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We present several examples, where the effect of the layers on the material force is examined.
In addition, the cohesive fracture theory is combined with the material force approach in order to increase the clarity of the interpretation of the approach in engineering applications.
The results show that the material force approach remains path independent only if all components of the momentum balance equation are properly included into the corresponding variational formulation.
First, the path dependency of the material force approach in elasto-plastic continua is found to be considerably depending on the so-called material body forces.
In this paper we examine the motion of a moving singularity within a continuum body under the use of the level-set method and the material force concept.
Finally, with further analyses on compact tension examples, it is shown that the introduced energy functions in the material momentum balance yield a difference for the evaluation of the material force approach and the traditional J-integral.
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After conducting a regression analysis on the material forces with respect to different tensile strength values, a parabolic relationship emerges between the material forces and tensile strengths.
In cosmological evolution, according to the Huainanzi, the Dao ("Way") originated from vacuity, and vacuity produced the universe, which in turn produced the material forces.
He doesn't provide a narration, but his increasingly powerful arrangement of the material forces a moral and spiritual reckoning with the events.
In primitive societies the material forces were few and simple for example, grains and the stone tools used to grind them into flour.
"The greatness of Howard's classification, for Goethe, was that it accounted for the material forces of cloud formation while allowing for the immaterial forces of poetic response to be heard".
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com