Development of Constitutive Equation for Infinite Body of Impact Problem

Author(s):  
Seung Yong Yang
2007 ◽  
Vol 353-358 ◽  
pp. 611-614
Author(s):  
Seung Yong Yang

A constitutive equation was developed for an infinite body in plane wave impact problem, and implemented using the finite element software ABAQUS user subroutine. Bilinear material behavior under monotonically increasing loading was considered for the constitutive equation. The finite element governed by this type of material behavior can be used as an infinite body transmitting longitudinal and shear plane waves, so that the number of finite elements can be reduced in impact simulations. To test the developed method, results of a plate impact experiment were examined. The numerical results show the accuracy of the developed constitutive equation.


Author(s):  
Tainan Gabardo ◽  
Cezar Otaviano Ribeiro Negrao

Author(s):  
David J. Steigmann

This chapter develops the general constitutive equation for transversely isotropic, fiber-reinforced materials. Applications include composite materials and bio-elasticity.


2020 ◽  
Vol 23 (6) ◽  
pp. 1570-1604
Author(s):  
Teodor Atanacković ◽  
Stevan Pilipović ◽  
Dora Seleši

Abstract Equations of motion for a Zener model describing a viscoelastic rod are investigated and conditions ensuring the existence, uniqueness and regularity properties of solutions are obtained. Restrictions on the coefficients in the constitutive equation are determined by a weak form of the dissipation inequality. Various stochastic processes related to the Karhunen-Loéve expansion theorem are presented as a model for random perturbances. Results show that displacement disturbances propagate with an infinite speed. Some corrections of already published results for a non-stochastic model are also provided.


2021 ◽  
pp. 1-26
Author(s):  
Ruth Schmidt ◽  
Katelyn Stenger

Abstract Despite widespread recognition that behavioral public policy (BPP) needs to move beyond nudging if the field is to achieve more significant impact, problem-solving approaches remain optimized to achieve tactical success and are evaluated by short-term metrics with the assumption of stable systems. As a result, current methodologies may contribute to the development of solutions that appear well formed but become ‘brittle’ in the face of more complex contexts if they fail to consider important contextual cues, broader system forces, and emergent conditions, which can take three distinct forms: contextual, systemic, and anticipatory brittleness. The Covid-19 pandemic and vaccination rollout present an opportunity to identify and correct interventional brittleness with a new methodological approach – strategic BPP (SBPP) – that can inform the creation of more resilient solutions by embracing more diverse forms of evidence and applied foresight, designing interventions within ecosystems, and iteratively developing solutions. To advance the case for adopting a SBPP and ‘roughly right’ modes of inquiry, we use the Covid-19 vaccination rollout to define a new methodological roadmap, while also acknowledging that taking a more strategic approach may challenge current BPP norms.


Materials ◽  
2021 ◽  
Vol 14 (9) ◽  
pp. 2456
Author(s):  
Zhijun Yang ◽  
Weixin Yu ◽  
Shaoting Lang ◽  
Junyi Wei ◽  
Guanglong Wang ◽  
...  

The hot deformation behaviors of a new Ti-6Al-2Nb-2Zr-0.4B titanium alloy in the strain rate range 0.01–10.0 s−1 and temperature range 850–1060 °C were evaluated using hot compressing testing on a Gleeble-3800 simulator at 60% of deformation degree. The flow stress characteristics of the alloy were analyzed according to the true stress–strain curve. The constitutive equation was established to describe the change of deformation temperature and flow stress with strain rate. The thermal deformation activation energy Q was equal to 551.7 kJ/mol. The constitutive equation was ε ˙=e54.41[sinh (0.01σ)]2.35exp(−551.7/RT). On the basis of the dynamic material model and the instability criterion, the processing maps were established at the strain of 0.5. The experimental results revealed that in the (α + β) region deformation, the power dissipation rate reached 53% in the range of 0.01–0.05 s−1 and temperature range of 920–980 °C, and the deformation mechanism was dynamic recovery. In the β region deformation, the power dissipation rate reached 48% in the range of 0.01–0.1 s−1 and temperature range of 1010–1040 °C, and the deformation mechanism involved dynamic recovery and dynamic recrystallization.


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