A thermodynamically consistent plastic-damage framework for localized failure in quasi-brittle solids: Material model and strain localization analysis
A thermodynamically consistent plastic-damage framework for localized failure in quasi-brittle solids: Material model and strain localization analysis
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DOI：
10.1016/j.ijsolstr.2016.03.005
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发表时间：
2016-06
影响因子：
3.6
通讯作者：
Jian‐Ying Wu;M. Cervera
中科院分区：
文献类型：
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作者：
Jian‐Ying Wu;M. Cervera
针对准脆性材料的局部化破坏问题，提出了一种相容的塑性损伤框架和相应的应变局部化分析方法。首先基于两种不同的运动分解，假设无限小的变形，提出了统一的弹塑性损伤模型，其中所涉及的内变量的演化规律用耗散流张量来表征。对于强（或正则化）的不连续性，形成在这样的非弹性准脆性固体，并最终演变成一个完全软化，然后建议一种新的应变局部化分析。一个运动学约束比经典的不连续分叉条件更苛刻的牵引连续性和加载/卸载状态的强（或正则化）的不连续性的运动学一致。更具体地说，由麦克斯韦运动学条件表征的应变跃变必须是完全非弹性的（能量耗散的）。这种运动学的再现意味着上述耗散流张量分量在与不连续方向正交的方向上消失。这个属性允许自然地开发一个局部塑性损伤模型的不连续性（带），其方向和基于牵引力的故障标准一致地确定从给定的基于应力的对应posterioria。然后将一般结果具体化为平面应力和平面应变的二维条件。据发现，在平面应力的情况下，应变局部化成一个强（或正则化）的不连续性，可以发生在应变软化的发病。相反，在平面应变条件下，由于额外的运动学约束，在应变局部化之前的软化区，通常会发生一些连续的非弹性变形和主应变方向的大幅度重新定向。以经典的Rankine准则、Mohr-Coulomb准则、von Mises（J2）准则和Drucker-Prager准则为例进行了分析。特别是，获得了经过数值模拟验证的不连续角的封闭解以及相应的基于牵引力的破坏准则。
Aiming for the modeling of localized failure in quasi-brittle solids, this paper addresses a thermodynamically consistent plastic-damage framework and the corresponding strain localization analysis. A unified elastoplastic damage model is first presented based on two alternative kinematic decompositions assuming infinitesimal deformations, with the evolution laws of involved internal variables characterized by a dissipative flow tensor. For the strong (or regularized) discontinuity to form in such inelastic quasi-brittle solids and to evolve eventually into a fully softened one, a novel strain localization analysis is then suggested. A kinematic constraint more demanding than the classical discontinuous bifurcation condition is derived by accounting for the traction continuity and the loading/unloading states consistent with the kinematics of a strong (or regularized) discontinuity. More specifically, the strain jumps characterized by Maxwell’s kinematic condition have to be completely inelastic (energy dissipative). Reproduction of this kinematics implies vanishing of the aforesaid dissipative flow tensorial components in the directions orthogonal to the discontinuity orientation. This property allows naturally developing a localized plastic-damage model for the discontinuity (band), with its orientation and the traction-based failure criterion consistently determineda posteriorifrom the given stress-based counterpart. The general results are then particularized to the 2D conditions of plane stress and plane strain. It is found that in the case of plane stress, strain localization into a strong (or regularized) discontinuity can occur at the onset of strain softening. Contrariwise, owing to an extra kinematic constraint, in the condition of plane strain some continuous inelastic deformations and substantial re-orientation of principal strain directions in general have to take place in the softening regime prior to strain localization. The classical Rankine, Mohr–Coulomb, von Mises (J2) and Drucker–Prager criteria are analyzed as illustrative examples. In particular, both the closed-form solutions for the discontinuity angles validated by numerical simulations and the corresponding traction-based failure criteria are obtained.