Inelastic anisotropic constitutive models based on evolutionary linear transformations on stress tensors with application to masonry

An anisotropic plastic‐damage model for 3D nonlinear simulation of masonry structures

“…For what follows, it is important that Equation (12a) is extended as: $$$$ \overline{F}\left(\overline{\boldsymbol{\sigma}},\boldsymbol{\kappa} \right)={F}^I\left({\boldsymbol{\sigma}}^{\boldsymbol{I}},{\boldsymbol{\kappa}}^{\boldsymbol{I}}\right)\kern1.75em \forall \boldsymbol{\kappa} $$$$ Equality (17) can be achieved with an arbitrary yield function $$$ {F}^I $$$ if the relationship $$$ {\boldsymbol{\kappa}}^{\boldsymbol{I}}\left(\boldsymbol{\kappa} \right) $$$ is selected appropriately and the tensor $$$ \boldsymbol{A} $$$ is governed by a suitable evolution law $$$ \boldsymbol{A}=\boldsymbol{A}\left(\boldsymbol{\kappa} \right). $$$ 46 In this work, given the scarce experimental evidence on the evolution of the homogenized masonry yield function, the approach has been simplified by selecting a suitable isotropic yield function, largely used for simulating concrete and masonry behavior, and assuming constant $$$ \boldsymbol{A} $$$ and the identity $$$ {\boldsymbol{\kappa}}^{\boldsymbol{I}}=\boldsymbol{\kappa} $$$. This allows for significant simplifications in the formulation of the model.…”

“…Equality ( 17) can be achieved with an arbitrary yield function F I if the relationship 𝜿 I (𝜿) is selected appropriately and the tensor A is governed by a suitable evolution law A = A(𝜿). 46 In this work, given the scarce experimental evidence on the evolution of the homogenized masonry yield function, the approach has been simplified by selecting a suitable isotropic yield function, largely used for simulating concrete and masonry behavior, and assuming constant A and the identity 𝜿 I = 𝜿. This allows for significant simplifications in the formulation of the model.…”

“…Generally, isotropic nonlinear plastic or damage models originally developed for concrete are used for predicting masonry response 35–39 . Masonry behavior, however, is markedly anisotropic, especially in the case of regular bonds with definite weak planes represented by mortar joints, and this has given rise to the development of few orthotropic failure criteria 40–43 and nonlinear models, generally with applications in two dimensions 31,44–47 . These models often belong to either damage or plasticity frameworks but very seldom couple both features, which is required to represent typical stiffness and strength degradation and residual plastic deformations of masonry under cyclic loading conditions.…”

“…[35][36][37][38][39] Masonry behavior, however, is markedly anisotropic, especially in the case of regular bonds with definite weak planes represented by mortar joints, and this has given rise to the development of few orthotropic failure criteria [40][41][42][43] and nonlinear models, generally with applications in two dimensions. 31,[44][45][46][47] These models often belong to either damage or plasticity frameworks but very seldom couple both features, which is required to represent typical stiffness and strength degradation and residual plastic deformations of masonry under cyclic loading conditions. Moreover, the extension of general theories to three-dimensional behavior is yet to be fully explored to the knowledge of the authors.…”

Multiscale Model Calibration by Inverse Analysis for Nonlinear Simulation of Masonry Structures Under Earthquake Loading

“…Applications of the Discrete Element Method can also be included in this category (Lemos, 2007;Baraldi, et al, 2018). Macroscale descriptions encompass i) generic finite element representations utilising several nonlinear continuum 2D plane stress/3D solid elements Berto, et al, 2002;Pelà, et al, 2011;Fu, et al, 2018;Gatta, et al, 2018) for modelling each masonry structural part, and ii) simplified models with macro-elements (Lagomarsino, et al, 2013;Pantò, et al, 2016), where different URM structural components (e.g. pier, spandrel etc.)…”