固体力学跨尺度计算若干问题研究

本文展示了固体力学领域跨尺度计算的若干问题和研究概况。（1）建立位错动力学与有限元耦合DDD-FEM的计算模型,实现了能够基于纳米尺度离散位错运动机制计算分析连续介质有限变形晶体塑性问题,提出微纳尺度（200 nm~10 μm）晶体塑性流动应力解析公式,结合试验数据揭示了在无应变梯度下强度和变形的尺寸效应;（2）建立具有微相分离结构的纳米尺度粗粒化分子动力学模型CG-MD,计算获得聚脲材料在时域和频域下的存储模量和损耗模量,通过动态加载分析的DMA试验和超声波试验的数据验证,解决了连续介质尺度下微相分离高分子共聚物的设计难题;（3）通过数据驱动关联高分辨率的微米尺度CT影像和临床低分辨率的毫米尺度CT影像的特征值,建立了围关节松质骨小梁的等效模量和结构张量,为骨组织增材制造点阵结构设计和实现个性化骨缺损重建奠定了基础。     

考虑应力梯度效应的金属微梁屈服模型研究

一系列微加载测试结果表明,金属微梁的弯曲强度会随着材料外部几何特征尺寸的减小而显著升高,呈现出明显的尺寸相关性.基于位错塞积模型,探讨了纯金属单晶微梁的初始屈服应力,并提出了描述其尺寸相关性行为的关键内禀特征长度.通过综合分析现有的微梁弯曲实验及其离散位错动力学数值模拟结果,并考虑到位错-自由表面交互作用的影响,提出了一种仅涉及位错源的位错塞积构型.在此构型下,对线性应力梯度作用下的位错塞积行为进行了连续性分析,并建立了一个由位错源主导的应力梯度屈服模型.该模型有效地解释了微梁初始屈服应力的尺寸相关性,并与实验结果一致.研究结果表明,针对外部几何特征尺寸在数微米及以下的纯金属单晶微梁,位错塞积行为是其尺寸相关性行为的主导机制,而且刻画这种行为需要两个内禀特征长度参数,即位错源长度和位错塞积长度.为解释非均匀加载条件下微尺度晶体材料屈服应力的尺寸相关性行为,特别是纯金属单晶微梁,提供了新的视角.     

微纳米晶金属的应变率敏感性及应变硬化行为分析

基于亚微米、纳米晶粒组织塑性变形过程中多种变形机制(位错机制、扩散机制及晶界滑动机制)共存,建立了理论模型,用于定量研究亚微米、纳米晶粒组织的塑性变形行为.以铜为模型材料,计算分析了晶粒尺度、应变率以及温度对亚微米、纳米晶粒组织塑性变形行为的影响.结果表明:相比粗晶铜,亚微米晶铜表现出明显的应变率敏感性,并且应变率敏感系数随晶粒尺度及变形速率的减小而增大;同时,增大变形速率或降低变形温度都能提高材料的应变硬化能力,延缓颈缩发生,进而提高材料的延性.计算分析结果与实验报道吻合.     

晶体塑性变形离散滑移模型及有限元分析

基于韧性单晶体实验现象，建立了描述晶体塑性变形的离散滑移模型．该模型的主要特点是：晶体滑移变形在宏观上是不均匀的，滑移带的分布是离散的．利用晶体塑性理论对模型进行了有限变形有限元分析，计算结果揭示了晶体滑移的离散行为，模拟的应力 应变曲线与实验曲线相吻合     

中子辐照金属材料的脆化模型研究

金属材料的辐照脆化问题一直以来都是核能安全领域亟待解决的关键问题之一.为了更准确地预测金属材料的辐照脆化行为,基于Johnson-Cook本构模型,将未辐照金属材料的断裂真应力取作辐照材料的断裂真应力,建立了通过辐照退火态金属材料屈服强度就能够预测其整个真应力$\!$-$\!$-$\!$应变曲线,以及断裂真应变的辐照脆化模型.实验研究了不同中子剂量辐照退火态高纯铝的准静态拉伸真应力$\!$-$\!$-$\!$应变曲线、断裂真应力和断裂真应变随辐照剂量的变化规律.结果表明,辐照剂量越高,高纯铝的屈服强度越高,断裂真应变越低,但断裂真应力几乎不变.通过TEM显微分析获得了高纯铝内部辐照缺陷的尺寸和数密度随辐照剂量的变化规律,结果表明,辐照剂量越高,孔洞的尺寸和数密度越高,但位错环尺寸和数密度始终很小,难以准确统计.由辐照高纯铝实验数据拟合得到了辐照脆化模型所需参数,并检验了该模型的预测效果.结果表明,无论是通过实验还是显微分析得到辐照高纯铝的屈服强度,模型的预测结果均能够与实验结果较好地吻合,且模型对退火态高纯铝临界中子剂量的预测值也与文献结果一致.      

