arXiv subjects

A. Piccolroaz

Publications and source records attributed to A. Piccolroaz.

At least 37 records · Page 2Linked to original sources

arXiv2015

Plastically-driven variation of elastic stiffness in green bodies during powder compaction: Part I Experiments and elastoplastic coupling

Cold compaction of ceramic powders is driven by plastic strain, during which the elastic stiffness of the material progressively increases from values typical of granular matter to those representative of a fully dense solid. This increase of stiffness strongly affects the mechanical behaviour of the green body and is crucial in the modelling of forming processes for ceramics. A protocol for ultrasonic experimental investigation (via P and S waves transmission) is proposed to quantify the elastic constants (Young modulus and Poisson's ratio) as functions of the forming pressure. Experimental results performed in uniaxial strain allow for the introduction of laws that describe the variation of the elastic constants during densification. These laws are motivated in terms of elastoplastic coupling through the simulation of an isostatic pressure compaction process of alumina powder. A micromechanical explanation of the stiffening of elastic properties during densification is deferred to Part II of this study.

cond-mat.mtrl-sci↗

arXiv2015

Plastically-driven variation of elastic stiffness in green bodies during powder compaction. Part II: Micromechanical modelling

A micromechanical approach is set-up to analyse the increase in elastic stiffness related to development of plastic deformation (the elastoplastic coupling concept) occurring during the compaction of a ceramic powder. Numerical simulations on cubic (square for 2D) and hexagonal packings of elastoplastic cylinders and spheres validate both the variation of the elastic modulus with the forming pressure and the linear dependence of it on the relative density as experimentally found in Part~I of this study, while the dependence of the Poisson's ratio on the green's density is only qualitatively explained.

cond-mat.mtrl-sci↗

arXiv2015

Boundary integral formulation for interfacial cracks in thermodiffusive bimaterials

An original boundary integral formulation is proposed for the problem of a semi-infinite crack at the interface between two dissimilar elastic materials in the presence of heat flows and mass diffusion. Symmetric and skew-symmetric weight function matrices are used together with a generalized Betti's reciprocity theorem in order to derive a system of integral equations that relate the applied loading, the temperature and mass concentration fields, the heat and mass fluxes on the fracture surfaces and the resulting crack opening. The obtained integral identities can have many relevant applications, such as for the modelling of crack and damage processes at the interface between different components in electrochemical energy devices characterized by multi-layered structures (solid oxide fuel cells and lithium ions batteries).

math-ph↗

arXiv2015

Strain localization and shear banding in ductile materials

A model of a shear band as a zero-thickness nonlinear interface is proposed and tested using finite element simulations. An imperfection approach is used in this model where a shear band, that is assumed to lie in a ductile matrix material (obeying von Mises plasticity with linear hardening), is present from the beginning of loading and is considered to be a zone in which yielding occurs before the rest of the matrix. This approach is contrasted with a perturbative approach, developed for a J$_2$-deformation theory material, in which the shear band is modelled to emerge at a certain stage of a uniform deformation. Both approaches concur in showing that the shear bands (differently from cracks) propagate rectilinearly under shear loading and that a strong stress concentration should be expected to be present at the tip of the shear band, two key features in the understanding of failure mechanisms of ductile materials.

cond-mat.mtrl-sci↗

arXiv2015

General transmission conditions for thin elasto-plastic pressure-dependent interphase between dissimilar materials

We consider a thin soft adhesive interphase between dissimilar elastic media. The material of the intermediate layer is modelled by elasto-plastic pressure-sensitive constitutive law. An asymptotic procedure, together with a novel formulation of the deformation theory of plasticity for pressure-sensitive materials, is used in order to derive nonlinear transmission conditions for the corresponding imperfect zero-thickness interface. A FEM analysis of the original three-phase structure is performed to validate the transmission conditions for the simplified bimaterial structure.

cond-mat.mtrl-sci↗

arXiv2014

Implicit yield function formulation for granular and rock-like materials

The constitutive modelling of granular, porous and quasi-brittle materials is based on yield (or damage) functions, which may exhibit features (for instance, lack of convexity, or branches where the values go to infinity, or false elastic domains) preventing the use of efficient return-mapping integration schemes. This problem is solved by proposing a general construction strategy to define an implicitly defined convex yield function starting from any convex yield surface. Based on this implicit definition of the yield function, a return-mapping integration scheme is implemented and tested for elastic-plastic (or -damaging) rate equations. The scheme is general and, although it introduces a numerical cost when compared to situations where the scheme is not needed, is demonstrated to perform correctly and accurately.

cond-mat.mtrl-sci↗

arXiv2014

Dispersion and localization in structured Rayleigh beams

This paper brings a comparative analysis between dynamic models of couple-stress elastic materials and structured Rayleigh beams on a Winkler foundation. Although physical phenomena have different physical origins, the underlying equations appear to be similar, and hence mathematical models have a lot in common. In the present work, our main focus is on the analysis of dispersive waves, band-gaps and localized waveforms in structured Rayleigh beams. The Rayleigh beam theory includes the effects of rotational inertia which are neglected in the Euler--Bernoulli beam theory. This makes the approach applicable to higher frequency regimes. Special attention is given to waves in pre-stressed Rayleigh beams on elastic foundations.

