On configurational forces in multiplicative elastoplasticity

The main goal of this work consists in the elaboration of the material or rather configurational mechanics in the context of multiplicative elastoplasticity. This nowadays well-established approach, which is inherently related to the concept of a material isomorphism or in other words to a local rearrangement, is adopted as a paradigm for the general modelling of finite inelasticity. The overall motion in space is throughout assumed to be compatible and sufficiently smooth. According to the underlying configurations, namely the material and the spatial configuration as well as what we call the intermediate configuration, different representations of balance of linear momentum are set up for the static case. The underlying flux terms are thereby identified as stress tensors of Piola and Cauchy type and are assumed to derive from a free energy density function, thus taking hyperelastic formats. Moreover, the incorporated source terms, namely the configurational volume forces, are identified by comparison arguments. These quantities include gradients of distortions as well as dislocation density tensors. In particular those dislocation density tensors related to the elastic or plastic distortion do not vanish due to the general incompatibility of the intermediate configuration. As a result, configurational volume forces which are settled in the intermediate configuration embody non-vanishing dislocation density tensors while their material counterparts directly incorporate non-vanishing gradients of distortions. This fundamental property enables us to recover the celebrated Peach–Koehler force for finite inelasticity, acting on a single dislocation, from the intermediate configuration volume forces.     

On configurational inertial forces at a phase interface

The evolution equations for a phase interface are discussed. Interfacial structure is neglected, as are thermal and compositional variations. The focus is on a new treatment of the inertial forces at the interface.     

基于构型力内变量的界面损伤问题研究

论文基于材料构型力的基本理论和损伤力学中含有内变量的热力学框架,提出了新的损伤变量定义方式,为研究界面损伤问题提供了一种新思路.首先,基于双相弹性体的能量分析,给出材料构型力表达式,通过构型力的离散化方法,实现了其在有限元中的数值计算.其次,定义构型力为界面损伤内变量,进而提出一种新的损伤演化模型,并采用刚度劣化的方法,对该界面损伤模型进行数值实现.最后,通过对复合材料界面损伤问题(有裂纹或无裂纹)进行数值模拟,分析了其界面损伤发展趋势,探讨了此模型的合理性和优越性.基于构型力内变量的界面损伤模型,可为复合材料的界面损伤失效问题提供一种新的研究方法.     

The energy jump condition for thermomechanical media in the presence of configurational forces

In the context of a propagating surface of discontinuity in a thermomechanical medium, this brief communication establishes a relationship between the supplies of material momentum, linear momentum, energy and entropy. The relationship is equivalent to the jump condition in energy and is also framed in the context of a driving traction.      

Investigation on thermomechanical fracture in the framework of configurational forces

A configurational force approach is developed for providing a fresh look onto classical aspects of thermomechanical fracture. The theoretical framework is based on the finite deformation and makes no restrictions on the material response. The integral form of configurational force balance at the crack tip is constructed, and the concentrated configurational body force is decomposed into the inertial and internal parts. The energy release rate is evaluated through the generalized second law of thermodynamics applicable to configurational force system. The theoretical investigation shows that the negative of the projection of the internal configurational force concentrated at the crack tip along the direction of crack propagation plays the role of the energy release rate and acts directly in response to crack propagation. This finding enables us to deal with the thermomechanical fracture problems in material space.     

Failure theory via the concept of material configurational forces associated with the M-integral