基于多尺度特征应变均匀化计算HCP多晶体塑性

结合基于位错密度的晶体塑性模型与特征应变均匀化方法来分析HCP晶体结构材料的力学行为,拟开发一种计算模型用于有效捕捉以及预测微观与结构尺度的裂纹产生。首先,与传统的晶体塑性有限元相比,该多尺度模型可以提高计算效率并同时保持微观尺度的捕捉精度。其次,将模型与试验结果的差值为优化目标,在满足物理学定义的条件下得到合理的材料参数。最终,结构尺度的模拟显示该模型可以获取在结构尺度与微观晶粒尺度的潜在裂纹生长区域。     

基于多尺度特征应变均匀化计算HCP多晶体塑性

结合基于位错密度的晶体塑性模型与特征应变均匀化方法来分析HCP晶体结构材料的力学行为，拟开发一种计算模型用于有效捕捉以及预测微观与结构尺度的裂纹产生。首先，与传统的晶体塑性有限元相比，该多尺度模型可以提高计算效率并同时保持微观尺度的捕捉精度。其次，将模型与试验结果的差值为优化目标，在满足物理学定义的条件下得到合理的材料参数。最终，结构尺度的模拟显示该模型可以获取在结构尺度与微观晶粒尺度的潜在裂纹生长区域。     

考虑微观结构特征长度演化的内变量黏塑性本构模型

在金属晶体材料高应变率大应变变形过程中,存在强烈的位错胞尺寸等微观结构特征长度细化现象,势必对材料加工硬化、宏观塑性流动应力产生重要影响。基于宏观塑性流动应力与位错胞尺寸成反比关系,提出了一种新型的BCJ本构模型。利用位错胞尺寸参数,修正了BCJ模型的流动法则、内变量演化方程,引入了考虑应变率和温度相关性的位错胞尺寸演化方程,建立了综合考虑微观结构特征长度演化、位错累积与湮灭的内变量黏塑性本构模型。应用本文模型,对OFHC铜应变率在10-4~103 s-1、温度在298~542 K、应变在0~1的实验应力-应变数据进行了预测。结果表明:在较宽应变率、温度和应变范围内,本文模型的预测数据与实验吻合很好;与BCJ模型相比,对不同加载条件下实验数据的预测精度均有较大程度的提高,最大平均相对误差从9.939%减小为5.525%。     

位错动力学方法在辐照损伤力学中的应用

核能是人类最理想的清洁能源之一,在世界能源结构中发挥着巨大作用。核裂变或核聚变导致的辐照环境会引起材料的辐照损伤,进而显著影响材料的力学性能,造成辐照硬化、脆化、蠕变、肿胀等现象。无论是预测辐照材料的服役寿命,还是设计新型的抗辐照材料,都迫切需要建立强辐照环境下的塑性力学和损伤力学理论。分子动力学方法为理解辐照材料中的原子级相互作用机理提供了诸多有价值的信息,然而受限于时空尺度难以直接用于力学理论模型的建立。晶体塑性有限元方法可用于预测辐照材料的力学响应,但是往往需要基于已知的物理模型,并且拟合实验数据。位错动力学方法是联系纳米力学与连续介质力学的桥梁,是揭示大量微结构的累积相互作用机理,建立基于物理机制的塑性力学和损伤力学理论的强有力手段。位错动力学方法起源于上个世纪八十年代,起初主要用于研究位错间的短程和长程相互作用、计算位错运动引起的塑性变形、硬化、软化、变形局部化等。本文将展示三种耦合位错动力学和辐照损伤场的方法,并系统地综述研究者近年来使用该方法在理解辐照硬化、塑性变形局部化、晶界效应、温度效应、和发展多尺度耦合方法等方面取得的进展。     

位错动力学方法在辐照损伤力学中的应用

核能是人类最理想的清洁能源之一，在世界能源结构中发挥着巨大作用。核裂变或核聚变导致的辐照环境会引起材料的辐照损伤，进而显著影响材料的力学性能，造成辐照硬化、脆化、蠕变、肿胀等现象。无论是预测辐照材料的服役寿命，还是设计新型的抗辐照材料，都迫切需要建立强辐照环境下的塑性力学和损伤力学理论。分子动力学方法为理解辐照材料中的原子级相互作用机理提供了诸多有价值的信息，然而受限于时空尺度难以直接用于力学理论模型的建立。晶体塑性有限元方法可用于预测辐照材料的力学响应，但是往往需要基于已知的物理模型，并且拟合实验数据。位错动力学方法是联系纳米力学与连续介质力学的桥梁，是揭示大量微结构的累积相互作用机理，建立基于物理机制的塑性力学和损伤力学理论的强有力手段。位错动力学方法起源于上个世纪八十年代，起初主要用于研究位错间的短程和长程相互作用、计算位错运动引起的塑性变形、硬化、软化、变形局部化等。本文将展示三种耦合位错动力学和辐照损伤场的方法，并系统地综述研究者近年来使用该方法在理解辐照硬化、塑性变形局部化、晶界效应、温度效应、和发展多尺度耦合方法等方面取得的进展。     