physics.class-ph↗

arXiv2014

Steady-State Propagation of a Mode II Crack in Couple Stress Elasticity

The present work deals with the problem of a semi-infinite crack steadily propagating in an elastic body subject to plane-strain shear loading. It is assumed that the mechanical response of the body is governed by the theory of couple-stress elasticity including also micro-rotational inertial effects. This theory introduces characteristic material lengths in order to describe the pertinent scale effects that emerge from the underlying microstructure and has proved to be very effective for modeling complex microstructured materials. It is assumed that the crack propagates at a constant sub-Rayleigh speed. An exact full field solution is then obtained based on integral transforms and the Wiener-Hopf technique. Numerical results are presented illustrating the dependence of the stress intensity factor and the energy release rate upon the propagation velocity and the characteristic material lengths in couple-stress elasticity. The present analysis confirms and extends previous results within the context of couple-stress elasticity concerning stationary cracks by including inertial and micro-inertial effects.

math-ph↗

arXiv2014

Experimental investigation of the elastoplastic response of aluminum silicate spray dried powder during cold compaction

Mechanical experiments have been designed and performed to investigate the elasto-plastic behaviour of green bodies formed from an aluminum silicate spray dried powder used for tiles production. Experiments have been executed on samples obtained from cold compaction into a cylindrical mould and include: uniaxial strain, equi-biaxial flexure and high-pressure triaxial compression/extension tests. Two types of powders have been used to realize the green body samples, differing in the values of water content, which have been taken equal to those usually employed in the industrial forming of traditional ceramics. Yielding of the green body during compaction has been characterized in terms of yield surface shape, failure envelope, and evolution of cohesion and void ratio with the forming pressure, confirming the validity of previously proposed constitutive models for dense materials obtained through cold compaction of granulates.

cond-mat.mtrl-sci↗

arXiv2014

Finite-strain formulation and FE implementation of a constitutive model for powder compaction

A finite-strain formulation is developed, implemented and tested for a constitutive model capable of describing the transition from granular to fully dense state during cold forming of ceramic powder. This constitutive model (as well as many others employed for geomaterials) embodies a number of features, such as pressure-sensitive yielding, complex hardening rules and elastoplastic coupling, posing considerable problems in a finite-strain formulation and numerical implementation. A number of strategies are proposed to overcome the related problems, in particular, a neo-Hookean type of modification to the elastic potential and the adoption of the second Piola-Kirchhoff stress referred to the intermediate configuration to describe yielding. An incremental scheme compatible with the formulation for elastoplastic coupling at finite strain is also developed, and the corresponding constitutive update problem is solved by applying a return mapping algorithm.

cond-mat.mtrl-sci↗

arXiv2014

Effective elastic properties of planar SOFCs: A non-local dynamic homogenization approach

The focus of the article is on the analysis of effective elastic properties of planar Solid Oxide Fuell Cell (SOFC) devices. An ideal periodic multi-layered composite (SOFC-like) reproducing the overall properties of multi-layer SOFC devices is defined. Adopting a non-local dynamic homogenization method, explicit expressions for overall elastic moduli and inertial terms of this material are derived in terms of micro-fluctuation functions. These micro-fluctuation function are then obtained solving the cell problems by means of finite element techniques. The effects of the temperature variation on overall elastic and inertial properties of the fuel cells are studied. Dispersion relations for acoustic waves in SOFC-like multilayered materials are derived as functions of the overall constants, and the results obtained by the proposed computational homogenization approach are compared with those provided by rigorous Floquet-Boch theory. Finally, the influence of the temperature and of the elastic properties variation on the Bloch spectrum is investigated.

cond-mat.mtrl-sci↗

arXiv2014

Elastoplastic coupling to model cold ceramic powder compaction

The simulation of industrial processes involving cold compaction of powders allows for the optimization of the production of both traditional and advanced ceramics. The capabilities of a constitutive model previously proposed by the authors are explored to simulate simple forming processes, both in the small and in the large strain formulation. The model is based on the concept of elastoplastic coupling providing a relation between density changes and variation of elastic properties and has been tailored to describe the transition between a granular ceramic powder and a dense green body. Finite element simulations have been compared with experiments on an alumina ready-to-press powder and an aluminum silicate spray-dried granulate. The simulations show that it is possible to take into account friction at the die wall and to predict the state of residual stress, density distribution and elastic properties in the green body at the end of the forming process.

