Related papers: Basis functions for residual stresses
The use of global displacement basis functions to solve boundary-value problems in linear elasticity is well established. No prior work uses a global stress tensor basis for such solutions. We present two such methods for solving stress…
Residual stresses are self-equilibrated stresses on unloaded bodies. Owing to their complex origins, it is useful to develop functions that can be linearly combined to represent any sufficiently regular residual stress field. In this work,…
We examine the well-posedness of inverse eigenstrain problems for residual stress analysis from the perspective of the non-uniqueness of solutions, structure of the corresponding null space and associated orthogonal range-null…
Residual stresses may appear in elastic bodies due to the formation of misfits in the micro-structure, driven by plastic deformations, thermal or growth processes. They are especially widespread in living matter, resulting from the dynamic…
This study presents an analytical investigation of stress distributions in square-shaped elastic bodies subjected to concentrated compressive loads under uniaxial and biaxial conditions. By employing the Airy stress function method, we…
The stressed state of flattened thin elastic sheet, as well as that of translationally symmetric 3D solids, are effectively 2D problems. This paper study equilibrium state-of-stress in metrically-incompatible 2D elastic materials. The…
The calculation of the stress field around an arbitrarily shaped crack in an infinite two-dimensional elastic medium is a mathematically daunting problem. With the exception of few exactly soluble crack shapes the available results are…
The existence of static, self-gravitating elastic bodies in the non-linear theory of elasticity is established. Equilibrium configurations of self-gravitating elastic bodies close to the reference configuration have been constructed in [6]…
Many interesting shapes appearing in the biological world are formed by the onset of mechanical instability. In this work we consider how the build-up of residual stress can cause a solid to buckle. In all past studies a fictitious…
We present the formulation for finding the distribution of eigenstrains, i.e. the sources of residual stress, from a set of measurements of residual elastic strain (e.g. by diffraction), or residual stress, or stress redistribution, or…
The study is devoted to geometrically non-linear modelling of viscoplastic structures with residual stresses. We advocate and develop a special approach to residual stresses based on the transition between reference configurations. The…
Bodies coupled to electromagnetic or other long-range fields are subject to radiation reaction and other effects in which their own fields can influence their motion. Self-force phenomena such as these have been poorly understood for…
We derive two consequences of the distributional form of the stress equilibrium condition while incorporating piecewise smooth stress and body force fields with singular concentrations on an interface. First we obtain the local equilibrium…
The dependence of the elastic tensor on the equilibrium stress is investigated theoretically. Using ideas from finite-elasticity, it is first shown that both the equilibrium stress and elastic tensor are given uniquely in terms of the…
In his work on stress functions Maxwell noted that given a planar truss the internal force distribution may be described by a piecewise linear, $C^0$ continuous version of the Airy stress function. Later Williams and McRobie proposed that…
Residual stress is ubiquitous and indispensable in most biological and artificial materials, where it sustains and optimizes many biological and functional mechanisms. The theory of volume growth, starting from a stress-free initial state,…
The multiplicative decomposition model is widely employed for predicting residual stresses and morphologies of biological tissues due to growth. However, it relies on the assumption that the tissue is initially in a stress-free state, which…
Acoustoelasticity theory has been widely used to evaluate the residual stress (or prestress), almost all the available ultrasonic stress detection methods are based on the relationship between the magnitude of stress and wave speed, but…
The equations of stress equilibrium and strain compatibility/incompatibility are discussed for fields with point singularities in a planar domain. The sufficiency (or insufficiency) of the smooth maps, obtained by restricting the singular…
We present a complete analytical solution for the stress field inside a homogeneous, inside a homogeneous, linearly elastic solid sphere subjected to a concentrated normal load applied on its surface. Starting from the three-dimensional…