In this paper we study the wedge disclination within the elastoplastic defect theory. Using the stress function method we found exact analytical solutions for all characteristic fields of a straight wedge disclination in a cylinder. The elastic stress, elastic strain, elastic bend-twist, displacement and rotation have no singularities at the disclination line. We found a modified stress functio...

The tensor M has 3 = 81 entries and no symmetries. Both the construction and application of M are somewhat expensive, and both can be avoided. If F = UΣV , then it turns out that Z(F, α) = UẐ(Σ, α)V and W(F) = UŴ(Σ)V , where Ẑ(Σ, α) and Ŵ(Σ) are diagonal matrices. It follows then that Y(F) = UŶ(Σ)V , with Ŷ(Σ) = Ŵ(Ẑ(Σ, α)), where Ŷ(Σ) is also a diagonal matrix. To be able to carry out these ste...

In this paper, we rst prove a convergence result on the Ka canov method for solving general nonlinear variational inequalities of the second kind. Then we apply the Ka canov method to solve a nonlinear variational inequality of the second kind arising in elastoplasticity. In addition to the convergence result, we show an a posteriori error estimate for the Ka canov iterates. In each step of the...

The boundary value problem representing one time step of the primal formulation of elastoplasticity with positive hardening leads to a variational inequality of the second kind with some non-differentiable functional. This paper establishes an adaptive finite element algorithm for the solution of this variational inequality that yields the energy reduction and, up to higher order terms, the R−l...

here we denote by σ the stress tensor, by ε the linearized strain tensor, by B(x) the compliance tensor and by ∂φ(·, x) the subdifferential of a convex function φ(·, x). This relation accounts for elasto-viscoplasticity, including a nonlinear version of the classical Maxwell model of viscoelasticity and the Prandtl–Reuss model of elastoplasticity. The constitutive law is coupled with the equati...

Experimental data are reported on the elastoplastic response of and moisture diffusion through a vinyl ester resin–montmorillonite clay nanocomposite with various amounts of filler. Two simple models are developed for the elastoplastic behavior of a nanocomposite and for the anomalous diffusion of penetrant molecules. Adjustable parameters in the constitutive equations are found by fitting the ...

We deal with quasistatic evolution problems in plasticity with softening, in the framework of small strain associative elastoplasticity. The presence of a nonconvex term due to the softening phenomenon requires a nontrivial extension of the variational framework for rate-independent problems to the case of a nonconvex energy functional. We argue that, in this case, the use of global minimizers ...

For a wide class of problems in continuum mechanics like those involving phase transitions or finite elastoplasticity, the governing potentials tend to be not quasiconvex. This leads to the occurrence of microstructures of in principle arbitrarily small scale, which cannot be resolved by standard discretization schemes. Their effective macroscopic properties, however, can efficiently be recover...

1. Basic Results in Continuum Mechanics 1.1. Kinematics 1.2. Stress Tensors and Balance of Momenta 1.3. Energy Balance Principle and Entropy Inequality 1.4. Fundamental Principles of Constitutive Models 2. Elastic and Hyperelastic Materials 2.1. Isotropic Hyperelastic Materials 2.2. Constitutive Models for Fiber-Reinforced Hyperelastic Materials 2.3. Examples of Numerical Applications 3. Elasto...

A novel approach is proposed for the modeling of rigid-wheel and soft-soil interaction to efficiently compute normal and shear stress distributions in the contact area. The authors propose a velocity field in the vicinity of the contact area based on the physical nature of the problem. Thereupon, the incremental changes to the stress field are computed by resorting to elastoplasticity theory an...