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New lattice model for the gradient elasticity is suggested. This lattice model gives a microstructural basis for second-order strain-gradient elasticity of continuum that is described by the linear elastic constitutive relation with the…

Materials Science · Physics 2015-01-08 Vasily E. Tarasov

In this paper, we study the anisotropy classes of the fourth order elastic tensors of the relaxed micromorphic model, also introducing their second order counterpart by using a Voigt-type vector notation. In strong contrast with the usual…

Modern inelastic material model formulations rely on the use of tensor-valued internal variables. When inelastic phenomena include softening, simulations of the former are prone to localization. Thus, an accurate regularization of the…

Computational Engineering, Finance, and Science · Computer Science 2024-08-13 Tim van der Velden , Tim Brepols , Stefanie Reese , Hagen Holthusen

We derive a simple tensor algebraic expression of the modified Eshelby tensor for a spherical inclusion embedded in an arbitrarily anisotropic matrix in terms of three tensor quantities (the 4th order identity tensor, the elastic stiffness…

Other Condensed Matter · Physics 2018-10-22 Sangryun Lee , Jinyeop Lee , Seunghwa Ryu

We present a novel framework for the probabilistic modelling of random fourth order material tensor fields, with a focus on tensors that are physically symmetric and positive definite (SPD), of which the elasticity tensor is a prime…

Computational Engineering, Finance, and Science · Computer Science 2025-04-03 Sharana Kumar Shivanand , Bojana Rosić , Hermann G. Matthies

Third-order elasticity (TOE) theory is predictive of strain-induced changes in second-order elastic coefficients (SOECs) and can model elastic wave propagation in stressed media. Although third-order elastic tensors have been determined…

Materials Science · Physics 2022-12-12 Chenxing Luo , Jeroen Tromp , Renata M. Wentzcovitch

The three-dimensional elastic-plastic deformation is considered. The catastrophe theory underlies the construction of this process model. It was shown that the variety of stable states consists on elastic states and can be depicted as a…

Materials Science · Physics 2007-05-23 L. N. Maurin , I. S. Tikhomirova

The representation theory of tensor functions is essential to constitutive modeling of materials including both mechanical and physical behaviors. Generally, material symmetry is incorporated in the tensor functions through a structural or…

Representation Theory · Mathematics 2025-09-12 Mohammad Madadi , Lin Cheng , Pu Zhang

In this work, the influence of the plastic size effect on the fracture process of metallic materials is numerically analyzed using the strain-gradient plasticity (SGP) theory established from the Taylor dislocation model. Since large…

Materials Science · Physics 2017-10-17 E. Martínez-Pañeda , C. Betegón

The strain-energy formulation of nonlinear elasticity can be extended to the case of significant compression by modulating suitable strain energy terms by a function of relative volume. For isotropic materials this can be accomplished by…

Geophysics · Physics 2021-03-17 B. L. N. Kennett

In the present paper, the simplest model of strain-gradient elasticity will be considered, that is the isotropy in a bidimensional space. Paralleling the definition of the classic elastic moduli, our aim is to introduce second-order…

Classical Physics · Physics 2015-06-17 Nicolas Auffray

Based on the fact that for an isotropic material model the elastic predictor and the projected stress tensors have the same eigenvectors, it is shown that the scalar damage can be obtained directly from the projection algorithm. This…

Materials Science · Physics 2007-05-23 Josko Ozbolt , Sergey Ananiev

We present a formulation for high-order generalized periodicity conditions in the context of a high-order electromechanical theory including flexoelectricity, strain gradient elasticity and gradient dielectricity, with the goal of studying…

Numerical Analysis · Mathematics 2023-11-15 J. Barceló-Mercader , D. Codony , A. Mocci , I. Arias

We propose a method for deriving equivalent one-dimensional models for slender non-linear structures. The approach is designed to be broadly applicable, and can handle in principle finite strains, finite rotations, arbitrary cross-sections…

Soft Condensed Matter · Physics 2021-02-03 Basile Audoly , Claire Lestringant

We present a data-driven framework for the multiscale modeling of anisotropic finite strain elasticity based on physics-augmented neural networks (PANNs). Our approach allows the efficient simulation of materials with complex underlying…

Computational Engineering, Finance, and Science · Computer Science 2024-10-07 Karl A. Kalina , Jörg Brummund , WaiChing Sun , Markus Kästner

Two-dimensional (2D) materials may have potential applications in thermoelectric devices. In this work, we systematically investigate the thermoelectric properties of orthorhombic group IV-VI monolayers $\mathrm{AB}$ (A=Ge and Sn; B=S and…

Materials Science · Physics 2017-02-01 San-Dong Guo

The Schwinger-Dyson Equations (SDEs) of matrix models are known to form (half) a Virasoro algebra and have become a standard tool to solve matrix models. The algebra generated by SDEs in tensor models (for random tensors in a suitable…

High Energy Physics - Theory · Physics 2015-06-11 Valentin Bonzom

The modeling of the elastic properties of granular or nanoscale systems requires the foundations of the theory of elasticity to be revisited, as one explores scales at which this theory may no longer hold. The only cases for which a…

Statistical Mechanics · Physics 2007-05-23 I. Goldhirsch , C. Goldenberg

The transformation theory of optics and acoustics is developed for the equations of linear anisotropic elasticity. The transformed equations correspond to non-unique material properties that can be varied for a given transformation by…

Materials Science · Physics 2011-06-28 A. N. Norris , A. L. Shuvalov

This study addresses the modelling of elastic bodies, particularly when the relaxed configuration is unknown or non-existent. We adopt the theory of initially stressed materials, incorporating the deformation gradient and stress state of…

Soft Condensed Matter · Physics 2024-11-28 M. Magri , D. Riccobelli