Gianpietro Del Piero, Giovanni Lancioni, Riccardo March
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Different solutions are found describing specific plastic strain processes, and correlations between the different evolution modes and the convexity/concavity properties of the plastic energy density are established.</p><p>The variety of solutions demonstrates the large versatility of the model in describing many failure mechanisms, ranging from brittle to ductile. Indeed, for a convex plastic energy, the plastic strain diffuses in the body, while, for a concave plastic energy, it localizes in regions whose amplitude depends on the internal length parameter included into the non-local energy term, and, depending on the convexity properties of the first derivative of the plastic energy, the localization band expands or contracts. Complex failure processes combining different modes can be reproduced by assuming plastic energy functionals with specific convex and concave branches.</p><p>The quasi-brittle failure of geomaterials in simple tension tests was reproduced by assuming a convex-concave plastic energy, and the accuracy of the analytical predictions was checked by comparing them with the numerical results of finite element simulations.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":null,"pages":null},"PeriodicalIF":1.8000,"publicationDate":"2023-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10659-023-09989-6.pdf","citationCount":"0","resultStr":"{\"title\":\"One-Dimensional Failure Modes for Bodies with Non-convex Plastic Energies\",\"authors\":\"Gianpietro Del Piero, Giovanni Lancioni, Riccardo March\",\"doi\":\"10.1007/s10659-023-09989-6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper, a complete picture of the different plastic failure modes that can be predicted by the strain gradient plasticity model proposed in Del Piero et al. (J. Mech. Mater. Struct. 8:109–151, 2013) is drawn. The evolution problem of the elasto-plastic strain is formulated in Del Piero et al. (J. Mech. Mater. Struct. 8:109–151, 2013) as an incremental minimization problem acting on an energy functional which includes a local plastic term and a non-local gradient contribution. Here, an approximate analytical solution of the evolution problem is determined in the one-dimensional case of a tensile bar. Different solutions are found describing specific plastic strain processes, and correlations between the different evolution modes and the convexity/concavity properties of the plastic energy density are established.</p><p>The variety of solutions demonstrates the large versatility of the model in describing many failure mechanisms, ranging from brittle to ductile. 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引用次数: 0
摘要
本文采用Del Piero et al. (J. Mech.)提出的应变梯度塑性模型对不同的塑性破坏模式进行了全面的预测。板牙。Struct. 8:109 - 151,2013)绘制。弹塑性应变的演化问题在Del Piero et al. (J. Mech。板牙。结构,8:109-151,2013)作为作用于能量泛函的增量最小化问题,其中包括一个局部塑性项和一个非局部梯度贡献。在这里,确定了一维拉伸杆的演化问题的近似解析解。找到了描述特定塑性应变过程的不同解,并建立了不同演化模式与塑性能量密度凹凸性之间的关系。各种各样的解决方案表明了该模型在描述从脆性到延性的许多破坏机制方面的通用性。事实上,对于凸塑性能,塑性应变在体内扩散,而对于凹塑性能,塑性应变局部化在区域,其幅度取决于包含在非局部能量项中的内部长度参数,并且根据塑性能一阶导数的凹凸性,局部化带扩展或收缩。通过假设具有特定凸、凹分支的塑性能量泛函,可以再现不同模态组合的复杂破坏过程。通过假设凸-凹塑性能,再现了简单拉伸试验中岩土材料的准脆性破坏,并与有限元数值模拟结果进行了对比,验证了分析预测的准确性。
One-Dimensional Failure Modes for Bodies with Non-convex Plastic Energies
In this paper, a complete picture of the different plastic failure modes that can be predicted by the strain gradient plasticity model proposed in Del Piero et al. (J. Mech. Mater. Struct. 8:109–151, 2013) is drawn. The evolution problem of the elasto-plastic strain is formulated in Del Piero et al. (J. Mech. Mater. Struct. 8:109–151, 2013) as an incremental minimization problem acting on an energy functional which includes a local plastic term and a non-local gradient contribution. Here, an approximate analytical solution of the evolution problem is determined in the one-dimensional case of a tensile bar. Different solutions are found describing specific plastic strain processes, and correlations between the different evolution modes and the convexity/concavity properties of the plastic energy density are established.
The variety of solutions demonstrates the large versatility of the model in describing many failure mechanisms, ranging from brittle to ductile. Indeed, for a convex plastic energy, the plastic strain diffuses in the body, while, for a concave plastic energy, it localizes in regions whose amplitude depends on the internal length parameter included into the non-local energy term, and, depending on the convexity properties of the first derivative of the plastic energy, the localization band expands or contracts. Complex failure processes combining different modes can be reproduced by assuming plastic energy functionals with specific convex and concave branches.
The quasi-brittle failure of geomaterials in simple tension tests was reproduced by assuming a convex-concave plastic energy, and the accuracy of the analytical predictions was checked by comparing them with the numerical results of finite element simulations.
期刊介绍:
The Journal of Elasticity was founded in 1971 by Marvin Stippes (1922-1979), with its main purpose being to report original and significant discoveries in elasticity. The Journal has broadened in scope over the years to include original contributions in the physical and mathematical science of solids. The areas of rational mechanics, mechanics of materials, including theories of soft materials, biomechanics, and engineering sciences that contribute to fundamental advancements in understanding and predicting the complex behavior of solids are particularly welcomed. The role of elasticity in all such behavior is well recognized and reporting significant discoveries in elasticity remains important to the Journal, as is its relation to thermal and mass transport, electromagnetism, and chemical reactions. Fundamental research that applies the concepts of physics and elements of applied mathematical science is of particular interest. Original research contributions will appear as either full research papers or research notes. Well-documented historical essays and reviews also are welcomed. Materials that will prove effective in teaching will appear as classroom notes. Computational and/or experimental investigations that emphasize relationships to the modeling of the novel physical behavior of solids at all scales are of interest. Guidance principles for content are to be found in the current interests of the Editorial Board.