It is often observed that thermal stress enhances crack propagation in materials, and, conversely, crack propagation can contribute to temperature shifts in materials. In this study, we first consider the thermoelasticity model proposed by M. A. Biot and study its energy dissipation property. The Biot thermoelasticity model takes into account the following effects. Thermal expansion and contraction are caused by temperature changes, and, conversely, temperatures decrease in expanding areas but increase in contracting areas. In addition, we examine its thermomechanical properties through several numerical examples and observe that the stress near a singular point is enhanced by the thermoelastic effect. In the second part, we propose two crack propagation models under thermal stress by coupling a phase field model for crack propagation and the Biot thermoelasticity model and show their variational structures. In our numerical experiments, we investigate how thermal coupling affects the crack speed and shape. In particular, we observe that the lowest temperature appears near the crack tip, and the crack propagation is accelerated by the enhanced thermal stress.

In a few years, Indonesia experienced difficulties in maintaining energy security, the problem is the decline in oil production from 1.6 million barrels per day to 861 thousand barrels per day in 2012. However, there is a difference condition in 2015 until the third week in 2016, world oil prices actually fell at the lowest price level since last 12 years. The decline in oil prices due to oversupply of oil by oil-producing countries of the world due to the instability of the world economy. Wave of layoffs in Indonesia is a response to the decline in oil prices, this led to the energy and mines portfolios Indonesia feared would not be more advantageous than the portfolio in other countries. In this research, portfolio analysis will be done on energy and mining in Indonesia by using stock price data of energy and mines in the period 26 November 2010 until April 1, 2016. It was found that the results have a wide effect of the market potential is high in the determination of the return on the portfolio energy and mines. Later, it was found that there are eight of the thirty stocks in the energy and mining portfolio of Indonesia which have a high probability of return relative to the average return of stocks in a portfolio of energy and mines.

The authors were not aware of typographical errors made in the writing phase, and, hence, wish to make the following corrections to the original paper

It is often observed that thermal stress enhances crack propagation in materials, and conversely, crack propagation can contribute to temperature shifts in materials. In this study, we first consider the thermoelasticity model proposed by M. A. Biot (1956) and study its energy dissipation property. The Biot thermoelasticity model takes into account the following effects. Thermal expansion and contraction are caused by temperature changes, and conversely, temperatures decrease in expanding areas but increase in contracting areas. In addition, we examine its thermomechanical properties through several numerical examples and observe that the stress near a singular point is enhanced by the thermoelastic effect. In the second part, we propose two crack propagation models under thermal stress by coupling a phase field model for crack propagation and the Biot thermoelasticity model and show their variational structures. In our numerical experiments, we investigate how thermal coupling affects the crack speed and shape. In particular, we observe that the lowest temperature appears near the crack tip, and the crack propagation is accelerated by the enhanced thermal stress.