A new failure theory based on the material configuration forces associated with the invariant M-integral is proposed to describe the content and evolution of the multi-defects localized in the body. The physical interpretation of the global M-integral is as the sum of the local energy release rate due to the self-similar expansion for each specific defect. It does provide an effective measure for the evaluation of damage level. It is found that the unique parameter of the M-integral cannot be used as a unified failure criterion to predict the damage evolution and the final failure due to the major obstacle that the critical value of the M-integral is not a problem-invariant constant and shows an apparent defect configuration-dependence. Consequently, a new failure parameter referred as the configurational damage parameter (abbreviated as Π-parameter) is proposed by the appropriate formulation via the M-integral, the remote uni-axial load, and the inner variable of the damaged area. A series of numerical examples are carried out to demonstrate that the critical value of Π-parameter is a material constant regardless of defect configurations. Furthermore, it is performed to validate the applicability of the Π-parameter as a failure criterion to predict the final failure of the locally damaged materials. Finally, a protocol of experimental measurement of the Π-parameter is proposed by method of digital image correlation to facilitate the wide application of the new failure criterion. It is concluded that the present failure theory via the configurational forces associated with the M-integral provides some outside variable features and has the advantage of predicting the structural integrity of damaged materials containing the locally distributed defects.     

The parallelogram of forces

Summary A brief historical outline and some epistemological suggestions are presented on the scientific debate about the parallelogram of forces.

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Sommario Si espone brevemente lo sviluppo storico del dibattito sulla regola del parallelogrammo delle forze e sui diversi tentativi di una sua dimostrazione razionale, alla luce di alcune considerazioni epistemologiche.

     

On configurational balance in slender bodies

We propose a new derivation of the evolution equation of a sharp, coherent interface in a two-phase body having elongated shape, a body which we regard as a one-dimensional micropolar continuum. To this aim, we introduce a system of forces acting at the interface, and we apply the method of virtual powers to derive a balance law involving these forces. By exploiting the dissipation inequality, we manage to write this balance law in terms of a scalar field whose form is reminiscent of a well-known expression for the configurational stress in three dimensional micropolar continua.     

The role of the configurational force balance in the nonequilibrium epitaxy of films

We discuss the epitaxial growth of an elastic film, allowing for stress and diffusion within the film surface as well as nonequilibrium interactions between the film and the vapor. Our approach, which relies on recent ideas concerning configurational forces, is based on: (i) standard (Newtonian) balance laws for forces and moments together with an independent balance law for configurational forces; (ii) atomic balances, one for each species of mobile atoms; (iii) a mechanical version of the second law that accounts for temporal changes in free energy, energy flows due to atomic transport, and power expended by both standard and configurational forces; (iv) thermodynamically consistent constitutive relations for the film surface and for the interaction between the surface and the vapor environment. The normal component of the configurational force balance at the surface represents a generalization, to a dynamical context involving dissipation, of a condition that would arise in equilibrium by considering variations of the total free energy with respect to the configuration of the film surface. Our final results consist of partial differential equations that govern the evolution of the film surface.     

The nanogranular nature of C-S-H

Despite its ubiquitous presence as binding phase in all cementitious materials, the mechanical behavior of calcium-silicate-hydrates (C-S-H) is still an enigma that has deceived many decoding attempts from experimental and theoretical sides. In this paper, we propose and validate a new technique and experimental protocol to rationally assess the nanomechanical behavior of C-S-H based on a statistical analysis of hundreds of nanoindentation tests. By means of this grid indentation technique we identify in situ two structurally distinct but compositionally similar C-S-H phases heretofore hypothesized to exist as low density (LD) C-S-H and high density (HD) C-S-H, or outer and inner products. The main finding of this paper is that both phases exhibit a unique nanogranular behavior which is driven by particle-to-particle contact forces rather than by mineral properties. We argue that this nanomechanical blueprint of material invariant behavior of C-S-H is a consequence of the hydration reactions during which precipitating C-S-H nanoparticles percolate generating contact surfaces. As hydration proceeds, these nanoparticles pack closer to center on-average around two characteristic limit packing densities, the random packing limit (η=64%) and the ordered face-centered cubic (fcc) or hexagonal close-packed (hcp) packing limit (η=74%), forming a characteristic LD C-S-H and HD C-S-H phase.     

