Volume 22, Issue 1-2

Continuum constitutive laws describe the plastic deformation of materials as a smooth, continuously differentiable process. However, provided that the measurement is done with a fine enough resolution, the plastic deformation of real materials is often found to comprise discrete events usually nanometric in size. For bulk-sized specimens, such nanoscale events are minute compared with the specimen size, and so their associated strain changes are negligibly small, and this is why the continuum laws work well. However, when the specimen size is in the micrometer scale or smaller, the strain changes due to the discrete events could be significant, and the continuum description would be highly unsatisfactory. Yet, because of the advent of microtechnology and nanotechnolgy, small-sized materials will be increasingly used, and so there is a strong need to develop suitable replacement descriptions for plasticity of small materials. As the occurrence of the discrete plastic events is also strongly stochastic, their satisfactory description should also be one of a probabilistic, rather than deterministic, nature.

We present a complete analytical solution for the plane elasticity problem of a concentrated force acting on a half-space weakened by a circular hole. The solution is based on the algorithm proposed by G.B. Jeffery in 1920 for elasticity problems, using bipolar coordinates to characterize the geometry. We found the biharmonic stress function describing stresses and strains in the half-space and the associated biharmonic function that allows determining the displacement field. Both functions are given in the form of Fourier series with quite compact coefficients. Particular attention is paid to the displacements at the plane boundary of the half-space. It is discussed how these displacements can be used in an inverse procedure for the identification of a circular hole diameter and position.

Rubber-like materials can deform largely and nonlinearly upon loading, and they return to the initial configuration when the load is removed. Such rubber elasticity is achieved due to very flexible long-chain molecules and a three-dimensional network structure that is formed via cross-linking or entanglements between molecules. Over the years, to model the mechanical behavior of such randomly oriented microstructures, several phenomenological and micromechanically motivated network models for nearly incompressible hyperelastic polymeric materials have been proposed in the literature. To implement these models for polymeric material (undoubtedly with widespread engineering applications) in the finite element framework for solving a boundary value problem, one would require two important ingredients, i.e., the stress tensor and the consistent fourth-order tangent operator, where the latter is the result of linearization of the former. In our previous work, 14 such material models are reviewed by deriving the accurate stress tensors and tangent operators from a group of phenomenological and micromechanical models at large deformations. The current contribution will supplement some further important models that were not included in the previous work. For comparison of all selected models in reproducing the well-known Treloar data, the analytical expressions for the three homogeneous defomation modes, i.e., uniaxial tension, equibiaxial tension, and pure shear, have been derived and the performances of the models are analyzed.

The present contribution is concerned with the modeling and computation of size effects in metallic glasses. For the underlying model description, we resort to a thermodynamically consistent, gradient-extended continuum mechanics approach. The numerical implementation is carried out with the help of the finite element method. Numerical examples are presented and compared with existing experimental findings to illustrate the performance of the constitutive model. In this regard, the influence of the material length scale is investigated. It is shown that with decreasing sample size or decreasing material length scale, a delay of the shear localization is obtained. In addition, the tension-compression asymmetry observed in experiments is captured by the proposed model. Further, the rate-dependent behavior as well as the influence of the results to initial local defects are investigated.

Materials show size effects in their strength, i.e., improved strength as size decreases. Size effects have been studied extensively at a wide range of scales, from atomistic to continuum. Size effects depend on the scale of reference, as the physics change with increasing or decreasing scale. The work reported herein concentrates at scales near the average grain size in polycrystalline solids, where they are examined in conjunction with Hall-Petch effects. It presents a process for isolating physical information on a problem at specific spatial or temporal scales and applies it to Hall-Petch and size effects in one spatial dimension, extendable to higher dimensions. Importantly, the scale-isolated information captures the interactions among scales. As material failure and Hall-Petch effects are highly stochastic, a probabilistic approach to the present work is more appropriate than a deterministic one.

A test program designed and carried out to mimic the repeated impact of the bow section of fast-moving small boats on the ocean surface provided some unique observations in terms of failure mode transition. Damage progression and modes of failure were evaluated for two types of sandwich composites with comparable global strength and stiffness but different foam density and facesheet strength. Testing was performed on flat rectangular specimens that contained symmetric semi-elliptical edge flaws produced near the end of the specimen held by the rotating cam. Type 1 specimens (softer core/stronger facesheet) consistently failed by interface and through-the-thickness core shear, independent of the flaw size. In contrast, a gradual decrease in flaw size in Type 2 specimens (denser core/weaker facesheet) produced a striking transition in the mode of failure from local buckling in the vicinity of the flaw site along with exponentially increasing lifetime, to interface shear failure at the free end accompanied by a dramatic drop in lifetime. The lifetime of Type 2 specimens was more than two orders of magnitude greater than that of Type 1 specimens.