Academic literature on the topic 'Nonlocal modelling of inelasticity in solids'

Our goal in this paper is to derive from a kinetic setting a diffusion model for the transport of charged particles trapped in a surface potential. The so-obtained model is derived through a diffusion approximation, as we assume the thermalization to be governed by particle-wall collisions. In order to take into account the possible inelasticity of such collisions, we introduce a nonlocal (in energy) collision operator on the boundary. At the macroscopic scale, this results in a coupled (in energy) Spherical Harmonics Expansion (SHE) model. The model is both formally and rigorously derived from the kinetic equation, and existence is obtained as a by-product of the derivation.

An overview of computational methods to model fracture in brittle and quasi-brittle materials is given. The overview focuses on continuum models for fracture. First, numerical difficulties related to modelling fracture for quasi-brittle materials will be discussed. Different techniques to eliminate or circumvent those difficulties will be described subsequently. In that context, regularization techniques such as nonlocal models, gradient enhanced models, viscous models, cohesive zone models, and smeared crack models will be discussed. The main focus of this paper will be on computational methods for discrete fracture (discrete cracks). Element erosion technques, inter-element separation methods, the embedded finite element method (EFEM), the extended finite element method (XFEM), meshfree methods (MMs), boundary elements (BEMs), isogeometric analysis, and the variational approach to fracture will be reviewed elucidating advantages and drawbacks of each approach. As tracking the crack path is of major concern in computational methods that preserve crack path continuity, one section will discuss different crack tracking techniques. Finally, cracking criteria will be reviewed before the paper ends with future research perspectives.

The purpose of the current work is the application of a recent nonlocal extension (Reusch, F., Svendsen, B., and Klingbeil, D., 2003, “Local and Non-Local Gurson-Based Ductile Damage and Failure Modelling at Large Deformation,” Eur. J. Mech. A∕Solids, 22, pp. 779–792; “A Non-Local Extension of Gurson-Based Ductile Damage Modeling,” Comput. Mater. Sci., 26, pp. 219–229) of the Gurson–Needleman–Tvergaard (GTN) model (Needleman, A., and Tvergaard, V., 1984, “An Analysis of Ductile Rupture in Notched Bars,” J. Mech Phys. Solids, 32, pp. 461–490) to the simulation of ductile damage and failure processes in metal matrix composites at the microstructural level. The extended model is based on the treatment of void coalescence as a nonlocal process. In particular, we compare the predictions of the local with GTN model with those of the nonlocal extension for ductile crack initiation in ideal and real Al–SiC metal matrix microstructures. As shown by the current results for metal matrix composites and as expected, the simulation results based on the local GTN model for both the structural response and predicted crack path at the microstructural level in metal matrix composites are strongly mesh-dependent. On the other hand, those based on the current nonlocal void-coalescence modeling approach are mesh-independent. This correlates with the fact that, in contrast to the local approach, the predictions of the nonlocal approach for the crack propagation path in the real Al–SiC metal matrix composite microstructure considered here agree well with the experimentally determined path.

Nonlocal interactions of material points play a vital role in modelling certain important aspects of inelastic phenomena such as plasticity and damage in solids. For plasticity problems, nonlocal interactions allow characterizations of size-dependence and energetic hardening. In the case of damage, nonlocality describes energetically favourable conditions for propagation as well as branching of cracks. The nonlocal description of inelastic phenomenon introduces certain internal length scales representative of the material micro-structure. A geometric perspective of the kinematics of inelastic deformation induces certain interesting attributes in the form of a non-trivial metric, curvature, etc. to the mathematical model. Towards realizing a unified and rational modelling setup, it is important to trace the geometric origins of the kinematics underlying nonlocal interactions. The first part of the thesis dwells on modelling of visco-plasticity and damage in metals by introducing gradients of plasticity and damage variables to capture the size-dependent plastic response and the nonlocal aspects of damage. We also try to account for dislocation inertia affecting the yield strength at high strain rates. In addition, the nonlocal flow rule also encapsulates energetic hardening. We describe temperature evolution, which is thermodynamically consistent and accounts for the heat dissipated. The coupled visco-plastic damage model is numerically implemented through peridynamics (PD) and validated via the simulations of adiabatic shear band propagation and shear plugging failure. The nonlocal terms can be accorded a geometric meaning using the concepts of gauge theory and differential geometry. We therefore focus on a geometric characterization of brittle damage via the gauge theory of solids. The local configurational changes in the manifold are captured using a non-trivial affine connection, called gauge connection. The resulting manifold is equipped with the gauge covariant quantities like gauge torsion and gauge curvature. Consequently, this theory serves as a natural device to model different aspects such as stiffness degradation, tension-compression asymmetry and microscopic inertia. The model is again numerically implemented using PD, and validated through the simulations of dynamic fracture instabilities and dynamic crack propagation. Similar to damage, the geometric underpinnings of plastic deformation are unveiled using ideas from differential geometry, e.g. the postulate that a plastically deforming body is a Riemannian manifold endowed with a metric structure and a non-trivial connection. The geometric approach provides a rational means of modelling several important features of plastic deformation, e.g. the free energy of defects, yielding and energetic hardening; and results into a nonlocal flow rule. The model is validated through the numerical simulations of homogeneous visco-plastic deformation and Taylor impact test. The brittle damage in materials undergoing small deformation typically correspond to small strain. The symmetry principles of gauge theory are also used to obtain a brittle damage model in the linearized setting that is invariant with respect to local or inhomogeneous transformations. The efficacy of the model is established through PD based quasi-static simulations and investigation of blast-induced fracture in rocks. The applied loads causing deformation may be of thermomechanical origin, rather than being purely mechanical. In the second part of thesis, brittle damage modelling under thermomechanical loading is undertaken. The deformation due to thermal and mechanical loads is coupled via Duhamel's postulate. The heat equation considers radiative and conductive heat transfer, temperature fluctuations due to thermomechanical effect and local temperature rise at crack tip. PD reformulation of this model involves a scalar entropy flux to incorporate nonlocal thermal interactions. The correspondence relations for entropy flux and other PD states, are derivable through energy and entropy equivalence. Numerical simulations include transient heat flow in a silica tile and its coupled thermomechanical analysis, and the temperature change study in Kalthoff's problem. The damage mechanism of certain materials like ceramics is sensitive to the rate of applied loading. The third part of the thesis develops a damage model for ceramics based on micro-mechanical considerations to account for its strain rate dependent behavior. PD is used to reformulate the equations in the integro-differential form, considering the discontinuities and fragmentation at high strain rates. Numerical studies include spherical cavity expansion problem, impact induced damage in a ceramic target and a composite ceramic target.