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相关概念视频

Elasticity01:12

Elasticity

3.5K
Elasticity is the ability of an object to withstand the effects of distortion and to return to its original size and shape once the forces causing deformation are removed. When an elastic material deforms under the action of an external force, it experiences internal resistance to the deformation. However, if no external force is applied, it returns to its original state.
The elasticity of an object can be described by a stress-strain curve, which represents the relationship between stress...
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Elasticity in Concrete01:20

Elasticity in Concrete

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Upon subjecting concrete to moderate or high uniaxial compressive or tensile stresses, the strain response is non-linear relative to the stress applied. As the stress is removed, the resulting stress-strain curve deviates from the original path traced during loading, creating a hysteresis loop, indicative of the concrete's non-linear and non-elastic properties. Typically, a material's modulus of elasticity, which is a measure of the material's stiffness, is inferred from the linear...
92
Hooke's Law01:26

Hooke's Law

379
Hooke's law, a pivotal principle in material science, establishes that the strain a material undergoes is directly proportional to the applied stress, defined by a factor called the modulus of elasticity or Young's modulus.
379
Generalized Hooke's Law01:22

Generalized Hooke's Law

906
The generalized Hooke's Law is a broadened version of Hooke's Law, which extends to all types of stress and in every direction. Consider an isotropic material shaped into a cube subjected to multiaxial loading. In this scenario, normal stresses are exerted along the three coordinate axes. As a result of these stresses, the cubic shape deforms into a rectangular parallelepiped. Despite this deformation, the new shape maintains equal sides, and there is a normal strain in the direction of the...
906
Elastic Strain Energy for Shearing Stresses01:20

Elastic Strain Energy for Shearing Stresses

183
As discussed in previous lessons, strain energy in a material is the energy stored when it is elastically deformed, a concept crucial in materials science and mechanical engineering. This energy results from the internal work done against the cohesive forces within the material. When a material undergoes shearing stress and corresponding shearing strain, the strain energy density, which is the energy stored per unit volume, is calculated. Within the elastic limit, where the stress is...
183
Elastic Collisions: Introduction01:00

Elastic Collisions: Introduction

12.8K
An elastic collision is one that conserves both internal kinetic energy and momentum. Internal kinetic energy is the sum of the kinetic energies of the objects in a system. Truly elastic collisions can only be achieved with subatomic particles, such as electrons striking nuclei. Macroscopic collisions can be very nearly, but not quite, elastic, as some kinetic energy is always converted into other forms of energy such as heat transfer due to friction and sound. An example of a nearly...
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相关实验视频

Updated: Jun 26, 2025

Subject-specific Musculoskeletal Model for Studying Bone Strain During Dynamic Motion
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Subject-specific Musculoskeletal Model for Studying Bone Strain During Dynamic Motion

Published on: April 11, 2018

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对数据驱动的超弹性进行基准物理信息框架的基准测试.

Vahidullah Taç1, Kevin Linka2, Francisco Sahli-Costabal3

  • 1School of Mechanical Engineering, Purdue University, West Lafayette, USA.

Computational mechanics
|May 14, 2024
PubMed
概括
此摘要是机器生成的。

三种数据驱动的方法 (构成型人工神经网络,输入形神经网络和神经普通微分方程) 准确地模拟了超弹性材料,同时尊重物理定律. 这些方法克服了传统方法的局限性,提供了更好的推断能力.

关键词:
构成性模型 构成性模型神经网络的神经网络的神经网络非线性力学 不线性力学基于物理的机器学习多凸性是一种多凸性.

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相关实验视频

Last Updated: Jun 26, 2025

Subject-specific Musculoskeletal Model for Studying Bone Strain During Dynamic Motion
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Subject-specific Musculoskeletal Model for Studying Bone Strain During Dynamic Motion

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Experimental and Data Analysis Workflow for Soft Matter Nanoindentation
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Experimental and Data Analysis Workflow for Soft Matter Nanoindentation

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Quantification of Strain in a Porcine Model of Skin Expansion Using Multi-View Stereo and Isogeometric Kinematics
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科学领域:

  • 材料科学 材料科学 材料科学
  • 计算力学 计算力学 计算力学
  • 人工智能的人工智能

背景情况:

  • 数据驱动的方法在材料建模中提供了灵活性,但存在外推问题和物理违规问题.
  • 现有的方法在过度拟合和确保预测与物理约束保持一致方面扎.

研究的目的:

  • 审查,扩展和比较三个以物理为基础的数据驱动的方法:构造性人工神经网络 (CANN),输入凸神经网络 (ICNN) 和神经普通微分方程 (NODE).
  • 在超弹性建模中确保对客观性,材料对称性和多凸性的自动满足.

主要方法:

  • 为应变能量潜力开发了一个共享的公式,将其扩展为不变数的凸非递减函数的和.
  • 这三种方法 (CANN,ICNN,NODE) 使用和皮肤的应力-应变数据进行训练.
  • 性能与传统的神经网络进行了基准测试,并对准确性,过拟合和推断进行了评估.

主要成果:

  • 这三种基于物理的方法 (CANN,ICNN,NODE) 均准确地捕获了训练数据,并且具有最小的过拟合和证明外推能力.
  • 与不受约束的网络不同,这些方法在训练范围之外产生了物理上有意义的预测.
  • 虽然应力预测是相似的,但确定的能量函数有所不同,特别是在第二导数中,可能会影响数值解析器.

结论:

  • CANN,ICNN和NODE成功地将数据驱动的灵活性与基于物理的约束相结合,用于超弹性材料建模.
  • 这些方法为传统方法提供了强大的替代方案,克服了额外推算和物理一致性的局限性.
  • 在CANN,ICNN和NODE之间做出选择可能取决于特定的应用需求和模型复杂性和准确性之间的所需权衡.