Computational and theoretical aspects of a grain-boundary model at finite deformations

A model to describe the role of grain boundaries in the overall response of a polycrystalline material at small length scales subject to finite deformations is presented. Three alternative thermodynamically consistent plastic flow relations on the grain boundary are derived and compared using a series of numerical experiments. The numerical model is obtained by approximating the governing relations using the finite element method. In addition, the infinitesimal and finite deformation theories are compared, and the limitations of the former made clear

Computational and theoretical aspects of a grain-boundary model that accounts for grain misorientation and grain-boundary orientation

A detailed theoretical and numerical investigation of the infinitesimal single-crystal gradient plasticity and grain-boundary theory of Gurtin (2008) "A theory of grain boundaries that accounts automatically for grain misorientation and grain-boundary orientation". Journal of the Mechanics and Physics of Solids 56 (2), 640-662, is performed. The governing equations and flow laws are recast in variational form. The associated incremental problem is formulated in minimization form and provides the basis for the subsequent finite element formulation. Various choices of the kinematic measure used to characterize the ability of the grain boundary to impede the flow of dislocations are compared. An alternative measure is also suggested. A series of three-dimensional numerical examples serve to elucidate the theory

Continuum-kinematics-inspired peridynamics. Mechanical problems

The main objective of this contribution is to develop a novel continuum-kinematics-inspired approach for peridynamics (PD), and to revisit PD’s thermodynamic foundations. We distinguish between three types of interactions, namely, one-neighbour interactions, two-neighbour interactions and three-neighbour interactions. While one-neighbour interactions are equivalent to the bond-based interactions of the original PD formalism, two- and three-neighbour interactions are fundamentally different to state-based interactions in that the basic elements of continuum kinematics are preserved exactly. In addition, we propose that an externally prescribed traction on the boundary of the continuum body emerges naturally and need not vanish. This is in contrast to, but does not necessarily violate, standard PD. We investigate the consequences of the angular momentum balance and provide a set of appropriate arguments for the interactions accordingly. Furthermore, we elaborate on thermodynamic restrictions on the interaction energies and derive thermodynamically-consistent constitutive laws through a Coleman–Noll-like procedure

Variational formulation of generalized interfaces for finite deformation elasticity

The objective of this contribution is to formulate generalized interfaces in a variationally consistent manner within a finite deformation continuum mechanics setting. The general interface model is a zero-thickness model that represents the finite thickness “interphase” between different constituents in a heterogeneous material. The interphase may be the transition zone between inclusion and matrix in composites or the grain boundaries in polycrystalline solids. The term “general” indicates that the interface model here accounts for both jumps of the deformation as well as the traction across the interface. Both the cohesive zone model and elastic interface model can be understood as two limits of the current interface model. Furthermore, some aspects of material modeling of generalized interfaces are elaborated and a consistent model is proposed. Finally, the proposed theory is elucidated via a series of numerical examples. © 2017, The Author(s) 2017

A unified computational framework for bulk and surface elasticity theory: a curvilinear-coordinate-based finite element methodology

A curvilinear-coordinate-based finite element methodology is presented as a basis for a straightforward computational implementation of the theory of surface elasticity that mimics the underlying mathematical and geometrical concepts. An efficient formulation is obtained by adopting the same methodology for both the bulk and the surface. The key steps to evaluate the hyperelastic constitutive relations at the level of the quadrature point in a finite element scheme using this unified approach are provided. The methodology is illustrated through selected numerical examples

Computational and theoretical aspects of a grain-boundary model at finite deformations

A model to describe the role of grain boundaries in the overall response of a polycrystalline material at small length scales subject to finite deformations is presented. Three alternative thermodynamically consistent plastic flow relations on the grain boundary are derived and compared using a series of numerical experiments. The numerical model is obtained by approximating the governing relations using the finite element method. In addition, the infinitesimal and finite deformation theories are compared, and the limitations of the former made clear

A versatile implicit computational framework for continuum-kinematics-inspired peridynamics

Continuum-kinematics-inspired peridynamics (CPD) has been recently proposed as a novel reformulation of peridynamics that is characterized by one-, two- and three-neighbor interactions. CPD is geometrically exact and thermodynamically consistent and does not suffer from zero-energy modes, displacement oscillations or material interpenetration. In this manuscript, for the first time, we develop a computational framework furnished with automatic differentiation for the implementation of CPD. Thereby, otherwise tedious analytical differentiation is automatized by employing hyper-dual numbers (HDN). This differentiation method does not suffer from round-off errors, subtractive cancellation errors or truncation errors and is thereby highly stable with superb accuracy being insensitive to perturbation values. The computational framework provided here is compact and model-independent, thus once the framework is implemented, any other material model can be incorporated via modifying the potential energy solely. Finally, to illustrate the versatility of our proposed framework, various potential energies are considered and the corresponding material response is examined for different scenarios.Deutsche Forschungsgemeinschaft http://dx.doi.org/10.13039/50110000165

Generalized interfacial energy and size effects in composites

The objective of this contribution is to explain the size effect in composites due to the interfacial energy between the constituents of the underlying microstructure. The generalized interface energy accounts for both jumps of the deformation as well as the stress across the interface. The cohesive zone and elastic interface are only two limit cases of the general interface model. A closed form analytical solution is derived to compute the effective interface-enhanced material response. Our novel analytical solution is in excellent agreement with the numerical results obtained from the finite element method for a broad variety of parameters and dimensions. A remarkable observation is that the notion of size effect is theoretically bounded verified by numerical examples. Thus, the gain or loss via reducing the dimensions of the microstructure is limited to certain ultimate values, immediately relevant for designing nano-composites

Micromechanical method for effective piezoelectric properties and electromechanical fields in multi-coated long fiber composites

This paper proposes a micromechanical framework for identifying the macroscopic behavior of multi-coated long fiber composites, as well as the average electromechanical microscopic fields of all phases (matrix, fibers, coating layers), generated upon known macroscopic conditions. The work aims at developing a unified micromechanical approach that provides an analytical solution standing for non-coated and multi-coated long fiber composites with transversely isotropic piezoelectric behavior. The proposed method solves specific boundary value problems and utilizes the Mori-Tanaka homogenization scheme, in which the dilute strain and electric field concentration tensors are obtained analytically with the help of an extended composite cylinders method that accounts for coupled electromechanical fields. The capabilities of this homogenization strategy are illustrated with the help of numerical examples, and comparisons with known solutions from the literature for non-coated and coated fiber piezoelectric composites are provided