A plane stress anisotropic plastic flow theory for orthotropic sheet metals

A phenomenological theory is presented for describing the anisotropic plastic flow of orthotropic polycrystalline aluminum sheet metals under plane stress. The theory uses a stress exponent, a rate-dependent effective flow strength function, and five anisotropic material functions to specify a flow potential, an associated flow rule of plastic strain rates, a flow rule of plastic spin, and an evolution law of isotropic hardening of a sheet metal. Each of the five anisotropic material functions may be represented by a truncated Fourier series based on the orthotropic symmetry of the sheet metal and their Fourier coefficients can be determined using experimental data obtained from uniaxial tension and equal biaxial tension tests. Depending on the number of uniaxial tension tests conducted, three models with various degrees of planar anisotropy are constructed based on the proposed plasticity theory for power-law strain hardening sheet metals. These models are applied successfully to describe the anisotropic plastic flow behavior of 10 commercial aluminum alloy sheet metals reported in the literature.     

QUASI－FLOW CORNER THEORY ON LARGE PLASTIC DEFORMATION OF DUCTILE METALS AND ITS APPLICATIONS

ＱＵＡＳＩ－ＦＬＯＷＣＯＲＮＥＲＴＨＥＯＲＹＯＮＬＡＲＧＥＰＬＡＳＴＩＣＤＥＦＯＲＭＡＴＩＯＮＯＦＤＵＣＴＩＬＥＭＥＴＡＬＳＡＮＤＩＴＳＡＰＰＬＩＣＡＴＩＯＮＳＨｕＰｉｎｇ（胡平）ＬｉｕＹｕｑｉ（柳玉启）ＧｕｏＷｅｉ（郭威）ＴａｉＦｅｎｇ（台风）（Ｒ...     

Evaluation of finite-plasticity theories for torsion-tension members made of tresca materials

Finite-incremental Tresca and von Mises theories are developed for solid circular-section torsion-tension members subjected to proportionate and nonproportionate loading. The materials are assumed to be isotropic and even. Two Tresca theories and a von Mises theory are compared with test data obtained from torsion-tension members. Three different kinds of steels were tested; they are hot-rolled mild steel, annealed mild steel, and hot-rolled SAE 1017 steel. The fully plastic values of axial load and torque predicted by the Tresca theories agree with the experimental results; however, the deformations, in the strain-hardening region, predicted by both of the Tresca theories were greater than observed. The von Mises theory is nonconservative in predicting the fully plastic loads of torsion members and torsion-tension members and in predicting the deformations of torsion members in the strain-hardening region, but gives good correlation between predicted and experimental deformations for the torsion-tension members in the strain-hardening region.     

弹塑性本构关系的Ilyushin应变空间理论研究进展

Ｉｌｙｕｓｈｉｎ提出五维偏应变矢量空间中的一般弹塑性本构理论，将应力表示为变形迹内蕴几何学参数的泛函，适合于描写复杂加载下金属材料的塑性响应特性。本文对其实验和理论两方面的研究进展作了综述，涉及关于塑性响应矢量特性的“局部确定性”假设，标量特性的“延心原理”假设及Ｉｌｙｕｓｈｉｎ关于矢量空间的“特殊各向同性”假设等的实验研究和验证，微分型和积分型本构模型的建立及所含本构泛函的形式和确定。     

