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 remodelling processes aiming at optimizing the overall structural response to environmental physical forces. From a mechanical viewpoint, residual stresses are classically modelled through the introduction of a virtual incompatible state that collects the local relaxed states around each material point. In this work, we instead employ an alternative approach based on a strain energy function that constitutively depends only on the deformation gradient and the residual stress tensor. In particular, our objective is to study the morphological stability of an incompressible sphere, made of a neo-Hookean material and subjected to given distributions of residual stresses. Firstly, we perform a linear stability analysis on the pre-stressed solid sphere using the method of incremental deformations. The marginal stability conditions are given as a function of a control parameter, being the dimensionless variable that represents the characteristic intensity of the residual stresses. Secondly, we perform finite element simulations using a mixed formulation in order to investigate the post-buckling morphology in the fully nonlinear regime. Considering different distributions of the residual stresses, we find that different morphological transitions occur around the material domain where the hoop residual stress reaches its maximum compressive value. The results provide useful guidelines in order to design morphable soft spheres, for example by controlling the residual stresses through active deformations. They finally suggest a viable solution for the nondestructive characterization of residual stresses in soft tissues, such as solid tumors.
Physical aging and relaxation of residual stresses in a colloidal glass following flow cessation
在低盐浓度下，将锂皂石悬浮液稀释在水中形成排斥性胶体玻璃，其显示物理老化。这种现象仍然没有完全理解，特别是，很少有人知道的流动历史之间的连接，作为系统的初始状态的决定因素，和随后的老化动力学。使用应力控制流变仪，我们进行应力跳变实验，以观察流动应力的弹性分量，仍然停止流动或流动淬火。我们调查这些残余应力的动态和物理老化的速率之间的连接淬火从稳态流动曲线上的不同点。从高速率淬火产生流体状态，G”> G '，具有小的、快速松弛的残余应力和复数模量的快速S形老化。相反，从较低的剪切速率淬火产生越来越多的堵塞状态，其特征在于缓慢松弛的应力和缓慢增加的复合模量与系统的年龄。流动停止从一个固定的剪切速率与不同的淬火持续时间表明，较慢的淬火产生较小的残余应力，在短时间内，在较长的时间内放松较小的程度，通过与较快的淬火。这些较小的应力与较高的模量相关，但系统的物理老化较慢。残余应力松弛的特征时间与淬火速率成反比。这意味着任何理想的无应力状态，简洁地反映了这些玻璃态系统的挫折性质的挫折方法。
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 (virtual) stress-free state was required to calculate the residual stress. In contrast, we use a model which is simple and allows the prescription of any residual stress field. We specialize the analysis to an elastic tube subject to a two-dimensional residual stress, and find that incremental wrinkles can appear on its inner or its outer face, depending on the loca…
The distribution of local residual stresses (threshold to instability) that controls the statistical properties of plastic flow in athermal amorphous solids is examined with an atomistic simulation technique. For quiescent configurations, the distribution has a pseudogap (power-law) form with an exponent that agrees well with global yielding statistics. As soon as deformation sets in, the pseudogap region gives way to a system size dependent plateau at small residual stresses that can be understood from the statistics of local residual stress {\em differences} between plastic events. Results f…
A thermodynamic framework has been developed for a class of amorphous polymers used in fused deposition modeling (FDM), in order to predict the residual stresses and the accompanying distortion of the geometry of the printed part (warping). When a polymeric melt is cooled, the inhomogeneous distribution of temperature causes spatially varying volumetric shrinkage resulting in the generation of residual stresses. Shrinkage is incorporated into the framework by introducing an isotropic volumetric expansion/contraction in the kinematics of the body. We show that the parameter for shrinkage also a…
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 conflicts with the observations that any growth state of tissue is under a significant level of residual stresses that helps to maintain its ideal mechanical conditions. Here, we propose a modified multiplicative decomposition model where the initial state (or reference configuration) of biological tissue is endowed with residual stress instead of being str…
In soft amorphous materials, shear cessation after large shear deformation leads to structures having residual shear stress. The origin of these states and the distribution of the local shear stresses within the material is not well understood, despite its importance for the change in material properties and consequent applications. In this work, we use molecular dynamics simulations of a model dense non-Brownian soft amorphous material to probe the non-trivial relaxation process towards a residual stress state. We find that, similar to thermal glasses, an increase in shear rate prior to the s…