cond-mat.mtrl-sci↗

arXiv2014

A simple and robust elastoplastic constitutive model for concrete

An elasto-plastic model for concrete, based on a recently-proposed yield surface and simple hardening laws, is formulated, implemented, numerically tested and validated against available test results. The yield surface is smooth and particularly suited to represent the behaviour of rock-like materials, such as concrete, mortar, ceramic and rock. A new class of isotropic hardening laws is proposed, which can be given both an incremental and the corresponding finite form. These laws describe a smooth transition from linear elastic to plastic behaviour, incorporating linear and nonlinear hardening, and may approach the perfectly plastic limit in the latter case. The reliability of the model is demonstrated by its capability of correctly describing the results yielded by a number of well documented triaxial tests on concrete subjected to various confinement levels. Thanks to its simplicity, the model turns out to be very robust and well suited to be used in complex design situations, as those involving dynamic loads.

cond-mat.mtrl-sci↗

arXiv2014

Integration algorithms of elastoplasticity for ceramic powder compaction

Inelastic deformation of ceramic powders (and of a broad class of rock-like and granular materials), can be described with the yield function proposed by Bigoni and Piccolroaz (2004, Yield criteria for quasibrittle and frictional materials. Int. J. Solids and Structures, 41, 2855-2878). This yield function is not defined outside the yield locus, so that 'gradient-based' integration algorithms of elastoplasticity cannot be directly employed. Therefore, we propose two ad hoc algorithms: (i.) an explicit integration scheme based on a forward Euler technique with a 'centre-of-mass' return correction and (ii.) an implicit integration scheme based on a 'cutoff-substepping' return algorithm. Iso-error maps and comparisons of the results provided by the two algorithms with two exact solutions (the compaction of a ceramic powder against a rigid spherical cup and the expansion of a thick spherical shell made up of a green body), show that both the proposed algorithms perform correctly and accurately.

cond-mat.soft↗

arXiv2014

Remarks on the energy release rate for an antiplane moving crack in couple stress elasticity

This paper is concerned with the steady-state propagation of an antiplane semi-infinite crack in couple stress elastic materials. A distributed loading applied at the crack faces and moving with the same velocity of the crack tip is considered, and the influence of the loading profile variations and microstructural effects on the dynamic energy release rate is investigated. The behaviour of both energy release rate and maximum total shear stress when the crack tip speed approaches the critical speed (either that of the shear waves or that of the localised surface waves) is studied. The limit case corresponding to vanishing characteristic scale lengths is addressed both numerically and analytically by means of a comparison with classical elasticity results.

math-ph↗

arXiv2014

Boundary integral formulation for cracks at imperfect interfaces

We consider an infinite bi-material plane containing a semi-infinite crack situated on a soft imperfect interface. The crack is loaded by a general asymmetrical system of forces distributed along the crack faces. On the basis of the weight function approach and the fundamental reciprocal identity, we derive the corresponding boundary integral formulation, relating physical quantities. The boundary integral equations derived in this paper in the imperfect interface setting show a weak singularity, in contrast to the perfect interface case, where the kernel is of the Cauchy type. We further present three alternative variants of the boundary integral equations which offer computationally favourable alternatives for certain sets of parameters.

cond-mat.mtrl-sci↗

arXiv2013

On fracture criteria for dynamic crack propagation in elastic materials with couple stresses

The focus of the article is on fracture criteria for dynamic crack propagation in elastic materials with microstructures. Steady-state propagation of a Mode III semi-infinite crack subject to loading applied on the crack surfaces is considered. The micropolar behavior of the material is described by the theory of couple-stress elasticity developed by Koiter. This constitutive model includes the characteristic lengths in bending and torsion, and thus it is able to account for the underlying microstructures of the material. Both translational and micro-rotational inertial terms are included in the balance equations, and the behavior of the solution near to the crack tip is investigated by means of an asymptotic analysis. The asymptotic fields are used to evaluate the dynamic J-integral for a couple-stress material, and the energy release rate is derived by the corresponding conservation law. The propagation stability is studied according to the energy-based Griffith criterion and the obtained results are compared to those derived by the application of the maximum total shear stress criterion.

cond-mat.mtrl-sci↗

arXiv2013

Perturbation analysis for an imperfect interface crack problem using weight function techniques

We analyse a problem of anti-plane shear in a bi-material plane containing a semi-infinite crack situated on a soft imperfect interface. The plane also contains a small thin inclusion (for instance an ellipse with high eccentricity) whose influence on the propagation of the main crack we investigate. An important element of our approach is the derivation of a new weight function (a special solution to a homogeneous boundary value problem) in the imperfect interface setting. The weight function is derived using Fourier transform and Wiener-Hopf techniques and allows us to obtain an expression for an important constant (which may be used in a fracture criterion) that describes the leading order of tractions near the crack tip for the unperturbed problem. We present computations that demonstrate how this constant varies depending on the extent of interface imperfection and contrast in material stiffness. We then perform perturbation analysis to derive an expression for the change in the leading order of tractions near the tip of the main crack induced by the presence of the small defect, whose sign can be interpreted as the inclusion's presence having an amplifying or shielding effect on the propagation of the main crack.

math-ph↗