A computational framework for the constitutive modeling of nonlinear micropolar media

Despite the large number of applications with micropolar models, the aspects of their implementation have been rarely addressed in the literature. In the present paper, a strategy for the computational modeling of micropolar media with elasto-plasticity and elastic degradation is investigated. The proposed strategy is based on the Object-Oriented Paradigm (OOP) and on the use of tensor objects. The presence of tensor objects inside the code allows to obtain a constitutive models framework that, with respect to existent implementations, is independent on both the adopted analysis model and numerical method. The OOP, with its properties of abstraction, inheritance, and polymorphism, leads to a framework highly modular and easy to expand. The theoretical basis is a compact tensorial representation for the micropolar equations that makes them formally identical to the ones of the classic continuum theory. This compatibility has been here extended to their computational expressions, making possible to use the same code structure for both the continuum models, taking advantage of existing implementations of classic constitutive models.

[1]  R. Borst.  SIMULATION OF STRAIN LOCALIZATION: A REAPPRAISAL OF THE COSSERAT CONTINUUM , 1991 .

[2]  Lapo Gori,et al.  A Generalized Elasto-Plastic Micro-Polar Constitutive Model , 2015 .

[3]  J. Reddy,et al.  A micropolar cohesive damage model for delamination of composites , 2015, 1504.06939.

[4]  Phillipe D. Alves,et al.  AN OBJECT-ORIENTED CLASS ORGANIZATION FOR GLOBAL-LOCAL GENERALIZED FINITE ELEMENT METHOD , 2016 .

[5]  Ching S. Chang,et al.  A micromechanical-based micropolar theory for deformation of granular solids , 1991 .

[6]  Paul Steinmann,et al.  Micropolar elastoplasticity and its role in localization , 1993 .

[7]  Samuel Forest,et al.  Elastoviscoplastic constitutive frameworks for generalized continua , 2003 .

[8]  E. Sacco,et al.  A micromechanical approach for the Cosserat modeling of composites , 2016 .

[9]  Egidio Rizzi,et al.  Localization analysis of elastic degradation with application to scalar damage , 1995 .

[10]  Egidio Rizzi,et al.  A unified theory of elastic degradation and damage based on a loading surface , 1994 .

[11]  D. Addessi,et al.  micromechanical approach for the micropolar modeling of heterogeneous periodic media , 2014 .

[12]  S. Walsh,et al.  Finite element methods for micropolar models of granular materials , 2006 .

[13]  Davide Bigoni,et al.  Analytical Derivation of Cosserat Moduli via Homogenization of Heterogeneous Elastic Materials , 2007 .

[14]  Boris Jeremić,et al.  TENSOR OBJECTS IN FINITE ELEMENT PROGRAMMING , 1998 .

[15]  René de Borst,et al.  A generalisation of J 2 -flow theory for polar continua , 1993 .

[16]  Roque Luiz da Silva Pitangueira,et al.  A computational framework for constitutive modelling , 2017 .

[17]  P. Trovalusci,et al.  Non-linear micropolar and classical continua for anisotropic discontinuous materials , 2003 .

[18]  Gouri Dhatt,et al.  Incremental displacement algorithms for nonlinear problems , 1979 .

[19]  E. Sacco,et al.  Micromechanical analysis of heterogeneous materials subjected to overall Cosserat strains , 2013 .

[20]  S. Sture,et al.  Finite element simulation of localization in granular materials by micropolar continuum approach , 2008 .

[21]  D. Addessi.  A 2D Cosserat finite element based on a damage-plastic model for brittle materials , 2014 .

[22]  P. Trovalusci,et al.  A multiscale description of particle composites: From lattice microstructures to micropolar continua , 2017 .

[23]  Kaspar Willam,et al.  Bifurcation investigations of coupled damage-plasticity models for concrete materials , 2016 .

[24]  Phillipe D. Alves,et al.  An object-oriented approach to the Generalized Finite Element Method , 2013, Adv. Eng. Softw..

[25]  Yeong-bin Yang,et al.  Solution method for nonlinear problems with multiple critical points , 1990 .

[26]  J. C. Simo,et al.  Strain- and stress-based continuum damage models—I. Formulation , 1987 .

