President Vladimir V. Putin of Russia has built a war machine in Ukraine with an insatiable demand for men. Underpinning that machine is a pattern of brutality and coercion in which commanders dole out abuse as punishment while exploiting soldiers — even the gravely ill or injured — to keep them on the battlefield, an investigation by The New York Times has found. Mr. Putin has hailed the troops fighting his war of attrition as sacred heroes, and Russian society as the most important weapon in his forces’ advance on the battlefield. But more than 6,000 confidential complaints about the war reviewed by The Times show that anger and discontent simmer beneath the surface as the Russian leader’s methods for sustaining the war destroy countless military families. “We’ve been living in fear for three years, keeping silent about everything,” the wife of a soldier from Saratov, a city in southwestern Russia, wrote in one complaint. “I’m being torn apart on the inside from the injustice!” Thousands of those petitioning the Russian government struggle to get …