elasticity

By G. Maugin. 2020

783 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Civil and Structural Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/94794a2e1111820ec20dd78305157878e64e5672

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In Biomedical Engineering

In Civil and Structural Engineering

In Mechanics of Materials

Citations in the corpus

On configurational forces in the context of the finite element method (2002, background): “results in a con%gurational force balance in the well-known local form (see also References [4; 5; 8]) Ckj; j + g k =0 (9) The con%gurational body forces g in this relation are given by g k =−Ckj; j =−fiui; k + ijui; jk − ; k (10) Note, that the con%gurational force system satis%es an equilibrium co”
Modeling Dislocations and Disclinations With Finite Micropolar Elastoplasticity (2006, background): “The texts of Nabarro (1967), Lardner (1974), Mura (1982), Maugin (1993), and Zubov (1997) also include precise mathematical descriptions and/or elastic solutions.”
On deformational and configurational mechanics of micromorphic hyperelasticity – Theory and computation (2007, background): “configurational mechanics in general and the material force method in particular, see for instance the contributions of Maugin and coworkers [5,19,20,23,21], Gurtin [10] or the group of Steinmann [27,28,30,17,18] as well as the references cite therein.”
Waves in microstructured materials and dispersion (2005, methodology): “or the microstructural quantities are separately taken into account in one set of conservation laws [5].”
A robust algorithm for configurational‐force‐driven brittle crack propagation with R‐adaptive mesh alignment (2007, neutral): “Local variational formulations for the evolution problem of brittle fracture as suggested by Stumpf and Le [5] and Maugin and Trimarco [6] base on material configurational forces acting on crack tip singularities in the sense of Eshelby [7, 8] and Rice [9], see also Maugin [10], Gurtin [11, 12], Kie”
On material forces and finite element discretizations (2002, methodology): “For brevity of the derivation we consider only elastic materials, but an extension to inelastic settings is possible and discussed in Maugin (1993).”
Nonsingular stress and strain fields of dislocations and disclinations in first strain gradient elasticity (2005, neutral): “ar X iv :c on d- m at /0 50 20 23 v1 [ co nd Keywords: gradient theory, dislocations, disclinations, nonlocal elasticity, hyperstress”
On the comparison of two approaches to compute material forces for inelastic materials. Application to single-slip crystal-plasticity (2004, methodology): “For a survey on the general underlying continuum theory we refer the reader to the monographs by Maugin [26] and”
Truss Modular Beams with Deformation Energy Depending on Higher Displacement Gradients (2003, background): “However, another equivalent formalization of continuum mechanics, based on the principle of virtual power and stemming from the dòAlembert concept of mechanics, is possible (for a modern description of such a point of view see, for instance, [8] and [9]).”