[27]  Zhaohui Yang,et al.  Template elastic‐plastic computations in geomechanics , 2002 .

[28]  Egidio Rizzi,et al.  A Formulation of Anisotropic Elastic Damage Using Compact Tensor Formalism , 2001 .

[29]  Ralph Johnson,et al.  design patterns elements of reusable object oriented software , 2019 .

[30]  Felício Bruzzi Barros,et al.  A computational framework for G/XFEM material nonlinear analysis , 2017, Adv. Eng. Softw..

[31]  Ignacio Carol,et al.  Spurious energy dissipation/generation in stiffness recovery models for elastic degradation and damage , 1996 .

[32]  Ching S. Chang,et al.  Constitutive relation for a particulate medium with the effect of particle rotation , 1990 .

[33]  J. Ganghoffer,et al.  Construction of micropolar continua from the asymptotic homogenization of beam lattices , 2012 .

[34]  P. Petersson.  Crack growth and development of fracture zones in plain concrete and similar materials , 1981 .

[35]  Ching S. Chang,et al.  Micro-mechanical modelling of granular material. Part 1: Derivation of a second-gradient micro-polar constitutive theory , 2001 .

[36]  René de Borst,et al.  A unified framework for concrete damage and fracture models including size effects , 1999 .

[37]  J. Chaboche,et al.  Mechanics of Solid Materials , 1990 .

[38]  Hrvoje Jasak,et al.  A tensorial approach to computational continuum mechanics using object-oriented techniques , 1998 .

[39]  K. Willam,et al.  Analytical and geometrical representation of localization in granular materials , 2007 .

[40]  Kaspar Willam,et al.  Localized failure analysis in elastoplastic Cosserat continua , 1998 .

[41]  Lapo Gori,et al.  Smoothed point interpolation methods for the regularization of material instabilities in scalar damage models , 2018, International Journal for Numerical Methods in Engineering.

[42]  Kenneth Runesson,et al.  Object-Oriented Approach to Hyperelasticity , 1999, Engineering with Computers.

[43]  Ching S. Chang,et al.  ELASTIC-MATERIAL CONSTANTS FOR ISOTROPIC GRANULAR SOLIDS WITH PARTICLE ROTATION , 1992 .

[44]  S. Penna,et al.  Discontinuous failure in micropolar elastic-degrading models , 2017 .

[45]  R. Pitangueira,et al.  A solution strategy for non-linear implicit BEM formulation using a unified constitutive modelling framework , 2016 .

[46]  Glenn R. Heppler,et al.  Micropolar elasticity theory: a survey of linear isotropic equations, representative notations, and experimental investigations , 2017 .

[47]  R. Borst,et al.  Localisation in a Cosserat continuum under static and dynamic loading conditions , 1991 .

[48]  Egidio Rizzi,et al.  Sulla localizzazione delle deformazioni in materiali e strutture , 1995 .

[49]  R. Pitangueira,et al.  High regularity partition of unity for structural physically non-linear analysis , 2017 .

[50]  B. Winkler,et al.  Application of a constitutive model for concrete to the analysis of a precast segmental tunnel lining , 2004 .

[51]  P. Steinmann.  Theory and numerics of ductile micropolar elastoplastic damage , 1995 .

[52]  A. Hazel,et al.  Homogenization Methods to Approximate theEffective Response of RandomFibre-reinforced Composites , 2012 .

[53]  Roque Luiz da Silva Pitangueira,et al.  An enhanced tensorial formulation for elastic degradation in micropolar continua , 2017 .

[54]  Siro Casolo,et al.  Macroscopic modelling of structured materials: Relationship between orthotropic Cosserat continuum and rigid elements , 2006 .

[55]  Jean-Jacques Marigo,et al.  MODELLING OF BRITTLE AND FATIGUE DAMAGE FOR ELASTIC MATERIAL BY GROWTH OF MICROVOIDS , 1985 .

[56]  Victor A. Eremeyev,et al.  Acceleration waves in micropolar elastic media , 2005 .

[57]  Patrizia Trovalusci,et al.  Scale{dependent homogenization of random composites as micropolar continua , 2015 .