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A new approach to finite elasto-plasticity of crystalline materials, with a differential geometry point of view toward the material description, is proposed. In order to define the plastic and elastic distortions, traditionally it is accepted the existence of an intermediate configuration, which is endowed with a differential manifold structure. A more restrictive but physically and mathematically well-motivated structure is assigned to the intermediate configuration, namely, a vector bundle structure. Two approaches to multiplicative decomposition of the deformation gradient can be rebuilt if on the same total space (intermediate configuration) the vector bundle structures are considered, but either the reference configuration, B (i.e., plastic assumption) or the deformed configuration, B t (i.e., elastic assumption) stands for the base space. As the base spaces are homeomorphic, a pullback vector bundle over one base space is provided by the other one through the motion diffeomorphism. Thus, the total space is endowed with different differential manifold structures. The plastic distortion and the inverse elastic distortion, respectively, are defined for any material points as linear, invertible, and non-integrable maps from the tangent vector space at their material points, with the value on the attached vector fiber. The multiplicative decompositions into their non-integrable components are derived, based on the associate inverse elastic distortion and plastic distortion, respectively. When the plastic and elastic assumptions are simultaneously accepted, then a three-term multiplicative decomposition of the deformation gradient is achieved. The transition functions, which characterize the compatibility of the overlapping charts which belong to these different structures, namely of the vector bundle and of the pullback vector bundle over the same configuration, say B define the non-uniqueness of the two-term multiplicative decomposition. The material symmetry transformation is defined for elastic-type materials. The compatibility of the models and examples of the bundle vector structures are also discussed. [ABSTRACT FROM AUTHOR]

Electrocatalytic CO2 reduction via renewable electricity provides a sustainable way to produce valued chemicals, while it suffers from low activity and selectivity. Herein, we constructed a novel catalyst with unique Ti3C2Tx MXene‐regulated Ag−ZnO interfaces, undercoordinated surface sites, as well as mesoporous nanostructures. The designed Ag−ZnO/Ti3C2Tx catalyst achieves an outstanding CO2 conversion performance of a nearly 100% CO Faraday efficiency with high partial current density of 22.59 mA cm−2 at −0.87 V versus reversible hydrogen electrode. The electronic donation of Ag and up‐shifted d‐band center relative to Fermi level within MXene‐regulated Ag−ZnO interfaces contributes the high selectivity of CO. The CO2 conversion is highly correlated with the dominated linear‐bonded CO intermediate confirmed by in situ infrared spectroscopy. This work enlightens the rational design of unique metal‐oxide interfaces with the regulation of MXene for high‐performance electrocatalysis beyond CO2 reduction. [ABSTRACT FROM AUTHOR]

This study proposes a new elastic–plastic deformation decomposition algorithm for metal clusters to calculate micro-nanoscale elastic and plastic deformation gradients. In the macroscopic plasticity theory, the intermediate configuration is usually constructed by the dissection–unloading method. Because an atomic cluster is equivalent to a small element on a macroscopic object, our decomposition algorithm regards the unloaded configuration as the intermediate configuration for atomic clusters. This algorithm uses a new unloading method to obtain the unloaded configuration. This micro-nanoscale unloading method is constructed based on the principle of minimum potential energy and the embedded-atom method. Moreover, this method rigidly fixes atoms around dislocations during unloading. Therefore, the unloading process will not cause new plastic flow. Once the intermediate configuration is obtained, elastic and plastic deformation gradients are calculated by the interpolation method. Numerical examples of Cu nanowire stretching and bending show that the new decomposition algorithm can accurately and rapidly conduct the elastic–plastic decomposition of the total deformation. This algorithm provides a computational basis for multiscale coupling analysis of mechanical behavior of metal materials from the micro-nanoscale to the macroscale. [ABSTRACT FROM AUTHOR]

A central tool of nonlinear anelasticity is the multiplicative decomposition of the deformation tensor that assumes that the deformation gradient can be decomposed as a product of an elastic and an anelastic tensor. It is usually justified by the existence of an intermediate configuration. Yet, this configuration cannot exist in Euclidean space, in general, and the mathematical basis for this assumption is on unsatisfactory ground. Here, we derive a sufficient condition for the existence of global intermediate configurations, starting from a multiplicative decomposition of the deformation gradient. We show that these global configurations are unique up to isometry. We examine the result of isometrically embedding these configurations in higher-dimensional Euclidean space, and construct multiplicative decompositions of the deformation gradient reflecting these embeddings. As an example, for a family of radially symmetric deformations, we construct isometric embeddings of the resulting intermediate configurations, and compute the residual stress fields explicitly. [ABSTRACT FROM AUTHOR]

At the early design stage of sheet metal forming processes, the well-known inverse approach provides an efficient formability analysis for the pre-designed final part. However, the evaluation of stress state is poor due to its lack of consideration in deformation histories. In this paper, the finite element multi-step method is developed to improve the stress estimations by introducing several intermediate configurations, which are efficiently solved and constructed by using the pseudo minimum area approach and the initial solutions respectively. Therefore, the new nonlinear kinematics are formulated to provide the forward finite logarithmic strain increments, and the classical implicit local integration is performed to update the stress for the anisotropic elastoplastic material. Numerical simulations are carried out to validate the proposed method. [ABSTRACT FROM AUTHOR]

Abstract: A continuum volumetric growth theory is presently elaborated based on the stress-free configuration. The total deformation gradient is the composition of a growth mapping followed by an elastic mapping ensuring the compatibility of the body. A measure of the growth rate fully lying in the stress-free configuration is elaborated, and the balance of momentum accounting for mass changes due to growth is written in the same configuration, highlighting measures of kinematic incompatibilities. An Eshelby stress is identified as the driving force for growth, in the sense that it appears as the true dissipative thermodynamic force conjugated to the growth rate. Examples of incompatible cylindrical growth with residual stress generation and tumor growth with mechanics coupled to diffusion of nutrients illustrate the proposed theory. [Copyright &y& Elsevier]

We consider a set of equations governing the behavior of a polymer melt which is modeled as a viscoelastic fluid possessing a natural, or stress-free state. The natural configuration is characterized through a symmetric, proper orthogonal intermediate deformation tensor, analogous to the left Cauchy-Green deformation tensor in continuum mechanics. This tensor is required to satisfy an evolution equation. It is shown that the constraint that the intermediate tensor be proper orthogonal is satisfied provided that its initial value satisfies this constraint. Local existence and uniqueness of solutions to the initial boundary value problem of the resulting viscoelastic fluid system are established. It is also shown that the local solutions can be extended globally provided that the data are small enough. [ABSTRACT FROM AUTHOR]