On configurational weak phase transitions in graphene

We report a study on configurational weak phase transitions for a freestanding monolayer graphene. Firstly, we characterize weak transformation neighborhoods by suitably bounding the metric components. Then, we distinguish between structural and configurational phase changes and elaborate on the second class of them. We evaluate the irreducible invariant subspaces corresponding to these phase changes and lay down symmetry-breaking as well as symmetry-preserving stretches. In the reduced bifurcation diagram, symmetry-preserving stretches are related to a turning point with a change of stability but not of symmetry. Symmetry-breaking stretches are related to a first-order weak phase transition. We evaluate symmetry-breaking stretches as well as their generating cosets. The reduced bifurcation diagram consists of three transcritical bifurcating curves which are all unstable but can be stabilized producing a subcritical bifurcation. We, also, shortly comment on the hysteretical behavior that might appear in this case.     

The physical nature of elastic layers

This paper gives an interpretation of the layers of elastic potentials, which are used to solve elastic boundary value problems of bodies and plates (extensional case). The layers appear as physical quantities on the boundary of the complement of the original body. The insight into the physical nature of the layers allows qualitative estimates to be made for the layers near critical points on the boundary of the body or plate.

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Zusammenfassung Der Aufsatz gibt eine physikalische Interpretation der Belegungen elastischer Potentiale, wie sie zur Lösung elastischer Randwertprobleme benutzt werden. Die Belegungen erscheinen als physikalische Größen auf dem Rand des Komplements des ursprünglichen Körpers. Die Einsicht in die physikalische Natur der Belegungen gestattet qualitative Abschätzungen für die Belegungen nahe kritischen Punkten auf dem Rand des Körpers oder der Platte.

     

The center of a system of non-parallel forces

From a discrete system F of applied forces given by a collection of vectors F_k applied to corresponding points P_k, a new system QF can be obtained through a rotation by Q of all F_k without changing P_k. In this note we examine invariant properties of F under arbitrary rotations. We also examine invariant properties of the family QF when all rotations share a fixed axis, giving a coordinate-free approach to the results of Kolosov (1927) .     

On configurational compatibility and multiscale energy momentum tensors

In this work the continuum theory of defects has been revised through the development of kinematic defect potentials. These defect potentials and their corresponding variational principles provide a basis for constructing a new class of conservation laws associated with the compatibility conditions of continua. These conservation laws represent configurational compatibility conditions which are independent of the constitutive behavior of the continuum. They lead to the development of a new concept termed configurational compatibility, dual to the concept of configurational force. The contour integral of the corresponding conserved quantity is path-independent, if the domain encompassed by the integral is defect-free. It is shown that the Peach-Koehler force can be recovered as one of these invariant integrals. Based on the proposed defect potentials and their corresponding defect energies, two-field multiscale mixed variational principles can be employed to construct multiscale energy momentum tensors. An application is outlined in the form of a mode III elasto-plastic crack problem for which the new configurational quantities are calculated.     

The nature of flows through porous media

The present paper points out that the pressure drop of a porous media flow is only due to a small extent to the shear force term usually employed to derive the Kozeny—Darcy law. For a more correct derivation, additional shear terms have to be taken into account since the fluid is also exposed to elongational forces when it passes through the porous media matrix. These are usually not taken into account in the conventional theoretical treatment of flow through porous media as is explained in the literature. This explains why the available theoretical derivations of the Kozeny—Darcy relationship, which are based on one part of the shear-caused pressure drop only, require an adjustment of the constant in the theoretically derived equation to be applicable to experimental results. Details of this derivation are given in this paper and existing derivations are extended to yield better agreement with experiments.To verify experimentally some of the results of the theoretical derivation provided, porous media flows of dilute polymer solutions are studied experimentally. It is shown that the addition of small amounts of high molecular weight polymers to a solvent with Newtonian flow properties causes drastic pressure drop increases if the flow rate exceeds an onset flow rate corresponding to a critical Deborah number of the porous matrix-polymer solution system. This can only be explained if the flow field in the porous medium is exposed to shear and elongational strain. The extent of this interaction is deduced from experimental findings.