Modelling the torsion of thin metal wires by distortion gradient plasticity

Under small strains and rotations, we apply a phenomenological higher-order theory of distortion gradient plasticity to the torsion problem, here assumed as a paradigmatic benchmark of small-scale plasticity. Peculiar of the studied theory, proposed about ten years ago by Morton E. Gurtin, is the constitutive inclusion of the plastic spin, affecting both the free energy and the dissipation. In particular, the part of the free energy, called the defect energy, which accounts for Geometrically Necessary Dislocations, is a function of Nye's dislocation density tensor, dependent on the plastic distortion, including the plastic spin. For the specific torsion problem, we implement this distortion gradient plasticity theory into a Finite Element (FE) code characterised by implicit (Backward Euler) time integration, numerically robust and accurate for both viscoplastic and rate-independent material responses. We show that, contrariwise to other higher-order theories of strain gradient plasticity (neglecting the plastic spin), the distortion gradient plasticity can predict some strengthening even if a quadratic defect energy is chosen. On the basis of the results of many FE analyses, concerned with (i) cyclic loading, (ii) switch in the higher-order boundary conditions during monotonic plastic loading, (iii) the use of non-quadratic defect energies, and (iv) the prediction of experimental data, we mainly show that (a) including the plastic spin contribution in a gradient plasticity theory is highly recommendable to model small-scale plasticity, (b) less-than-quadratic defect energies may help in describing the experimental results, but they may lead to anomalous cyclic behaviour, and (c) dissipative (unrecoverable) higher-order finite stresses are responsible for an unexpected mechanical response under non-proportional loading.     

Plastic collapse of general frames

A structural theory is presented for the large static plastic deformation of space frames composed of thin walled members. Displacements comparable to the overall structural dimensions are contemplated. The frame is considered to consist of an arbitrary number of beam elements connected at node points. The analysis assumes that plastic deformation is confined to idealized hinges located at the node points. As a basis for a general frame computer program, the equations for a beam element are derived as a relationship between appropriate generalized force and deformation rates. The structural constitutive theory employed for the plastic hinge includes biaxial bending, torsion, and axial extension. It accounts for reduction in the load carrying capacity of the hinge due to local deformation. Predicted force-deformation curves for a space frame are in good agreement with experimental results.     

Constitutive modeling and computational implementation for finite strain plasticity

This paper describes a simple alternate approach to the difficult problem of modeling material behavior. Starting from a general representation for a rate-type constitutive equation, it is shown by example how sets of test data may be used to derive restrictions on the scalar functions appearing in the representation. It is not possible to determine these functions from experimental data, but the aforementioned restrictions serve as a guide in their eventual definition. The implications are examined for hypo-elastic, isotropically hardening plastic, and kinematically hardening plastic materials. A simple model for the evolution of the “back-stress,” in a kinematic-hardening plasticity theory, that is entirely analogous to a hypoelastic stress-strain relation is postulated and examined in detail in modeling a finitely plastic tension-torsion test. The implementation of rate-type material models in finite element algorithms is also discussed.     

Finite viscoplasticity of amorphous glassy polymers in the logarithmic strain space

The paper outlines a new constitutive model and experimental results of rate-dependent finite elastic–plastic behavior of amorphous glassy polymers. In contrast to existing kinematical approaches to finite viscoplasticity of glassy polymers, the formulation proposed is constructed in the logarithmic strain space and related to a six-dimensional plastic metric. Therefore, it a priori avoids difficulties concerning with the uniqueness of a plastic rotation. The constitutive framework consists of three major steps: (i) A geometric pre-processing defines a total and a plastic logarithmic strain measures determined from the current and plastic metrics, respectively. (ii) The constitutive model describes the stresses and the consistent moduli work-conjugate to the logarithmic strain measures in an analogous structure to the geometrically linear theory. (iii) A geometric post-processing maps the stresses and the algorithmic tangent moduli computed in the logarithmic strain space to their nominal, material or spatial counterparts in the finite deformation space. The analogy between the formulation of finite plasticity in the logarithmic strain space and the geometrically linear theory of plasticity makes this framework very attractive, in particular regarding the algorithmic implementation. The flow rule for viscoplastic strains in the logarithmic strain space is adopted from the celebrated double-kink theory. The post-yield kinematic hardening is modeled by different network models. Here, we compare the response of the eight chain model with the newly proposed non-affine micro-sphere model. Apart from the constitutive model, experimental results obtained from both the homogeneous compression and inhomogeneous tension tests on polycarbonate are presented. Besides the load–displacement data acquired from inhomogeneous experiments, quantitative three-dimensional optical measurements of the surface strain fields are carried out. With regard to these experimental data, the excellent predictive quality of the theory proposed is demonstrated by means of representative numerical simulations.     

含主应力轴旋转的广义塑性位势理论

大量岩土实验与工程实践表明传统塑性位势理论无法合理反映岩土材料的基本变形机制。从塑性位势理论角度来看,当存在主应力轴旋转时,塑性应变增量与应力不共主轴,此时最一般情况下的塑性应变增量须用六个线性无关的塑性势函数来表述,从而提出含主应力轴旋转的广义塑性位势理论一般表达式。通过矩阵分析,将一般应力增量分解成共轴分量与旋转分量之和。在应力增量分解的基础上,提出含主应力轴旋转的广义塑性位势理论的分解表达式