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A theory of dissipative generalized continuum mechanics is presented in the framework of weakly nonlocal non-equilibrium thermodynamics. The evolution equation of microdeformation is obtained by thermodynamic principles. Conditions of…
This work focuses on the bearing rigidity theory, namely the branch of knowledge investigating the structural properties necessary for multi-element systems to preserve the inter-units bearings when exposed to deformations. The original…
The development of a nonlinear structural theory (model) for isotropic linear-elastic finite continua is the main objective of the study. To derive the theory, we used Taylor's multivariable expansion and Bubnov-Galerkin's weak formulation.…
Since they represent fundamental physical properties in turbulence (conservation laws, wall laws, Kolmogorov energy spectrum, ...), symmetries are used to analyse common turbulence models. A class of symmetry preserving turbulence models is…
The hardness of materials plays an important role in material design. There are numerous experimental methods to measure the hardness of materials, but theoretical prediction of hardness is challenging. By investigating the correlation…
One of the main theoretical issues in developing a theory of anisotropic viscoelastic media at finite strains lies in the proper definition of the material symmetry group and its evolution with time. In this paper the matter is discussed…
Basic issues of the general model-building framework of the mechanics of complex bodies are discussed. Attention is focused on the representation of the material elements, the conditions for the existence of ground states in conservative…
Recent experiments have exploited elastic instabilities in membranes to create complex patterns. However, the rational design of such structures poses many challenges, as they are products of nonlinear elastic behavior. We pose a simple…
We consider a heterogeneous elastic structure which is stratified in some direction. We derive the limit problem under the assumption that the Lam\'e coefficients and their inverses weakly* converge to Radon measures. Our method applies…
In the spirit of Germain the most general objective stored elastic energy for a second gradient material is deduced using a literature result of Fortun\'e & Vall\'ee. Linear isotropic constitutive relations for stress and hyperstress in…
A new model for elucidating the mathematical foundation of plasticity yield criteria is proposed. The proposed ansatz uses differential geometry and group theory concepts in addition to elementary hypotheses based on well-established…
Explicit expressions, for efficient application in engineering practice, are derived for generalized displacements and stresses in simply supported multi-layered wide plates and beams subjected to steady-state thermal and mechanical…
The aim of this short note is to give a synthetic presentation of the mathematical elements that are used to solve the elastic wave system of equations in a bounded anisotropic elastic body, in a general framework. In particular, the proof…
Explicit expressions for the behavior of statistically isotropic composites with viscoelastic matrices and linear elastic inclusions are determined by application of the correspondence principle. The behavior of the matrix is linear in…
We obtain linear elasticity as $\Gamma$-limit of finite elasticity under incompressibility assumption and Dirichlet boundary conditions. The result is shown for a large class of energy densities for rubber-like materials.
Deformational structures, in many aspects generalizing standard elasticity theory, are investigated in abstract form. Within free deformational structures we define algebra of deformations, classify them by its special properties, define…
We propose and analyze a generalized finite element method designed for linear quasistatic thermoelastic systems with spatial multiscale coefficients. The method is based on the local orthogonal decomposition technique introduced by…
A general model covering a large variety of the so-called adhesive or cohesive, possibly also frictional, contact interfaces between visco-elastic bodies with inertia considered in a thermodynamical context is presented. A semi-implicit…
This paper shows the complementary roles of mathematical and engineering points of view when dealing with truss analysis problems involving systems of linear equations and inequalities. After the compatibility condition and the mathematical…
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…